Stress-Based Finite Element Methods in Linear and Nonlinear Solid Mechanics

摘要

A comparison of stress-based finite element methods is given for the prototype problem of linear elasticity and then extended to finite-strain hyperelasticity. Of particular interest is the accuracy of traction forces in reasonable Sobolev norms with an emphasis on uniform approximation behavior in the incompressible limit. The mixed formulation of Hellinger-Reissner type leading to a saddle-point problem as well as a first-order system least-squares approach are investigated and the strong connections between these two methods are studied. In addition, we also discuss stress reconstruction techniques based on displacement approximations by nonconforming finite elements.