Mathematical programming approaches for the safety assessment of semirigid elastoplastic frames

Abstract

a b s t r a c tThis 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 statickinematic 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.

An MPEC approach for the critical post-collapse behavior of rigid-plastic structures

“…A conventional lumped plasticity model within a ''line'' finite element framework (e.g. Cocchetti and Maier, 2003;Tangaramvong and Tin-Loi, 2011) is adopted. Plasticity is thus accommodated through the traditional concept of the generalized plastic hinge model, for which the formation of such hinges is confined only to the member ends.…”

“…We have found that such reformulations are particularly effective for solving the MPECs that arise in engineering mechanics problems (e.g. Ferris and Tin-Loi, 2001;Tangaramvong and Tin-Loi, 2011). In the present work, we have adopted the socalled ''relaxation'' algorithm that performed remarkably well in solving block structures involving frictional contact (Ferris and Tin-Loi, 2001).…”

“…The elastoplastic Case c analyses were performed using the mathematical programming based stepwise holonomic algorithm described in Tangaramvong and Tin-Loi (2011).…”

Flexure and shear response of an impulsively loaded rigid-plastic beam by enhanced linear complementarity approach

“…Mathematical programming is seemingly one of the most natural formalisms in which to cast the skeletal structures for determining the extreme dynamic response 12 . It readily offers an ideal framework capable of finite element modeling of structures, and also provides considerable physical insights into the dynamic behavior of structures 13 – 18 .…”