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 of<br />inelastic frame structures. The convected material frame approach is a modification of the co-rotational<br />approximation by incorporating an adaptive convected material frame in the basic definition of the<br />displacement vector and strain tensor. In the formulation, each discrete element is associated with a local<br />coordinate system that rotates and translates with the element. For each load increment, the corresponding<br />strain-displacement and nodal force-stress relationships are defined in the updated local coordinates, and<br />based on the updated element geometry. The rigid body motion and deformation displacements are<br />decoupled for each increment. This modified approach incorporates the geometrical nonlinearities through<br />the continuous updating of the material frame geometry. A generalized nonlinear function is used to<br />derive the inelastic constitutive relation and the kinematic hardening is considered. The equation of<br />motion is integrated by an explicit procedure and it involves only vector assemblage and vector storage in<br />the analysis by assuming a lumped mass matrix of diagonal form. Several numerical examples are<br />demonstrated in close agreement with the solutions obtained by the ANSYS code. Numerical studies show<br />that the proposed approach is capable of investigating large deflection of inelastic planar structures and<br />providing an excellent numerical performance.