Large displacement analysis of inelastic frame structures by convected meterial frame approach

This paper presents the convected material frame approach to study the nonlinear behavior ofinelastic frame structures. The convected material frame approach is a modification of the co-rotationalapproximation by incorporating an adaptive convected material frame in the basic definition of thedisplacement vector and strain tensor. In the formulation, each discrete element is associated with a localcoordinate system that rotates and translates with the element. For each load increment, the correspondingstrain-displacement and nodal force-stress relationships are defined in the updated local coordinates, andbased on the updated element geometry. The rigid body motion and deformation displacements aredecoupled for each increment. This modified approach incorporates the geometrical nonlinearities throughthe continuous updating of the material frame geometry. A generalized nonlinear function is used toderive the inelastic constitutive relation and the kinematic hardening is considered. The equation ofmotion is integrated by an explicit procedure and it involves only vector assemblage and vector storage inthe analysis by assuming a lumped mass matrix of diagonal form. Several numerical examples aredemonstrated in close agreement with the solutions obtained by the ANSYS code. Numerical studies showthat the proposed approach is capable of investigating large deflection of inelastic planar structures andproviding an excellent numerical performance.