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EAS-elements for two-dimensional, three-dimensional, plate and shell structures and their equivalence to HR-elements. (English) Zbl 0772.73071
Summary: The enhanced assumed strain (EAS) method, recently proposed by J. C. Simo and M. S. Rifai [Int. J. Numer. Methods Eng. 29, No. 8, 1595- 1638 (1990; Zbl 0724.73222)], is used to develop new four-node membrane, plate and shell elements and eight-node solid elements. The equivalence of certain EAS-elements with Hellinger-Reissner (HR) elements is discussed. For instance, the seven-parameter element EAS-7 with \(2\times 2\) integration is identical to the HR-element of T. H. H. Pian and K. Sumihara [Int. J. Numer. Methods Eng. 20, 1685-1695 (1984; Zbl 0544.73095)]. Eight-node solid elements which are free of volumetric locking and four-node shell elements which have an improved membrane and bending behaviour, compared to the Bathe-Dvorkin shell element [E. N. Dvorkin and K. J. Bathe, Eng. Comp. 1, 77-88 (1984)], are introduced. Numerical tests for linear elastic problems show an improved performance of the EAS-elements.

MSC:
74S05 Finite element methods applied to problems in solid mechanics
74K20 Plates
74K15 Membranes
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[1] Lee, Int. j. numer. methods eng. 21 pp 1629– (1986)
[2] Pian, Int. j. numer. methods eng. 20 pp 1685– (1984)
[3] Pian, Int. j. numer. methods eng. 22 pp 173– (1986)
[4] Pian, Int. j. numer. methods eng. 26 pp 2331– (1988)
[5] Rhiu, Int. j. numer. methods eng. 24 pp 581– (1987)
[6] Saleeb, Comp. Struct. 26 pp 787– (1987)
[7] Dvorkin, Eng. Comp. 1 pp 77– (1984)
[8] Huang, Int. j. numer. methods eng. 22 pp 73– (1986)
[9] Hughes, J. Appl. Mech. 48 pp 587– (1981)
[10] MacNeal, Nucl. Eng. Des. 70 pp 3– (1982)
[11] Parks, J. Appl. Mech. 53 pp 278– (1986)
[12] Simo, J. Appl. Mech. 53 pp 51– (1986)
[13] Simo, Int. j. numer. methods eng. 29 pp 1595– (1990)
[14] , and , ’Triangular elements in plate bending-conforming and nonconforming solutions’, Proc. 1st Conf. Matrix Methods in Structural Mechanics, Wright-Patterson ATBFB, Ohio, 1965.
[15] Taylor, Int. j. numer. methods eng. 10 pp 1211– (1976)
[16] , and , ’Incompatible displacement models’, in: et al., (eds.), Numerical and Computational Methods in Structural Mechanics Academic Press, London, pp. 43-57, 1973.
[17] Wu, Comp. Struct. 27 pp 639– (1987)
[18] Ahmad, Int, j. numer. methods eng. 2 pp 419– (1970)
[19] Liu, Comp. Methods Appl. Mech. Eng. 55 pp 259– (1986)
[20] and , ’2D- and 3D-enhanced assumed strain elements and their application in plasticity’, in: and (eds.), Proc. 3rd Int. Conference on Computational Plasticity, Fundamentals and Applications, Barcelona, April 1992, Pineridge Press, Swansea, 1992.
[21] ’Displacement and equilibrium models in the finite element method’, in: and (eds.), Stress Analysis Wiley, London, 1965.
[22] and , The Finite Element Method, 4th edn., Vol. 1, McGraw-Hill, London, 1989.
[23] Wang, Int. j. numer. methods eng. 28 pp 2223– (1989)
[24] Simo, Comp. Methods Appl. Mech. Eng. 73 pp 53– (1989)
[25] ’Untersuchungen zur Zuverlässigkeit hybrid-gemischter Finiter Elemente für Flächentragwerke’, Dissertation, Institut für Baustatik, Universität Stuttgart, 1991.
[26] and , Theory of Plates and Shells, 2nd edn., McGraw-Hill, New York, 1970.
[27] ’Skew Plates and Structures’; Pergamon Press, Oxford, 1963. · Zbl 0124.17704
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