Nonlinear analysis of plane frames using rigid body-spring discrete element method

摘要

Based on the rigid body-spring element discrete model, this paper presents the large displacement and elasticoplastic incremental formulation to analyze the ultimate load-carrying capacity of plane framed structures. A given structure is divided into a number of rigid body finite elements mutually connected by spring systems between elements. In such a discrete model, displacements of an element can be completely described by the rigid body motions of its centroid, while the deformation energy of the structure is stored only in the spring systems. The detailed tangential stiffness matrix for plane frames has been derived under a global coordinate system. The elastic-plastic spring coefficient matrix is also developed in terms of the elastic-plastic incremental theory and the internal force yielding interaction surface equation. An efficient numerical procedure is established by implementing the plastic hinge concept. The formulation has been applied to a variety of nonlinear problems of plane frames involving large displacements, large rotations but small strains and elastic-plasticity. Results obtained from this approach agree with independent analytical and other published finite element solutions. Numerical results show that the formulation is considerably effective and time saving.