Abstract
In this paper, we describe the development of nonlinear analysis capabilities in our general-purpose finite element program, VAST, for combined geometrically and materially nonlinear analyses of shell and beam structures. This development is based on a co-rotational formulation, in which the total displacement field is divided into two parts. The first part corresponds to the rigid body motion and fully characterizes the geometric nonlinearity in the problem, whereas the second part represents the pure relative deformation and is solely involved in the constitutive relations. Because the co-rotational strain and stress measures adopted in this formulation meet the requirement of computational objectivity, the inclusion of nonlinear material models becomes relatively easy. In this study, the commonly used J2-flow theory of plasticity is considered. Various numerical integration algorithms for integrating the rate-type constitutive relations have been included along with the corresponding consistent tangent moduli. Mixed isotropic and kinematic strain hardening can also be characterized. To handle structural instabilities in general nonlinear analyses, a group of advanced solution strategies for nonlinear finite element systems have been implemented. Extensive numerical experiments have been conducted for verification purposes, and the accuracy and robustness of the current approach have been demonstrated.
