Numerical solution of large deformation problems involving stability and unilateral constraints

Abstract

The present study is concerned with the numerical treatment of large deformation beam problems where stability as well as post-buckling behaviour is coupled with frictional contact constraints. The flexible beams are described according to a nonlinear rod-type theory which accounts for both finite rotations and large deformations. The contact conditions are introduced via a penalty function method. From these conditions we obtain a linear complementary problem (LCP) resulting from the variational inequality formulation. For the examination of the post-buckling behaviour the displacement control method is applied. Particular attention is paid to the development of the linear complementary problem combining with the computational strategy for tracing limit points. Finally, the modification algorithms of the linear complementary problem, in which the penalty factors have been eliminated, are proposed. The numerical techniques not only allow some limit points to be passed, but also guarantee the computational stability characteristics during the Newton-Raphson's iterative process. Numerical examples are presented that illustrate the performances of the proposed algorithms.