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

Sarigul, Nesrin; Gallagher, Richard H.

Int. J. Numer. Methods Eng. 28, No. 7, 1577-1598 (1989).

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

Keywords:

complementary energy-based finite element formulation; blending function interpolants; traction boundary conditions; family of rectangular elements

References:

[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.