×

Assumed strain formulation for triangular \(C^ 0\) plate elements based on a weak form of the Kirchhoff constraints. (English) Zbl 0717.73067

Summary: Application of a weak form of the Kirchhoff constraints in the formulation of triangular assumed shear strain \(C^ 0\) plate element is described. It is shown that, compared to a similar formulation of the quadrilateral elements, formulation of the triangles requires some additional considerations which lead to additional terms in the energy expression. With those terms performance of the assumed shear strain triangular elements is comparable to that of the quadrilateral elements.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74K20 Plates
Full Text: DOI

References:

[1] Argyris, Ing. Archiv 35 pp 102– (1966)
[2] Bathe, Int. j. numer. methods eng. 22 pp 667– (1986)
[3] Belytschko, Int. j. numer. methods eng. 20 pp 787– (1984)
[4] Carpenter, Comp. Struct. 22 pp 39– (1986)
[5] Criesfield, Comp. Struct. 18 pp 833– (1984)
[6] Donea, Comp. Methods Appl. Mech. Eng. 63 pp 183– (1987)
[7] Dvorkin, Eng. Comp. 1 pp 77– (1984)
[8] Fried, Comp. Methods Appl. Mech. Eng. 56 pp 283– (1986)
[9] Hinton, Comp. Struct. 23 pp 409– (1986)
[10] Huang, Comp. Struct. 25 pp 147– (1987)
[11] Hughes, Comp. Struct. 9 pp 445– (1978)
[12] and , The linear triangular bending element, Proc. MAFELAP Conference, Brunel University, 1981.
[13] Hughes, J. Appl. Mech. 48 pp 587– (1981)
[14] Hughes, Nucl. Eng. Des. 46 pp 203– (1978)
[15] Jang, Int. j. numer. methods eng. 12 pp 2389– (1988)
[16] Jang, Int. j. numer. methods eng. 26 pp 329– (1988)
[17] MacNeal, Nucl. Eng. Des. 70 pp 3– (1982)
[18] ’A flat triangular shell element stiffness matrix’, Proc. First Conf. on Matrix Methods in Structural Mechanics, Wright-Paterson Air Force Base, Ohio, 1965.
[19] ’The integrated bending field finite element for thick and layered plates’, Sixth ASCE Eng. Mech. Div. Spec. Conf., State University of New York at Buffalo, May 1987.
[20] Park, J. Appl: Mech. 53 pp 278– (1986)
[21] Rhiu, Int. j. numer. methods eng. 24 pp 581– (1987)
[22] Simo, J. Appl. Mech. 53 pp 51– (1986)
[23] Somashekar, Comp. Struct. 25 pp 345– (1987)
[24] Stolarski, Comp. Methods Appl. Mech. Eng. 58 pp 249– (1986)
[25] Stolarski, Comp. Methods Appl. Mech. Eng. 58 pp 265– (1986)
[26] Stolarski, Int. j. numer. methods eng. 26 pp 913– (1988)
[27] Stolarski, European J. Mech. Solids
[28] Stolarski, J. Struct. Mech. 11 pp 153– (1983) · doi:10.1080/03601218308907439
[29] Stolarski, Comp. Methods Appl. Mech. Eng. 50 pp 121– (1985)
[30] Tessler, Comp. Methods Appl. Mech. Eng. 50 pp 71– (1985)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.