Abstract
An unified and effective method, which enable one to trace the elasto-plastic; finite deformation behaviors and to evaluate the so-called shake-down limits considered on the geometrical non-linearity, of structures subjected to repeated variable loads, is presented. It is assumed that the domain of the variable loads is given as a hyperpolyhedron and the instantaneous loads move arbitrarily inside the prescribed load domain during the loading time. Likewise, the domains of the the response displacements, strains and stresses of the structures under the above loading are also supposed to be the hyperpolyhedra, vertex of which are the extreme responses corresponding to those of the polyhedric load domain, respectively. Under these assumptions, basic equations governing the relations between the parameter: P^* (which denotes the magnitude of the load domain) and each of the extreme responses, are derived, in which the well-established total Lagrangian formulation is employed to introduce the finite de-formation effects. Elasto-plastic, finite deformation analyses of the plane truss structure composed of 11 members are performed, and show that the present approach might be very advantageous and effective for investigating the plastic-collapse behavior of structures and structural elements, such as offshore structures, under repeated variable loading.
