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Assumed stress function finite element method: Two-dimensional elasticity. (English) Zbl 0724.73218

Summary: A complementary energy-based finite element formulation, using assumed stress functions as the approximating functions, is developed for the linear elastic two-dimensional stress analysis. It features the use of blending function interpolants, enabling the convenient representation of traction boundary conditions, which in the past have posed difficulties. A family of rectangular elements is constructed. Numerical results assessing the behaviour of these elements are presented. An advantage of this approach is in the accurate prediction of stress distributions.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74B10 Linear elasticity with initial stresses
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[1] and , Energy Theorems and Structural Analysis, Butterworths, London, 1960.
[2] and , ’Direct flexibility finite element elastoplastic analysis’. SMIRT, 1972, 444-462.
[3] Rybicki, AIAA J. 8 pp 1805– (1969)
[4] Belytschko, J. Eng. Mech. Div. ASCE 96 pp 931– (1970)
[5] Anderheggen, J. Eng. Mech. Div. ASCE 95 pp 841– (1969)
[6] ’Upper and lower bounds in matrix structural analysis’, in (ed.), Matrix Methods of Structural Analysis, MacMillan, New York, 1964, pp. 165-201.
[7] Fraeijs de Veubeke, J. Franklin Inst. 302 pp 389– (1976)
[8] Watwood, Int. J. Solids Struct. 4 pp 857– (1968)
[9] and , ’Complementary energy with penalty functions in finite element analysis’, in et al. (eds.), Energy Methods in Finite Element Analysis, Wiley, New York, 1979, Chapter 8, pp. 154-174.
[10] ’Dual formations of linear elasticity using finite elements’, in (ed.), Computer Aided Engineering, University of Waterloo, 1971.
[11] Elias, J. Eng. Mech. Div. ASCE 94 pp 931– (1968)
[12] Finite Element Analysis: Fundamentals, Prentice-Hall, Englewood Cliffs, New Jersey, 1975.
[13] Michell, Proc. London Math. Soc. XXXI pp 100– (1899)
[14] Michell, Proc. London Math. Soc. XXXI pp 130– (1899)
[15] Truesdell, Archive Rat. Mech. Anal. 4 pp 1– (1960)
[16] Fraeijs de Veubeke, J. Strain Anal. 2 pp 265– (1967)
[17] Harvey, Int. j. numer. methods eng. 19 pp 971– (1983)
[18] Vallabhan, Int. j. numer. methods eng. 18 pp 291– (1982)
[19] and , ’Single domain equilibrium approximations in two dimensional elasticity’. Proc. 3rd Int. Conf. in Australia on FEM, 1979, 101-103.
[20] Tabarrok, Int. j. numer. methods eng. 5 pp 532– (1972)
[21] Sundararajan, Int. j. numer. methods eng. 15 pp 343– (1980)
[22] ’Assumed stress function finite element method’. University of Arizona, Tucson, AZ, 1984.
[23] ’Surfaces for computer aided design of space forms’, Project MAC, Design Division, Department of Mechanical Engineering, MIT, 1964.
[24] Gordon, SIAM J. Numer. Anal. 8 pp 158– (1971)
[25] Gordon, Numer. Math. 21 pp 109– (1973)
[26] Gordon, Int. j. numer. methods eng. 7 pp 461– (1973)
[27] Marshall, J. Inst. Math. Appl. 12 pp 355– (1973)
[28] Frey, J. Inst. Math. Appl. 20 pp 191– (1977)
[29] Hall, J. Inst. Math. Appl. 21 pp 237– (1978)
[30] Hall, J. Math. Mech. 19 pp 1– (1969)
[31] Cavendish, Int. j. numer. methods eng. 20 pp 241– (1984)
[32] , and , ’Triangular elements in plate bending–Conforming and non-conforming solutions’. Proc. Conf. on Matrix Methods in Structural Mechanics., Dayton, Ohio, AFFDL 66280, 1965, 547-576.
[33] Wood, Int. j. numer. methods eng. 26 pp 489– (1988)
[34] and , Theory of Elasticity, 3rd edn, McGraw-Hill, New York, 1970, pp. 258-261.
[35] and , Graphics-oriented Interactive Finite-Element Time-sharing System GIFTS 5, University of Arizona, Tueson, AZ, 1984.
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