Mathematical programming approaches for the safety assessment of semirigid elastoplastic frames

• Published in: International journal of solids and structures Vol. 48; no. 6; pp. 1011 - 1023
• Main Authors: Tangaramvong, S., Tin-Loi, F.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 15.03.2011; Elsevier
• Subjects: Algorithms; Assessments; Complementarity; Elastoplastic analysis; Elastoplasticity; Exact sciences and technology; Fracture mechanics (crack, fatigue, damage...); Fundamental areas of phenomenology (including applications); Inelasticity (thermoplasticity, viscoplasticity...); Limit analysis; Limit load; Mathematical analysis; Mathematical models; Mathematical programming; Nonlinearity; Physics; Safety assessment; Semirigid connections; Solid mechanics; Structural and continuum mechanics; Elastoplastic analysis; Limit analysis; Complementarity; Semirigid connections; Safety assessment; Mathematical programming; Non linear material; Ductility; Stress strain relation; Yield criterion; Iterative method; Quasi static theory; Complementarity problem; Optimization; Predictor corrector method; Inelasticity; Elastoplasticity; Kinematics; Multiplier; Path independent; Mixed problem; Safety; Non linear effect; Ultimate load
• ISSN: 0020-7683; 1879-2146
• DOI: 10.1016/j.ijsolstr.2010.12.003

This paper presents two complementary mathematical programming based approaches for the accurate safety assessment of semirigid elastoplastic frames under quasistatic loads. The inelastic behavior of the flexible connections and material plasticity are accommodated through piecewise linearized nonlinear yield surfaces. As is necessary for this class of structures, geometric nonlinearity is taken into account. Moreover, only a 2nd-order geometric approximation is included as this is sufficiently accurate for practical structures. The work described has a twofold contribution. First, we develop an algorithm that can robustly and efficiently process the complete (path-dependent) nonholonomic response of the structure in a stepwise (path-independent) holonomic fashion. The governing formulation is cast in mixed static-kinematic variables and leads naturally to what is known in the mathematical programming literature as a mixed complementarity problem (MCP). The novelty of the proposed algorithm is that it processes the MCP directly without using some iterative (and often cumbersome) predictor–corrector procedure. Second, in the spirit of simplified analyses, the classical limit analysis approach is extended to compute the limit load multiplier under the simultaneous influence of joint flexibility, material and geometric nonlinearities, and limited ductility. Our formulation is an instance of the challenging class of optimization problems known as a mathematical program with equilibrium constraints (MPEC). Various nonlinear programming based algorithms are proposed to solve the MPEC. Finally, four numerical examples, concerning practical structures and benchmark cases, are provided to illustrate application of the analyses as well as to validate the accuracy and robustness of the proposed schemes.