This thesis presents a series of integrated computation-orientated methods using mathematical programming (MP) approaches to carry out, in the presence of simultaneous material and geometric nonlinearities, the realistic analysis of skeletal structures that exhibit softening and limited ductility. In particular, four approaches are developed. First, the entire structural behavior is traced by using the nonholo-nomic (path-dependent) elastoplastic analysis. Second, the stepwise holonomic anal-ysis approximates the actual nonholonomic behavior by using a series of holonomic counterparts. Third, the more tractable holonomic (path-independent) analysis is implemented to approximate the overall nonholonomic response. Finally, classical limit analysis is extended to cater for this class structures; the aim is to compute in a single step ultimate load and corresponding deformations, simultaneously. The nonholonomic, stepwise holonomic and holonomic state formulations are developed as special instances of the well-known MP problem known as a mixed complementarity problem (MCP). Geometric nonlinearity is tackled via two alternative approaches, namely one that can cater for arbitrarily large deformations and the second for 2nd-order geometry effects only. The effects of combined bending and axial forces are included through a (hexagonal) piecewise linear yield locus that can accommodate either perfect plasticity or isotropic softening or hardening. The extended limit analysis problem is formulated as an instance of the challenging class of so-called mathematical programs with equilibrium constraints (MPECs). Two classes of solution approaches, namely nonlinear programming (NLP) based approaches and an equation based smoothing approach, are proposed to solve the MPEC. A number of numerical examples are provided to validate the robustness and efficiency of all proposed methods, and to illustrate some key mechanical features expected of realistic frames that exhibit local softening behavior.

This thesis presents a series of integrated computation-orientated methods using mathematical programming (MP) approaches to carry out, in the presence of simultaneous material and geometric nonlinearities, the realistic analysis of skeletal structures that exhibit softening and limited ductility. In particular, four approaches are developed. First, the entire structural behavior is traced by using the nonholo-nomic (path-dependent) elastoplastic analysis. Second, the stepwise holonomic anal-ysis approximates the actual nonholonomic behavior by using a series of holonomic counterparts. Third, the more tractable holonomic (path-independent) analysis is implemented to approximate the overall nonholonomic response. Finally, classical limit analysis is extended to cater for this class structures; the aim is to compute in a single step ultimate load and corresponding deformations, simultaneously. The nonholonomic, stepwise holonomic and holonomic state formulations are developed as special instances of the well-known MP problem known as a mixed complementarity problem (MCP). Geometric nonlinearity is tackled via two alternative approaches, namely one that can cater for arbitrarily large deformations and the second for 2nd-order geometry effects only. The effects of combined bending and axial forces are included through a (hexagonal) piecewise linear yield locus that can accommodate either perfect plasticity or isotropic softening or hardening. The extended limit analysis problem is formulated as an instance of the challenging class of so-called mathematical programs with equilibrium constraints (MPECs). Two classes of solution approaches, namely nonlinear programming (NLP) based approaches and an equation based smoothing approach, are proposed to solve the MPEC. A number of numerical examples are provided to validate the robustness and efficiency of all proposed methods, and to illustrate some key mechanical features expected of realistic frames that exhibit local softening behavior.