×

Dual analysis by a meshless method. (English) Zbl 1073.74641

Summary: A meshless method to solve elastostatic problems based on an equilibrium model is presented. This means that the equilibrium and constitutive equations are satisfied a priori, and that the approximation only concerns the compatibility equations. The application of this method together with the classical displacement meshless method leads to upper and lower bounds on the energy. The difference between these bounds gives a global error estimation on the solution.

MSC:

74S30 Other numerical methods in solid mechanics (MSC2010)
74B05 Classical linear elasticity
Full Text: DOI

References:

[1] Fraeijs de Veubeke, AGARDograph 72: Matrix Methods of Structural Analysis pp 165– (1963) · Zbl 0139.20302
[2] Fraeijs de Veubeke, Stress Analysis pp 145– (1965) · Zbl 0122.00205
[3] Debongnie, Dual analysis with general boundary conditions, Computer Methods in Applied Mechanics and Engineering 122 pp 183– (1995) · Zbl 0851.73057
[4] Belytschko, Element-free Galerkin methods, International Journal for Numerical Methods in Engineering 37 pp 229– (1994) · Zbl 0796.73077
[5] Fraeijs de Veubeke, Strain-energy bounds in finite-element analysis by slab analogy, Journal of Strain Analysis 2 (4) pp 265– (1967)
[6] Gallagher RH Dhalla AK Direct flexibility finite element elastoplastic analysis 1971 443 462
[7] Vallabhan, A finite element model for plane elasticity problems using the complementary energy theorem, International Journal for Numerical Methods in Engineering 18 pp 291– (1982) · Zbl 0473.73074
[8] Sarigul, Assumed stress function finite element method: two-dimensional elasticity, International Journal for Numerical Methods in Engineering 28 pp 1577– (1989) · Zbl 0724.73218
[9] Timoshenko, Theory of Elasticity (1987)
[10] Zhong HG Estimateurs d’erreur a posteriori et adaptation de maillages dans la méthode des éléments finis 1991
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.