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Extension of field consistence approach into developing plane stress elements
KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.ORCID iD: 0000-0002-5819-4544
1999 (English)In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 173, no 1-2, 111-134 p.Article in journal (Refereed) Published
Abstract [en]

In this research paper, the possibilities for extending the field consistence approach [L. Yunhua, On shear locking in finite elements, Licentiate Thesis, Stockholm, 1997; L. Yunhua, Explanation and elimination of shear locking and membrane locking with field consistence approach, Comput. Methods Appl. Mech. Engrg., in press], starting from different variational principles, to plane stress elements are investigated. In the extension, two main difficulties are: explicitly solving a set of coupled partial differential equations and satisfying inter-element compatibility. The first one is alleviated by constructing element interpolations from a set of quasi-general solutions, rather than the real general solutions, to the Euler-Lagrangian equations. The second one is solved by combining the field consistence approach with the iso-parametric interpolation technique. The traditional assumed stress method is improved and an efficient plane stress element is obtained. It seems that the relations between the three commonly used variational principles can be more reasonably established in the framework of the field consistence approach.

Place, publisher, year, edition, pages
1999. Vol. 173, no 1-2, 111-134 p.
Keyword [en]
Interpolation, Lagrange multipliers, Partial differential equations, Problem solving, Stress analysis, Variational techniques, Euler-Lagrangian equations, Plane stress elements, Finite element method
National Category
Applied Mechanics
Identifiers
URN: urn:nbn:se:kth:diva-119537OAI: oai:DiVA.org:kth-119537DiVA: diva2:611576
Note

References: Yunhua, L., (1997) On Shear Locking in Finite Elements, , Licentiate Thesis, Stockholm; Yunhua, L., Explanation and elimination of shear locking and membrane locking with field consistence approach (1998) Comput. Methods Appl. Mech. Engrg., 162, pp. 249-269; Argyris, J., Dunne, P.C., Malejannakis, G.A., Schelkle, E., A simple triangular facet shell element with applications to linear and non-linear equilibrium and elastic stability problem (1977) Comput. Methods Appl. Mech. Engrg., 10, pp. 371-403; Argyris, J., Tenek, L., Natural mode method: A practicable and novel approach to the global analysis of laminated composite plates and shells (1996) Appl. Mech. Rev., 49, pp. 381-399; Argyris, J., Tenek, L., Olofsson, L., TRIC: A simple but sophisticated 3-node triangular element based on 6 rigid-body and 12 straining modes for fast computational simulations of arbitrary isotropic and laminated composite shells (1997) Comput. Methods Appl. Mech. Engrg., 145, pp. 11-85; Tenek, L., Argyris, J., Computational aspects of the natural-mode finite element method (1997) Comm. Numer. Methods Engrg., 13, pp. 705-713; De Veubeke Fraeijs, B., Displacement and equilibrium models in the finite element method Stress Analysis, pp. 145-196. , O.C. Zienkiewicz and G.S. Holister, eds., (Wiley, London); Stolarski, H., Belytschko, T., Limitation principles for mixed finite elements based on the Hu-Washizu variational formulation (1987) Comput. Methods Appl. Mech. Engrg., 60, pp. 195-216; Pian, T.H.H., Sumihara, K., Rational approach for assumed stress finite elements (1984) Int. J. Numer. Methods Engrg., 20, pp. 1685-1695; Bathe, K.J., (1996) Finite Element Procedure, , Prentice Hall, Englewood Cliffs, NJ; Fröier, M., Nilsson, L., Samuelsson, A., The rectangular plane stress element by Turner, Pian and Wilson (1974) Int. J. Numer. Methods Engrg., 8, pp. 433-437; Feng, W., Hoa, S.V., Huang, Q., Classification of stress modes in assumed stress fields of hybrid finite elements (1997) Int. J. Numer. Methods Engrg., 40, pp. 4313-4339; Simo, J.C., Rifai, M.S., A class of mixed assumed strain methods and the method of incompatible modes (1990) Int. J. Numer. Methods Engrg., 29; Stolarski, H., Belytschko, T., On the equivalence of mode decomposition and mixed finite elements based on the Hellinger-Reissner principle. Part I: Theory (1986) Comput. Methods Appl. Mech. Engrg., 58, pp. 249-263; Stolarski, H., Belytschko, T., On the equivalence of mode decomposition and mixed finite elements based on the Hellinger-Reissner principle. Part II: Application (1986) Comput. Methods Appl. Mech. Engrg., 58, pp. 265-284; Zhao, P.-J., Pian, T.H.H., Yong, S., A new formulation of isoparametric finite elements and the relationship between hybrid stress element and incompatible element (1997) Int. J. Numer. Methods Engrg., 40, pp. 15-27; Pian, T.H.H., Tong, P., Relations between incompatible displacement model and hybrid stress model (1986) Int. J. Numer. Methods Engrg., 22, pp. 173-181; Simo, J.C., Armero, F., Geometrically nonlinear enhanced mixed methods and the method of incompatible modes (1992) Int. J. Num. Meth. Engrg., 33, pp. 1413-1449; Crisfield, M.A., Incompatible modes, enhanced strains and substitute strains continuum elements (1995) Advances in Finite Element Technology, , N.-E. Wiberg, ed., CIMNE, Barcelona; Zienkiewicz, O.C., (1971) The Finite Element Method in Engineering Science, , McGraw-Hill, London; (1991) MAPLE V Language Reference Manual, , Springer-Verlag, New York; Eriksson, A., Pacoste, C., Symbolic derivation of finite elements (1997) Proc. NSCM, 10. , Tallinn; Eriksson, A., Pacoste, C., Symbolic software in linear and non-linear FEM development (1997) Proc. Euromech. Colloquium, 371; Pian, T.H.H., Chen, D.P., Alternative ways for formulation of hybrid stress elements (1982) Int. J. Numer. Methods Engrg., 18, pp. 1679-1684; Pian, T.H.H., On the equivalence of non-conforming element and hybrid stress element (1982) Applied Mathematics and Mechanics (English Edition), 3 (6), pp. 773-776; Yuan, K.-Y., Huang, Y.-S., Pian, T.H.H., New strategy for assumed stress for 4-node hybrid stress membrane element (1993) Int. J. Numer. Methods Engrg., 36, pp. 1747-1763; Simo, J.C., Hughes, T.J.R., On the variational foundations of assumed strain methods (1986) ASME J. of Appl. Mech., 53, pp. 51-54; Simo, J.C., Armero, F., Taylor, R.L., Improved version of assumed enhanced strain tri-linear elements for 3D finite deformation problems (1993) Comput. Methods Appl. Mech. Engrg., 110, pp. 359-386; Yuan, K.-Y., Wen, J.-C., Pian, T.H.H., A unified theory for formulation of hybrid stress membrane elements (1994) Int. J. Numer. Methods Engrg., 37, pp. 457-474

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