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Contact between elastic bodies. III. Dual finite element analysis

Jaroslav Haslinger, Ivan Hlaváček (1981)

Aplikace matematiky

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.

Control variational method approach to bending and contact problems for Gao beam

Jitka Machalová, Horymír Netuka (2017)

Applications of Mathematics

This paper deals with a nonlinear beam model which was published by D. Y. Gao in 1996. It is considered either pure bending or a unilateral contact with elastic foundation, where the normal compliance condition is employed. Under additional assumptions on data, higher regularity of solution is proved. It enables us to transform the problem into a control variational problem. For basic types of boundary conditions, suitable transformations of the problem are derived. The control variational problem...

Convergence of an equilibrium finite element model for plane elastostatics

Ivan Hlaváček (1979)

Aplikace matematiky

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.

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