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  • 1. Alsafadie, R.
    et al.
    Battini, Jean -Marc
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges.
    Somja, H.
    Hjiaj, M.
    Local formulation for elasto-plastic corotational thin-walled beams based on higher-order curvature terms2011In: Finite elements in analysis and design (Print), ISSN 0168-874X, E-ISSN 1872-6925, Vol. 47, no 2, p. 119-128Article in journal (Refereed)
    Abstract [en]

    The paper deals with the derivation of a local elasto-plastic finite element formulation of three dimensional corotational beams with arbitrary cross- section. Based on Bernoulli beam kinematics, an improved displacement field is constructed by inclusion of second-order terms of cross-section local rotations. The formulation captures both the Saint-Venant and warping torsional effects of open cross sections. Numerical tests show that the inclusion of the second-order terms of the local bending curvatures gives more accurate and more efficient element that allows a significant reduction of the computational time.

  • 2. Alsafadie, R.
    et al.
    Hjiaj, M.
    Battini, Jean-Marc
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges.
    Corotational mixed finite element formulation for thin-walled beams with generic cross-section2010In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 199, no 49-52, p. 3197-3212Article in journal (Refereed)
    Abstract [en]

    The corotational technique is adopted here for the analysis of three-dimensional beams. The technique exploits the technology that applies to a two-noded element, a coordinate system which continuously translates and rotates with the element. In this way, the rigid body motion is separated out from the deformational motion. In this paper, a mixed formulation are adopted for the derivation of the local element tangent stiffness matrix and nodal forces. The mixed finite element formulation is based on an incremental form of the two-field Hellinger-Reissner variational principle to permit elasto-plastic material behavior. The local beam kinematics is based on a low-order nonlinear strain expression using Bernoulli assumption. The present formulation captures both the Saint-Venant and warping torsional effects of thin-walled open cross-sections. Shape functions that satisfy the nonlinear local equilibrium equations are selected for the interpolation of the stress resultants. In particular, for the torsional forces and the twist rotation degree of freedom, a family of hyperbolic interpolation functions is adopted in lieu of conventional polynomials. Governing equations are expressed in a weak form, and the constitutive equations are enforced at each integration cross-section along the element length. A consistent state determination algorithm is proposed. This local element, together with the corotational framework, can be used to analyze the nonlinear buckling and postbuckling of thin-walled beams with generic cross-section. The present corotational mixed element solution is compared against the results obtained from a corotational displacement-based model having the same beam kinematics and corotational framework. The superiority of the mixed formulation is clearly demonstrated.

  • 3. Alsafadie, R.
    et al.
    Hjiaj, M.
    Battini, Jean-Marc
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges.
    Three-dimensional formulation of a mixed corotational thin-walled beam element incorporating shear and warping deformation2011In: Thin-walled structures, ISSN 0263-8231, E-ISSN 1879-3223, Vol. 49, no 4, p. 523-533Article in journal (Refereed)
    Abstract [en]

    This paper presents a corotational formulation of a three-dimensional elasto-plastic mixed beam element that can undergo large displacements and rotations. The corotational approach applies to a two-noded element a coordinate system which continuously translates and rotates with the element. In this way, the rigid body motion is separated out from the deformational motion. In this paper, a mixed formulation is adopted for the derivation of the local element tangent stiffness matrix and nodal forces based on a two-field Hellinger-Reissner variational principle. The local beam kinematics is based on a low-order nonlinear strain expression using Timoshenko assumption. The warping effects are characterized by adopting Benscoter theory that describes the warping degree of freedom by an independent function. Shape functions that satisfy the nonlinear local equilibrium equations are selected for the interpolation of the stress resultants. This local element, together with the corotational framework, can be used to analyze the nonlinear buckling and postbuckling of thin-walled beams with generic cross-section. The mixed formulation solution is compared against the results obtained from a corotational displacement-based formulation having the same beam kinematics. The superiority of the mixed formulation is clearly demonstrated.

  • 4. Alsafadie, Rabe
    et al.
    Battini, Jean-Marc
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges.
    Hjiaj, Mohammed
    Efficient local formulation for elasto-plastic corotational thin-walled beams2011In: The International Journal for Numerical Methods in Biomedical Engineering, ISSN 2040-7939, Vol. 27, no 4, p. 498-509Article in journal (Refereed)
    Abstract [en]

    A local elasto-plastic formulation, based on a low-order nonlinear strain expression using Bernoulli beam kinematics, is presented in this paper. This element, together with the corotational framework proposed in (Comput. Meth. Appl. Mech. Eng. 2002; 191(17): 1755-1789) can be used to analyze the nonlinear buckling and postbuckling of thin-walled beams with arbitrary cross-section. The formulation captures both the Saint-Venant and warping torsional effects of open cross-sections. Numerical examples show that this local formulation is more efficient than the one proposed in (Comput. Meth. Appl. Mech. Eng. 2002; 191(51):5811-5831) based on a Timoshenko beam assumption.

  • 5. Alsafadie, Rabe
    et al.
    Hjiaj, Mohammed
    Structural Engineering Research Group/LGCGM, INSA de Rennes, France.
    Battini, Jean-Marc
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Design and Bridges (name changed 20110630).
    Corotational mixed three-dimensional finite element for structural stability problems2010In: ECCM 2010, IV European Conference on Computational Mechanics, 2010Conference paper (Refereed)
    Abstract [en]

    The corotational technique exploits the technology that applies to a two–noded element a coordinatesystem which continuously translates and rotates with the element. In this way, the rigid bodymotion is separated out from the deformational motion. In this paper, a mixed formulation is adoptedfor the derivation of the local element tangent stiffness matrix and nodal forces. The mixed finiteelement formulation is based on the two–field Hellinger–Reissner variational principle. This localelement, together with the corotational framework, can be used to analyze the nonlinear bucklingand postbuckling of thin–walled beams with arbitrary cross–section. The mixed formulation solutionis compared against the results obtained from a corotational displacement–based formulation havingthe same beam kinematics. The superiority of the mixed formulation is clearly demonstrated.

  • 6. Alsafadie, Rabe
    et al.
    Hjiaj, Mohammed
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges.
    Battini, Jean-Marc
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges.
    Stability analysis for 3D frames using mixed corotational formulation2010In: SDSS-Rio 2010 Stability and ductility of steel structures / [ed] E. Batista, P. Vellasco, L. de Lima, 2010, p. 547-554Conference paper (Refereed)
    Abstract [en]

    The corotational technique is adopted for the analysis of 3D beams. The technique applies to atwo-noded element a coordinate system which continuously translates and rotates with the element. Inthis way, the rigid body motion is separated out from the deformational motion. Then, a mixedformulation is adopted for the derivation of the local element tangent stiffness matrix and nodal forces.The mixed finite element formulation is based on an incremental form of the two-field Hellinger-Reissnervariational principle to permit elasto-plastic material behavior. The proposed element can be used toanalyze the nonlinear buckling and postbuckling of 3D beams. The mixed formulation solution iscompared against the results obtained from a corotational displacement-based formulation having thesame beam kinematics. The superiority of the mixed formulation is clearly demonstrated.

  • 7. Alsafadie, Rabe
    et al.
    Hjiaj, Mohammed
    Structural Engineering Research Group, Université Européenne de Bretagne, Rennes, France.
    Somja, Hugues
    Battini, Jean-Marc
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges.
    A comparative study of displacement and mixed-based corotational finite element formulations for elasto-plastic three-dimensional beam analysis2011In: Engineering computations, ISSN 0264-4401, E-ISSN 1758-7077, Vol. 28, no 7, p. 939-982Article in journal (Refereed)
    Abstract [en]

    The purpose of this paper is to present eight local elasto-plastic beam element formulations incorporated into the corotational framework for two-noded three-dimensional beams. These formulations capture the warping torsional effects of open cross-sections and are suitable for the analysis of the nonlinear buckling and post-buckling of thin-walled frames with generic cross-sections. The paper highlights the similarities and discrepancies between the different local element formulations. The primary goal of this study is to compare all the local element formulations in terms of accuracy, efficiency and CPU-running time.

  • 8.
    Axelsson, Erik
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges.
    Syk, Annelie
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges.
    Ülker Kaustell, Mahir
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges.
    Battini, Jean-Marc
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges.
    Effect of axle load spreading and support stiffness on the dynamic response of short span railway bridges2014In: Structural Engineering International, ISSN 1016-8664, E-ISSN 1683-0350, Vol. 4, p. 457-465Article in journal (Refereed)
    Abstract [en]

    In dynamic analyses of railway bridges, the train axle loads are often modeled as moving point forces. However, one effect of the ballast is to spread these point forces. This can lead to large reductions of the bridge response, especially for short span bridges. For this reason, Eurocode prescribes to distribute the axle loads over three adjacent sleepers. In this paper, the axle load distribution is first studied using a plane finite element analysis and based on that, a triangular load distribution is proposed. Then, numerical simulations are performed to compare the effect of this load distribution with the Eurocode one. Both simply supported bridges and bridges with integrated backwalls, all with span lengths less than 10m, are studied. For the later bridges, the effect of the stiffness of the foundation has been studied by adding springs at the supports.

  • 9.
    Axelsson, Erik
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges.
    Syk, Annelie
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges.
    Ülker Kaustell, Mahir
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges.
    Battini, Jean-Marc
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges.
    Effect of the spreading of the axle load through the ballast on the dynamic response of short span railway bridges2013In: Ballast: Issues & Challenges, 2013, p. 25-25Conference paper (Refereed)
  • 10.
    Battini, Jean-Marc
    KTH, School of Engineering Sciences (SCI), Mechanics.
    A modified corotational framework for triangular shell elements2007In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 196, no 13-16, p. 1905-1914Article in journal (Refereed)
    Abstract [en]

    The corotational framework for triangular shell elements has been presented by different authors (see the Introduction). The purpose of this paper is to introduce three modifications in this approach. The first one is a simplified definition of the local rotations. The second one is a reduction of the number of local degrees of freedom from 18 to 15. The third and principal one concerns the parameterisation of the global finite rotations. A new approach based on Euler parameters (quaternion) is proposed. In particular, it is shown that only three parameters are required. The purpose of these three modifications is to obtain a formulation which gives the same numerical results but which is computationally more efficient than the original one. This aspect is illustrated in several numerical examples.

  • 11.
    Battini, Jean-Marc
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges.
    A non-linear corotational 4-node plane element2008In: Mechanics research communications, ISSN 0093-6413, E-ISSN 1873-3972, Vol. 35, no 6, p. 408-413Article in journal (Refereed)
    Abstract [en]

    A non-linear corotational 4-node plane element is presented. The main interested of the Received 14 September 2007 approach is that accurate and efficient linear elements can be transformed to non-linear elements with little work and without considering the assumptions used to derive these linear elements. Two numerical examples are presented.

  • 12.
    Battini, Jean-Marc
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges.
    A rotation-free corotational plane beam element for non-linear analyses2008In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 75, no 6, p. 672-689Article in journal (Refereed)
    Abstract [en]

    This paper presents a plane beam element without rotational degrees of freedom that can be used for the analysis of non-linear problems. The element is based on two main ideas. First, a corotational approach is adopted, which means that the kinematics of the element is decomposed into a rigid body motion part and a deformational part. Next, in the deformational part. the local nodal rotations are extrapolated as a function of the local displacements of the two nodes of the element and the first nodes to the left and right of the element. Six numerical applications are presented in order to assess the performance of the formulation.

  • 13.
    Battini, Jean-Marc
    KTH, Superseded Departments, Structural Engineering.
    Co-rotational beam elements in instability problems2002Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    The purpose of the work presented in this thesis is to implement co-rotational beam elements and branch-switching procedures in order to analyse elastic and elastoplasticinstability problems. For the 2D beam elements, the co-rotational framework is taken from Crisfield [23]. The main objective is to compare three different local elasto-plastic elements. The 3D co-rotational formulation is based on the work of Pacoste and Eriksson [73],with new items concerning the parameterisation of the finite rotations, the definitionof the local frame, the inclusion of warping effects through the introduction of aseventh nodal degree of freedom and the consideration of rigid links. Differenttypes of local formulations are considered, including or not warping effects. It isshown that at least some degree of non-linearity must be introduced in the localstrain definition in order to obtain correct results for certain classes of problems. Within the present approach any cross-section can be modelled, and particularly, the centroid and shear center are not necessarily coincident.Plasticity is introduced via a von Mises material with isotropic hardening. Numericalintegration over the cross-section is performed. At each integration point, theconstitutive equations are solved by including interaction between the normal andshear stresses. Concerning instabilities, a new numerical method for the direct computation of elasticcritical points is proposed. This is based on a minimal augmentation procedure asdeveloped by Eriksson [32–34]. In elasto-plasticity, a literature survey, mainly concernedwith theoretical aspects is first presented. The objective is to get a completecomprehension of the phenomena and to give a basis for the two branch-switchingprocedures presented in this thesis.A large number of examples are used in order to assess the performances of the elements and the path-following procedures.

  • 14.
    Battini, Jean-Marc
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges.
    Large Rotations and Nodal Moments in Corotational Elements2008In: CMES - Computer Modeling in Engineering & Sciences, ISSN 1526-1492, E-ISSN 1526-1506, Vol. 33, no 1, p. 1-15Article in journal (Refereed)
    Abstract [en]

    This paper deals with the parameterisation of large rotations in corotational beam and shell elements. Several alternatives, presented in previous articles, are summarised, completed and compared to each other. The implementation of applied external moments and eccentric forces, consistent with the different parameterisations, is also considered.

  • 15.
    Battini, Jean-Marc
    KTH, Superseded Departments, Structural Engineering.
    Plastic instability analysis of plane frames using a co-rotational approach1999Licentiate thesis, monograph (Other scientific)
  • 16.
    Battini, Jean-Marc
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges.
    The corotational method: an alternative to derive nonlinear finite elements2015Conference paper (Refereed)
    Abstract [en]

    The corotational method is an alternative approach to derive efficient nonlinear finite elements, in particular for beams and shells. The idea is to decompose the large motion of the element into rigid body and pure deformational parts. Then, if an appropriate mesh size is taken, the deformational part can be assumed as small and can be modelled by using classical linear (or low order nonlinear) finite element formulations. One main interest of this method is that once the corotational framework has been derived, several local formulations can be used, giving different finite formulations well suited to different types of problems.

    The purpose of this paper is to present a review of some new developments obtained during the last fifteen years utilizing the corotational method. In particularly, the development of corotational formulations for composite two-dimensional beams with interlayer slips and for dynamic two-dimensional and three-dimensional beams are addressed. Corotational formulations for plane, solid and shell elements also are presented and discussed.

    Several corotational formulations can be found in the literature. All these formulations are based on the idea presented above. However, their implementations, especially for three-dimensional beams and shells, can be rather different. This paper focuses mainly on the recent work carried out in a collaboration between KTH, the Royal Institute of Technology in Sweden and INSA de Rennes in France.

  • 17.
    Battini, Jean-Marc
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges.
    The non-linear influence of ballast on the vibrations of railway bridges2012In: Proceedings of the Eleventh International Conference on Computational Structures Technology, 2012Conference paper (Refereed)
    Abstract [en]

    In numerical dynamic analyses of railway bridges, the ballast is either considered as an additional mass or modeled using a mass-spring-damper system between the bridge deck and the sleepers. In both cases, the influence of the ballast on the natural frequencies of the bridge is neglected. However, a research project at the Division of Structural Engineering and Bridges at KTH has shown that the ballast may influence significantly the first natural frequency of bridges. To consider that aspect, a new finite beam element model has been developed. The main feature of the element is that the effect of the ballast is introduced through a non-linear longitudinal stiffness associated to the slip at the interface between the bridge and the ballast. This simple element can be used to model accurately the vertical vibrations in bridges, which allows a better prediction of the fatigue life.

  • 18.
    Battini, Jean-Marc
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges.
    Nguyen, Q. H.
    Hjiaj, M.
    Non-linear finite element analysis of composite beams with interlayer slips2009In: Computers & structures, ISSN 0045-7949, E-ISSN 1879-2243, Vol. 87, no 13-14, p. 904-912Article in journal (Refereed)
    Abstract [en]

    This article presents a new non-linear finite element formulation for the analysis of two-layer composite plane beams with interlayer slips. The element is based on the corotational method. The main interest of this approach is that different linear elements can be automatically transformed to non-linear ones. To avoid curvature locking that may occur for low order element(s). a local linear formulation based on the exact stiffness matrix is used, Five numerical applications are presented in order to assess the performance of the formulation.

  • 19.
    Battini, Jean-Marc
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges.
    Nguyen, Quang-Huy
    Hjiaj, Mohammed
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges.
    Geometrically non-linear finite element analysis of two-layer composite beams with interlayer slip2010Conference paper (Refereed)
  • 20.
    Battini, Jean-Marc
    et al.
    KTH, Superseded Departments, Civil and Architectural Engineering.
    Pacoste, Costin
    KTH, Superseded Departments, Civil and Architectural Engineering.
    Co-rotational beam elements with warping effects in instability problems2002In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 191, no 17-18, p. 1755-1789Article in journal (Refereed)
    Abstract [en]

    The present paper investigates the formulation of 3D co-rotational beam elements for the buckling and post-buckling analysis of frame structures. Following Pacoste and Eriksson [Comput. Methods Appl. Mech. Engrg. 144 (1997) 163], the term co-rotational relates here to the provision of a local reference frame that continuously rotates and translates with the element. Within this context, several issues are emphasised. The first one refers to the parameterisation of finite 3D rotations. The alternative put forth in the paper is based on the spatial form of the incremental rotational vector. The second issue concerns warping effects which are introduced by adding a seventh degree of freedom at each node. Different types of local formulations are considered and it is shown that at least some degree of non-linearity must be introduced in the local strain definition in order to obtain correct results for certain classes of problems. Within the present approach the centroid and shear center of the cross-section are not necessarily coincident. Finally, in the context of instability problems, a method for the direct computation of critical points is also briefly discussed, This is based on a minimal augmentation procedure as developed by Eriksson [Comput. Methods Appl. Mech. Engrg. 156 (1998) 45; Comput. Methods Appl. Mech. Engrg. 179 (1999) 265; Int. J. Struct. Stability Dynamic 1 (1) (2001)]. Ten examples, including large displacement and stability problems, are used in order to assess the performances of the elements.

  • 21.
    Battini, Jean-Marc
    et al.
    KTH, Superseded Departments, Structural Engineering.
    Pacoste, Costin
    KTH, Superseded Departments, Structural Engineering.
    Elements poutres co-rotationels avec gauchissement2001In: Proceedings CSMA 5éme colloque national en calcul des structures, Giens, 2001Conference paper (Refereed)
  • 22.
    Battini, Jean-Marc
    et al.
    KTH, Superseded Departments, Mechanics.
    Pacoste, Costin
    On the choice of local element frame for corotational triangular shell elements2004In: Communications in Numerical Methods in Engineering, ISSN 1069-8299, E-ISSN 1099-0887, Vol. 20, no 10, p. 819-825Article in journal (Refereed)
    Abstract [en]

    In the context of corotational triangular shell elements, the objective of this paper is to show that for certain stability problems it is interesting to choose a local element frame invariant to the element node ordering. Two methods of obtaining such a local frame are presented. These two methods, already proposed by other authors, are reformulated. For the first one, based on the minimisation of local nodal displacements, it is shown that the iterative process can be avoided.

  • 23.
    Battini, Jean-Marc
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Pacoste, Costin
    On the choice of the linear element for corotational triangular shells2006In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 195, no 44-47, p. 6362-6377Article in journal (Refereed)
    Abstract [en]

    The corotational formulation for triangular thin shell elements presented in [A. Eriksson, C. Pacoste, Element formulation and numerical techniques for stability problems in shells, Comput. Methods Appl. Mech. Engrg. 191 (2002) 3775-3810] is further developed in order to incorporate elasto-plastic deformations. Several local formulations are implemented and tested. These local elements are geometrically linear and are obtained by the by superposition of a membrane and a plate part. Eleven elastic and elasto-plastic examples are presented. Both the incremental and deformation theories of plasticity are considered. The first objective is to assess the performance of the present formulation in modelling elasto-plastic instability problems. The second objective is to compare the different linear local formulations: it is shown that some of them give better results in instability problems.

  • 24.
    Battini, Jean-Marc
    et al.
    KTH, Superseded Departments, Civil and Architectural Engineering.
    Pacoste, Costin
    KTH, Superseded Departments, Civil and Architectural Engineering.
    Plastic instability of beam structures using co-rotational elements2002In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 191, no 51-52, p. 5811-5831Article in journal (Refereed)
    Abstract [en]

    In a previous paper [Comput. Methods Appl. Mech. Engrg. 191 (2002) 1755], the authors have presented a 3D co-rotational elastic beam element including warping effects. This formulation is now further developed in order to incorporate elasto-plastic deformations. The element possesses seven degrees of freedom at each node and can be used to model beams with arbitrary cross-sections. Thus, within the present approach, the centroid and shear center of the cross-section are not necessarily coincident. The main purpose of this element is to model elasto-plastic instability problems. In this context, two methods of branch-switching are tested and discussed. In the first one, the bifurcation point is isolated by successive bisections and the branch-switching is operated by using the eigenvector associated to the negative eigenvalue. In the second one, introduced by Petryk, an energy approach is used to select automatically the stable post-bifurcation path. Six examples, including large displacement and stability problems, are used in order to assess the performances of the element.

  • 25.
    Battini, Jean-Marc
    et al.
    KTH, Superseded Departments, Structural Engineering.
    Pacoste, Costin
    KTH, Superseded Departments, Structural Engineering.
    Eriksson, Anders
    KTH, Superseded Departments, Structural Engineering.
    Improved minimal augmentation procedure for the direct computation of critical points2003In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 192, no 16-18, p. 2169-2185Article in journal (Refereed)
    Abstract [en]

    This paper presents a new numerical procedure for the direct computation of critical points for elastic beam structures undergoing large displacements and rotations. Compared to the approach described by Wriggers et al. [Comput. Methods Appl. Mech. Engrg. 70 (1988) 329; Int. J. Numer. Methods Engrg. 30 (1990) 1551, two main modifications are introduced. First, following Eriksson [Comput. Methods Appl. Mech. Engrg. 114 (1994) 77; Comput. Methods Appl. Mech. Engrg. 156 (1998) 45; Comput. Methods Appl. Mech. Engrg. 179 (1999) 265; Int. J. Struct. Stability Dynam. l(l) (2001)], the condition of criticality is expressed by a scalar equation instead of a vectorial one. Next, the present procedure does not use exclusively the extended system obtained from the equilibrium equations and the criticality condition, but also introduces intermediate iterations based purely on equilibrium equations under load or displacement control, Eight numerical examples, presenting bifurcation and limit points, are used in order to compare the performances of this new method and the one presented in [Comput. Methods Appl. Mech. Engrg. 70 (1988) 329; Int. J. Numer. Methods Engrg. 30 (1990) 155].

  • 26.
    Battini, Jean-Marc
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges.
    Ülker-Kaustell, Mahir
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Design and Bridges (name changed 20110630).
    A simple finite element to consider the non-linear influence of the ballast on vibrations of railway bridges2011In: Engineering structures, ISSN 0141-0296, E-ISSN 1873-7323, Vol. 33, no 9, p. 2597-2602Article in journal (Refereed)
    Abstract [en]

    This article proposes a new and simple finite element which can be used to analyze vertical vibrations in railway bridges. The main feature of the element is that the effect of the ballast is introduced through a non-linear longitudinal stiffness associated to the slip at the interface between the bridge and the ballast. Two numerical applications show that this element can be used to model the variation of the natural frequencies of the bridge as a function of the amplitude of vibration.

  • 27. Bornet, Lucie
    et al.
    Andersson, A.
    Zwolski, J.
    Battini, Jean-Marc
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Building Technology and Design.
    Influence of the ballasted track on the dynamic properties of a truss railway bridge2014In: Civil-Comp Proceedings, ISSN 1759-3433, Vol. 106Article in journal (Refereed)
    Abstract [en]

    This paper presents numerical and experimental analyses of a steel truss railway bridge. The main interest of this work is that dynamic experiments have been performed before and after the ballasted track was placed on the bridge. Consequently, it has been possible to quantify the effect of the ballast and the rails on the dynamic properties of the bridge. For that, two finite element models, with and without the ballasted track, have been implemented and calibrated using the experimental results. It appears that the ballast gives an additional stiffness of about 25-30% for the lowest three eigenmodes. This additional stiffness can be only partly explained by the stiffness of the ballast. In fact, it seems that this additional stiffness also results from a change of the support conditions.

  • 28.
    Bornet, Lucie
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges.
    Andersson, Andreas
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges.
    Zwolski, Jaroslaw
    Battini, Jean-Marc
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges.
    Influence of the ballasted track on the dynamic properties of a truss railway bridge2014Conference paper (Refereed)
  • 29.
    Bornet, Lucie
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges.
    Andersson, Andreas
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges.
    Zwolski, Jaroslaw
    Wroclaw University of Technology, Department of Civil Engineering.
    Battini, Jean-Marc
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges.
    Influence of the ballasted track on the dynamic properties of a truss railway bridge2015In: Structure and Infrastructure Engineering, ISSN 1573-2479, E-ISSN 1744-8980, Vol. 11, no 6, p. 796-803Article in journal (Refereed)
    Abstract [en]

    This article presents numerical and experimental analyses of a steel truss railway bridge. The main interest of this work is that dynamic experiments have been performed before and after the ballasted track was placed on the bridge. Consequently, it has been possible to quantify the effect of the ballast and the rails on the dynamic properties of the bridge. For that, two finite element models, with and without the ballasted track, have been implemented and calibrated using the experimental results. It appears that the ballast gives an additional stiffness of about 25-30% for the lowest three eigenmodes. This additional stiffness can be only partly explained by the stiffness of the ballast. In fact, it seems that this additional stiffness is also due to a change of the support conditions.

  • 30.
    Chhang, Sophie
    et al.
    KTH.
    Sansour, C.
    Hjiaj, M.
    Battini, Jean-Marc
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Building Technology and Design.
    An energy-momentum co-rotational formulation for nonlinear dynamics of planar beams2017In: Computers & structures, ISSN 0045-7949, E-ISSN 1879-2243, Vol. 187, p. 50-63Article in journal (Refereed)
    Abstract [en]

    This article presents an energy-momentum integration scheme for the nonlinear dynamic analysis of planar Euler-Bernoulli beams. The co-rotational approach is adopted to describe the kinematics of the beam and Hermitian functions are used to interpolate the local transverse displacements. In this paper, the same kinematic description is used to derive both the elastic and the inertia terms. The classical midpoint rule is used to integrate the dynamic equations. The central idea, to ensure energy and momenta conservation, is to apply the classical midpoint rule to both the kinematic and the strain quantities. This idea, developed by one of the authors in previous work, is applied here in the context of the co-rotational formulation to the first time. By doing so, we circumvent the nonlinear geometric equations relating the displacement to the strain which is the origin of many numerical difficulties. It is rigorously shown that the proposed method conserves the total energy of the system and, in absence of external loads, the linear and angular momenta remain constant. The accuracy and stability of the proposed algorithm, especially in long term dynamics with a very large number of time steps, is assessed through four numerical examples.

  • 31.
    Chhang, Sophy
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering. Université Bretagne, France.
    Hjiaj, M.
    Battini, Jean-Marc
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering.
    Sansour, C.
    An energy-momentum formulation for nonlinear dynamics of planar co-rotating beams2017In: COMPDYN 2017 - Proceedings of the 6th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering, National Technical University of Athens , 2017, Vol. 2, p. 3682-3696Conference paper (Refereed)
    Abstract [en]

    This article presents an energy-momentum integration scheme for the nonlinear dynamic analysis of planar Bernoulli/Timoshenko beams. The co-rotational approach is adopted to describe the kinematics of the beam and Hermitian functions are used to interpolate the local transverse displacements. In this paper, the same kinematic description is used to derive both the elastic and the inertia terms. The classical midpoint rule is used to integrate the dynamic equations. The central idea, to ensure energy and momenta conservation, is to apply the classical midpoint rule to both the kinematic and the strain quantities. This idea, developed by one of the authors in previous work, is applied here in the context of the co-rotational formulation to the first time. By doing so, we circumvent the nonlinear geometric equations relating the displacement to the strain which is the origin of many numerical difficulties. It can be rigorously shown that the proposed method conserves the total energy of the system and, in absence of external loads, the linear and angular momenta remain constant. The accuracy and stability of the proposed algorithm, especially in long term dynamics with a very large number of time steps, is assessed through two numerical examples.

  • 32.
    Chhang, Sophy
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges.
    Hjiaj, Mohammed
    INSA de Rennes, France.
    Battini, Jean-Marc
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges.
    Sansour, Carlo
    INSA de Rennes, France.
    Energy-momentum method for nonlinear dynamic of 2D corotational beams.2016In: Eccomas 2016 Proceedings, Computational Methods in Structural Dynamics & Earthquake Engineering , 2016Conference paper (Refereed)
    Abstract [en]

    This paper presents an energy-momentum method for nonlinear dynamics of 2D Bernoulli corotational beams. It is shown that the time stepping algorithm conserves energy, linear momentum and angular momentum. To be consistent in the corotational approach, cubic interpolations of Bernoulli element are employed to derive both inertia and elastic terms. The shallow arch strain definition is used to get an element which produce accurate results for less number of elements. To avoid membrane locking, we use a constant and average value of the axial strains. In addition, the energy-momentum method is used to preserve the conserving properties, which is able to maintain the stability and accuracy in a non-dissipative system for a long period. The midpoint velocities of kinematic fields and strains are used to tackle any non-linear form of strain displacement relations. Finally, two examples including large overall displacement are presented to illustrate the stability and efficiency of the proposed algorithms.

  • 33.
    Heng, Piseth
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges.
    Alhasawi, Anas
    Battini, Jean-Marc
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges.
    Hjiaj, Mohammed
    Co-rotating rigid beam with generalized plastic hinges for the nonlinear dynamic analysis of planar framed structures subjected to impact loading2017In: Finite elements in analysis and design (Print), ISSN 0168-874X, E-ISSN 1872-6925Article in journal (Refereed)
  • 34.
    Heng, Piseth
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering. Univ Europeenne Bretagne, France.
    Hjiaj, M.
    Battini, Jean-Marc
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering.
    Limam, A.
    A simplified model for nonlinear dynamic analysis of steel column subjected to impact2016In: International Journal of Non-Linear Mechanics, ISSN 0020-7462, E-ISSN 1878-5638, Vol. 86, p. 37-54Article in journal (Refereed)
    Abstract [en]

    This paper presents a new simplified model of the nonlinear dynamic behavior of a steel column subjected to impact loading. In this model, the impacted column, which undergoes large displacement, consists of two rigid bars connected by generalized elastic–plastic hinges where the deformation of the entire steel column as well as the connections is concentrated. The effect of the rest of the structure on the column is modeled by an elastic spring and a point masse both attached to the top end of the column which is also loaded by a compressive force. The plastification of the hinges follows the normality rule with a yield surface that accounts for the interaction between M and N. The latter is described by a super-elliptic yield surface that allows ones to consider a wide range of convex yield criterion by simply varying the roundness factor that affects the shape of the limit surface. By including these features, the model captures both geometry and material nonlinearities. Both the flow rule and the equations of motion are integrated using the midpoint scheme that conserves energy. The non-smooth nature of impact is considered by writing the equations of motion of colliding masses using differential measures. Contact conditions are written in terms of velocity and combined with Newton's law to provide the constitutive law describing interactions between masses during impact. Numerical applications show that the model is able to capture the behavior of a column subjected to impact.

  • 35.
    Heng, Piseth
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges.
    Hjiaj, Mohammed
    INSA de Rennes, France.
    Battini, Jean-Marc
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges.
    A simplified model of a steel column subjected to impact2016Conference paper (Refereed)
  • 36.
    Heng, Piseth
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges.
    Hjiaj, Mohammed
    Battini, Jean-Marc
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges.
    Limam, Ali
    An enhanced SDOF model to predit the behaviour of a steel column impacted by a rigid body2017In: Engineering structures, ISSN 0141-0296, E-ISSN 1873-7323, Vol. 152, p. 771-789Article in journal (Refereed)
    Abstract [en]

    The transient dynamic response of a steel beam-column subjected to impact loading is a complex phenomenon involving large localized plastic deformations and non-smooth contact interactions. Exposed to high intensity of the contact force generated from impact, the beam-column may undergo large displacement and inelastic deformation. Previous research has shown that a calibrated elasto-plastic single degree of freedom system is able to reproduce both the displacement and the force time-history of a steel beam subjected to non-impulsive loading or low-velocity impact. In these models, the static force-displacement curve is derived from either experiments or detailed 3D nonlinear analysis. Tri-linear resistance function has been extensively used to reproduce the different stages of the response including catenary effects. A rigorous treatment of such a complex problem calls for the use of non-smooth analysis tools to handle the impulsive nature of the impact force, the unilateral constraint, the impenetrability condition and the discontinuity of the velocity in a rigorous manner. In this paper, we present a non-smooth elasto-plastic single degree of freedom model under impact loading that permits the use of arbitrary resistance function. Adopting the non-smooth framework offers tools such as differential measures and convex analysis concepts to deal with unilateral contact incorporating Newton’s impact law. The mid-point scheme is adopted to avoid numerical unrealistic energy decay or blowup. Furthermore, the non-penetration condition is numerically satisfied by imposing the constraint at only the velocity level to guarantee energy-momentum conservation [1]. The explicit expression of resistance functions of the beam that are used in the SDOF model are obtained from a simplified nonlinear static analysis of two beam-column models. In the analysis, a linear relation between normal force and bending moment is assumed for the plastification of the hinges. Two proposals to simplify the explicit expressions of the model’s response behavior are given. Performing an energy-based analysis, we predict maximum displacement that is needed to absorb the kinetic energy arising from the impact for different coefficient of restitution. The numerical examples underline the validity of the model by showing good agreement with the predictions of reference models.

  • 37. Hjiaj, Mohammed
    et al.
    Battini, Jean-Marc
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges.
    Nguyen, Quang Huy
    Large displacement analysis of shear deformable composite beams with interlayer slips2012In: International Journal of Non-Linear Mechanics, ISSN 0020-7462, E-ISSN 1878-5638, Vol. 47, no 8, p. 895-904Article in journal (Refereed)
    Abstract [en]

    This paper presents a novel geometric non-linear finite element formulation for the analysis of shear deformable two-layer beams with interlayer slips. We adopt the co-rotational approach where the motion of the element is decomposed into two parts: a rigid body motion which defines a local coordinate system and a small deformational motion of the element relative to this local coordinate system. The main advantage of this approach is that the transformation matrices relating local and global quantities are independent to the choice of the geometrical linear local element. The effect of transverse shear deformation of the layers is taken into account by assuming that each layer behaves as a Timoshenko beam element. The layers are assumed to be continuously connected and partial interaction is considered by considering a continuous relationship between the interface shear flow and the corresponding slip. In order to avoid curvature and shear locking phenomena, the local linear element is formulated using "exact" displacement shape functions derived from the closed-form solution of the governing equations of a two-layer beam element. Finally, three numerical applications are presented in order to assess the performance of the proposed formulation.

  • 38. Hjiaj, Mohammed
    et al.
    Nguyen, Quang Huy
    Battini, Jean-Marc
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges.
    Geometrically nonlinear analysis of shear deformable composite members with partial interaction2012Conference paper (Refereed)
  • 39.
    Le, Thanh Nam
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges.
    Battini, Jean-Marc
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges.
    Hjiaj, Mohammed
    A consistent 3D corotational beam element for nonlinear dynamic analysis of flexible structures2014In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 269, p. 538-565Article in journal (Refereed)
    Abstract [en]

    The purpose of the paper is to present a corotational beam element for the nonlinear dynamic analysis of 3D flexible frames. The novelty of the formulation lies in the use of the corotational framework (i.e., the decomposition into rigid body motion and pure deformation) to derive not only the internal force vector and the tangent stiffness matrix but also the inertia force vector and the tangent dynamic matrix. As a consequence, cubic interpolations are adopted to formulate both inertia and internal local terms. In the derivation of the dynamic terms, an approximation for the local rotations is introduced and a concise expression for the global inertia force vector is obtained. To enhance the efficiency of the iterative procedure, an approximate expression of the tangent dynamic matrix is adopted. Four numerical examples are considered to assess the performance of the new formulation against the one suggested by Simo and Vu-Quoc (1988) [48]. It was observed that the proposed formulation proves to combine accuracy with efficiency. In particular, the present approach achieves the same level of accuracy as the formulation of Simo and Vu-Quoc but with a significantly smaller number of elements.

  • 40.
    Le, Thanh Nam
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges. Structural Engineering Research Group, LGCGM, France.
    Battini, Jean-Marc
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges. Structural Engineering Research Group, LGCGM, France.
    Hjiaj, Mohammed
    Co-rotational dynamic formulation for 2D beams2011In: ECCOMAS Thematic Conference - COMPDYN 2011, 2011Conference paper (Refereed)
    Abstract [en]

    The corotational method is an attractive approach to derive non-linear finite beam elements. In a number of papers, this method was employed to investigate the non-linear dynamic analysis of 2D beams. However, most of the approaches found in the literature adopted either a lumped mass matrix or linear local interpolations to derive the inertia terms (which gives the classical linear and constant Timoshenko mass matrix), although local cubic interpolations were used to derive the elastic force vector and the tangent stiffness matrix. In this paper, a new corotational formulation for dynamic nonlinear analysis is presented. Cubic interpolations are used to derive both the inertia and elastic terms. Numerical examples show that the proposed approach is more efficient than using lumped or Timoshenko mass matrices.

  • 41.
    Le, Thanh Nam
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges.
    Battini, Jean-Marc
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges.
    Hjiaj, Mohammed
    Corotational formulation for nonlineardynamics of beams with arbitrary thin-walled open cross-sectionsManuscript (preprint) (Other academic)
  • 42.
    Le, Thanh Nam
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Design and Bridges (name changed 20110630).
    Battini, Jean-Marc
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Design and Bridges (name changed 20110630).
    Hjiaj, Mohammed
    Efficient dynamic formulation for co-rotational 2D beams2011In: Proceedings of the 8th International Conference on Structural Dynamics Eurodyn 2011, 2011, p. 1976-1981Conference paper (Refereed)
    Abstract [en]

    2D beam element, Corotational method, Nonlinear dynamic analysis, Dynamics, Interpolation, Matrix algebra, Nonlinear analysis, Stiffness matrix, Structural dynamics, Beam elements, Co-rotational formulation, Cubic interpolation, Dynamic non-linear analysis, Finite-element approach, Local interpolation, Tangent stiffness matrix, Finite element method.

  • 43.
    Le, Thanh Nam
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges.
    Battini, Jean-Marc
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges.
    Hjiaj, Mohammed
    Efficient formulation for dynamics of corotational 2D beams2011In: Computational Mechanics, ISSN 0178-7675, E-ISSN 1432-0924, Vol. 48, no 2, p. 153-161Article in journal (Refereed)
    Abstract [en]

    The corotational method is an attractive approach to derive non-linear finite beam elements. In a number of papers, this method was employed to investigate the non-linear dynamic analysis of 2D beams. However, most of the approaches found in the literature adopted either a lumped mass matrix or linear local interpolations to derive the inertia terms (which gives the classical linear and constant Timoshenko mass matrix), although local cubic interpolations were used to derive the elastic force vector and the tangent stiffness matrix. In this paper, a new corotational formulation for dynamic nonlinear analysis is presented. Cubic interpolations are used to derive both the inertia and elastic terms. Numerical examples show that the proposed approach is more efficient than using lumped or Timoshenko mass matrices.

  • 44.
    Le, Thanh Nam
    et al.
    INSA Rennes, Struct Engn Res Grp LGCGM, Rennes, France.
    Hjiaj, Mohammed
    INSA Rennes, Struct Engn Res Grp LGCGM, Rennes, France.
    Battini, Jean-Marc
    INSA Rennes, Struct Engn Res Grp LGCGM, Rennes, France.
    Efficient formulation for nonlinear dynamics of steel frames2012In: STESSA 2012: PROCEEDINGS OF THE 7TH INTERNATIONAL CONFERENCE ON BEHAVIOUR OF STEEL STRUCTURES IN SEISMIC AREAS, 2012, p. 1113-1118Conference paper (Refereed)
    Abstract [en]

    The corotational finite element approach is a well known method to develop nonlinear beam elements in case of large displacements and small deformations. Many authors used this method to investigate the nonlinear dynamic analysis of planar beams. Nevertheless, concerning the derivation of the inertia terms, most of the approaches found in the literature adopted either a lumped mass matrix or linear local interpolations (which gives the classical linear and constant Timoshenko mass matrix), although local cubic interpolations were used to derive the elastic force vector and tangent stiffness matrix. In this paper, a new corotational formulation for dynamic nonlinear analysis is presented. Cubic interpolations are used to derive both the inertia and elastic terms. Several examples of elastic beam with large displacements show that the proposed approach is more efficient than using classical mass matrices found in literature.

  • 45.
    Le, Thanh-Nam
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges. Université Européenne de Bretagne, France.
    Battini, Jean-Marc
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges.
    Hjiaj, M.
    Université Européenne de Bretagne, France.
    Corotational formulation for nonlinear dynamics of beams with arbitrary thin-walled open cross-sections2014In: Computers & structures, ISSN 0045-7949, E-ISSN 1879-2243, Vol. 134, p. 112-127Article in journal (Refereed)
    Abstract [en]

    A new consistent corotational formulation for nonlinear dynamics of beams with arbitrary thin-walled cross-section is presented. The novelty is that the warping deformations and the eccentricity of the shear center are fully taken into account. Therefore, additional terms are introduced in the expressions of the inertia force vector and the tangent dynamic matrix. Their contribution is then investigated considering several numerical examples. Besides, the element has seven degrees of freedom at each node and cubic shape functions are used to interpolate local transverse displacements and axial rotations. The formulation's accuracy is assessed considering five examples with comparisons against 3D-solid solutions.

  • 46.
    Le, Thanh-Nam
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges.
    Battini, Jean-Marc
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges.
    Hjiaj, Mohammed
    A new corotational element for nonlinear dynamic analysis of 3D beams2013In: ECCOMAS Thematic Conference - COMPDYN 2013: 4th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering, Proceedings - An IACM Special Interest Conference, 2013, p. 3586-3608Conference paper (Refereed)
    Abstract [en]

    The purpose of the paper is to present a corotational beam element for the nonlinear dynamic analysis of 3D flexible frames. The novelty of the formulation lies in the use of the corotational framework (i.e. the decomposition into rigid body motion and pure deformation) to derive not only the internal force vector and the tangent stiffness matrix but also the inertia force vector and the tangent dynamic matrix. As a consequence, cubic interpolations are adopted to formulate both inertia and internal local terms. In the derivation of the dynamic terms, an approximation for the local rotations is introduced and a concise expression for the global inertia force vector is obtained. To enhance the efficiency of the iterative procedure, an approximate expression of the tangent dynamic matrix is adopted. Several numerical examples are considered to assess the performance of the new formulation against the one suggested by Simo and Vu-Quoc[37]. It was observed that the proposed formulation proves to combine accuracy with efficiency. In particular, the present approach achieves the same level of accuracy as the formulation of Simo and Vu-Quoc but with a significantly smaller number of elements.

  • 47.
    Le, Thanh-Nam
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges.
    Battini, Jean-Marc
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges.
    Hjiaj, Mohammed
    Dynamics of 3D beam elements in a corotational context: A comparative study of established and new formulations2012In: Finite elements in analysis and design (Print), ISSN 0168-874X, E-ISSN 1872-6925, Vol. 61, p. 97-111Article in journal (Refereed)
    Abstract [en]

    This paper deals with Newmark time stepping methods and finite rotations for nonlinear finite element analysis of flexible beam structures. The corotational method is used to develop expressions of the internal forces and the corresponding tangent stiffness matrices. For the dynamic part, four formulations based on different parameterizations of rotations are compared. The first three are classic formulations taken from the literature with some modifications for two of them. The last one is new and uses three of the four Euler parameters (quaternion) as rotational variables. For all these approaches, theoretical derivations as well as practical implementations are given in detail. The similarities and differences between the formulations are pointed out. Six numerical examples are studied in order to compare these four formulations in terms of numerical accuracy and computational efficiency. Regarding efficiency, the choice of the predictor at each time step and the possibility to simplify the tangent inertia matrix are carefully investigated. The numerical results show that these four formulations have the same numerical accuracy, but that the computational efficiency depends on the choice of the tangent inertia matrix. Besides, the new formulation proposed in this paper turns out to be the fastest one.

  • 48. Le, T.-N.
    et al.
    Battini, Jean-Marc
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges.
    Hjiaj, M.
    A new 3D co-rotational beam element for nonlinear dynamic analysis2015In: COMPDYN 2015, 2015, p. 1087-1110Conference paper (Refereed)
    Abstract [en]

    The paper investigates the contribution of the warping deformations and the shear center location on the dynamic response of 3D thin-walled beams obtained with an original consistent co-rotational formulation developed by the authors. Consistency of the formulation is ensured by employing the same kinematic assumptions to derive both the static and dynamic terms. Hence, the element has seven degrees of freedom at each node and cubic shape functions are used to interpolate local transversal displacements and axial rotations. Accounting for warping deformations and the position of the shear center produces additional terms in the expressions of the inertia force vector and the tangent dynamic matrix. The performance of the present formulation is assessed by comparing its predictions against 3D-solid FE solutions.

  • 49.
    Lind Östlund, Johan
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges.
    Andersson, Andreas
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges.
    Mahir, Ülker-Kaustell
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges.
    Battini, Jean-Marc
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges.
    Soil-Structure Interaction for foundations on High-Speed Railway Bridges2017Report (Other academic)
    Abstract [en]

    This report contains a parametric study on the dynamic response of railway bridges on flexible supports. The results are based on simulations using 2D and 3D models. The dynamic stiffness of the supports is described by separate models of the foundation, including relevant stress and strain dependent soil properties from permanent loading that is linearized in a subsequent dynamic analysis. The complex-valued dynamic stiffness constitutes the boundary conditions in a separate analysis of the bridge superstructure that is solved in frequency domain.

    Two different foundation types are studied; shallow slab foundation with relatively good ground conditions, and pile group foundations with relatively poor ground conditions. In both cases, the foundation slab and the pile group have fixed geometry. In the parametric study, the corresponding vertical static foundation stiffness range from 2 – 20 GN/m for the slab foundation and 5 – 25 GN/m for the pile group foundation.

    For the slab foundations, both the stiffness and damping highly depends on the properties of the soil, foundation depth and geometry of the foundation slab. For the pile group foundations, the stiffness is mainly governed by the pile group and the damping by the soil.

    Based on the simulations, the additional damping from the slab foundation is in most cases negligible. Only for relatively soft foundations and short-span bridges significant additional damping is seen. For the pile group foundations, the additional damping is in some cases significant, especially for deeper foundations and short-span bridges. Considering a lower bound of the parametric study does however result in a negligible contribution.

    The dynamic response from passing trains show that the assumption of fixed supports in most cases is conservative. However, the flexible supports may result in a lower natural frequency that should be accounted for in order to not underestimate the resonance speed of the train.

    If flexible supports are included in a dynamic analysis, both the stiffness and damping component needs to be included. The frequency-domain approach presented in this report is a viable solution technique but is not implemented in most commercial software used in the industry.

  • 50.
    Liu, Fangzhou
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges.
    Battini, Jean-Marc
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges.
    Pacoste, Costin
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges. ELU Konsult, Sverige.
    Granberg, A.
    Experimental and Numerical Dynamic Analyses of Hollow Core Concrete Floors2017In: Structures, ISSN 2352-0124, Vol. 12, p. 286-297Article in journal (Refereed)
    Abstract [en]

    Due to their low self-weight and high strength, precast and prestressed hollow core concrete slabs are widely used in construction. However, the combination of low self-weight and long span implies that the slabs are sensitive to vibrations induced by human activities. In this work, experimental tests and numerical analyses are performed in order to understand the dynamic behaviour of hollow core concrete floors. For the experiments, a test floor of dimension 10 m × 7.2 m and consisting of 6 hollow core elements was built. Very good agreements between experimental and numerical results have been obtained. Comprehensive numerical parametric analyses have been performed in order to determine the optimal value of the material parameters.

12 1 - 50 of 53
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