A series of problems in mechanics and physics are governed by the ordinary Poisson equation which demands linearity,isotropy,and material homo- geneity.In this paper a generalization with respect to nonlinearity,aniso...A series of problems in mechanics and physics are governed by the ordinary Poisson equation which demands linearity,isotropy,and material homo- geneity.In this paper a generalization with respect to nonlinearity,anisotropy,and inhomogeneity is made.Starting from the canonical basic equations in the primal and dual formulation respectively we derive systematically the corresponding generalized variational principles;under certain conditions they can be extended to so called complementary extremum principles allowing for global bounds.For simplicity a restriction to two dimensional problems is made,including twice-connected domains.展开更多
A nonlinear analysis of the energy consistency of multivariable finite elements based onincompatible trial functions is presented. The nonlinear forms of the convergence and opti-mization condition are set up. The rel...A nonlinear analysis of the energy consistency of multivariable finite elements based onincompatible trial functions is presented. The nonlinear forms of the convergence and opti-mization condition are set up. The relevant optimization approach for hybrid elements andthe optimal parameter matching is suggested and applied to the 3-dimensional problem ofelasticity.展开更多
文摘A series of problems in mechanics and physics are governed by the ordinary Poisson equation which demands linearity,isotropy,and material homo- geneity.In this paper a generalization with respect to nonlinearity,anisotropy,and inhomogeneity is made.Starting from the canonical basic equations in the primal and dual formulation respectively we derive systematically the corresponding generalized variational principles;under certain conditions they can be extended to so called complementary extremum principles allowing for global bounds.For simplicity a restriction to two dimensional problems is made,including twice-connected domains.
基金The work was undertaken with the support of the Alexader von Humboldt Foundation.
文摘A nonlinear analysis of the energy consistency of multivariable finite elements based onincompatible trial functions is presented. The nonlinear forms of the convergence and opti-mization condition are set up. The relevant optimization approach for hybrid elements andthe optimal parameter matching is suggested and applied to the 3-dimensional problem ofelasticity.
