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1999 (English)In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 178, no 1-2, p. 23-37Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

1999. Vol. 178, no 1-2, p. 23-37
##### Keywords [en]

Assumed strain, Euler-Lagrangian equation, Hu-Washizu variational principle, Mindlin-Reissner plate, Equations of motion, Finite element method, Strain, Stress analysis, Variational techniques, Alternative assumed strain (AAS) method, Structural analysis
##### National Category

Applied Mechanics
##### Identifiers

URN: urn:nbn:se:kth:diva-119538OAI: oai:DiVA.org:kth-119538DiVA, id: diva2:611575
#####

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##### Note

In this paper, an Alternative Assumed Strain (AAS) method is put forward, on the basis of a previous work. The method has two main features: the stresses are eliminated from the finite element formulation by satisfying the stress-strain equations with the assumed strains, which is much more convenient than the L2-orthogonal condition in Enhanced Assumed Strain (EAS) method for developing finite elements; the stresses, obtained from the assumed strains with the stress-strain relations, are forced to satisfy the equilibrium equations identically to reduce the number of assumed strain parameters and to improve finite element efficiency. The method is applied to develop several variations of 3-node triangular and 4-node quadrilateral Mindlin plate elements. Numerical examples show that efficient elements could be obtained from the suggested method.

References: Bathe, K.J., Dvorkin, E.N., A four node plate bending element based on mindlin reissner plate theory and a mixed interpolation (1985) Int. J. Num. Meth. Engng, 21, pp. 367-383; Simo, J.C., Rifai, M.S., A class of mixed assumed strain methods and the method of incompatible modes (1990) Int. J. Num. Meth. Engng., 29; Simo, J.C., Armero, F., Geometrically nonlinear enhanced mixed methods and the method of incompatible modes (1992) Int. J. Num. Meth. Engng, 33, pp. 1413-1449; 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; Militello, C., Felippa, C.A., A variational justification of the assumed natural strain formulation of finite elements - I. variational principles II. the C0 four-node plate element (1990) Computers & Structures, 34, pp. 439-444; Bathe, K.J., (1996) Finite Element Procedures, , Englewood, NJ: Prentice Hall; Argyris, J.H., 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., 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. Engng., 145, pp. 11-85; Korelc, J., (1996) Symbolic Approach in Computational Mechanics and Its Application to the Enhanced Strain Method, , Ph. D. dissertation, Darmstadt; Luo, Y.-H., Field consistence method with application to the development of finite element (1997) NACM X, , Tallinn; Luo, Y.-H., (1997) On Shear Locking in Finite Elements, , Licentiate thesis, Stockholm; Luo, Y.-H., Explanation and elimination of shear locking and membrane locking with field consistence approach (1998) Comput. Methods Appl. Mech. Engrg., 162, pp. 249-269; Luo, Y.-H., Eriksson, A., Extension of field consistence approach into developing plane stress elements (1998) Accepted by Comput. Methods Appl. Mech. Engrg.; Reissner, E., The effect of transverse shear deformation on the bending of elastic plates (1945) Journal of Applied Mechanics, 67, pp. 69-A77; Mindlin, R.D., Influence of rotary inertia and shear on flexural motion of isotropic elastic plates (1951) Journal of Applied Mechanics, 18, pp. 31-38; Luo, Y.-H., A technique for reducing finite element sensitivity to geometric distortion (1998) Manuscript Submitted to Computers and Structures; Timoshenko, S., (1940) Theory of Plates and Shells, , New York: McGraw-Hill; Hughes, T.J.R., Tezduyar, T.E., Finite elements based upon Mindlin plate theory with particular reference to the four-node bilinear isoparametric element (1981) Journal of Applied Mechanics, 48, pp. 587-595

Available from: 2013-03-18 Created: 2013-03-18 Last updated: 2017-12-06Bibliographically approved
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