An equilibrium finite element method in three-dimensional elasticity

Michal Křížek

Displaying similar documents to “An equilibrium finite element method in three-dimensional elasticity”

Convergence of an equilibrium finite element model for plane elastostatics

Ivan Hlaváček (1979)

Aplikace matematiky

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An equilibrium triangular block-element, proposed by Watwood and Hartz, is subjected to an analysis and its approximability property is proved. If the solution is regular enough, a quasi-optimal error estimate follows for the dual approximation to the mixed boundary value problem of elasticity (based on Castigliano's principle). The convergence is proved even in a general case, when the solution is not regular.

Dual finite element analysis for contact problem of elastic bodies with an enlarging contact zone

Van Bon Tran (1986)

Aplikace matematiky

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Dual finite element analysis of the contact problem of two elastic bodies with an enlarging contact zone is presented. Approximations of the solution are defined on two types of triangulations by piecewise constant stress fields. Convergence is proved in both cases.

Contact between elastic bodies. III. Dual finite element analysis

Jaroslav Haslinger, Ivan Hlaváček (1981)

Aplikace matematiky

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The problem of a unilateral contact between elastic bodies with an apriori bounded contact zone is formulated in terms of stresses via the principle of complementary energy. Approximations are defined by means of self-equilibriated triangular block-elements and an $L 2$ -error estimate is proven provided the exact solution is regular enough.

Contact between elastic perfectly plastic bodies

Jaroslav Haslinger, Ivan Hlaváček (1982)

Aplikace matematiky

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If the material of the bodies is elastic perfectly plastic, obeying the Hencky's law, the formulation in terms of stresses is more suitable than that in displacements. The Haar-Kármán principle is first extended to the case of a unilateral contact between two bodies without friction. Approximations are proposed by means of piecewise constant triangular finite elements. Convergence of the method is proved for any regular family of triangulations.