Elastoplastic dynamics of skeletal structures by mathematical programming
The thesis is concerned with investigating the role of mathematical programming in expressing the general theory of and facilitating effective computation for elasto-plastic skeletal structures subjected to deterministic sources of dynamic excitations, Static-kinematic duality, a common feature in the static analysis of structures, is extended to dynamic systems through the adoption of d'Alembert's principle. This allows the full use of graph theoretic methods for describing the fundamental structural relations in both mesh and nodal forms. For structures whose dynamic characteristics can be effectively described by a rigid-plastic constitutive law, mathematical programming formulations are presented. They are compared and contrasted with existing formulations, especially those associated with impact loading. Elasto-plastic structures are studied and their dynamic response is shown to be given by the solution of a differential linear complementarity problem. Four equivalent formulations are presented and are solved numerically through the use of direct integration methods. The effects of change of geometry may also be important in the dynamic analysis of structures. Firstly, for relatively small displacements, the method of fictitious forces is shown to lead to alternative mesh and nodal formulations. For large displacements, only the nodal method proves to be effective. An incremental differential linear complementarity problem is obtained and a suitable numerical solution procedure is proposed. Finally, a perturbation technique is established for solving the resulting differential equations and differential linear complementarity problems. It is proved that this technique is more general and flexible than the direct integration methods.