Simultaneous ultimate load and deformation analysis of strain softening frames under combined stresses

• Published in: Engineering structures Vol. 30; no. 3; pp. 664 - 674
• Main Authors: Tangaramvong, S., Tin-Loi, F.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Ltd 01.03.2008; Elsevier
• Subjects: Applied sciences; Buildings. Public works; Combined stresses; Complementarity; Computation methods. Tables. Charts; Elastoplastic analysis, Holonomic behavior; Exact sciences and technology; Frames; Strain softening; Structural analysis. Stresses; Ultimate load; Elastoplastic analysis, Holonomic behavior; Frames; Complementarity; Strain softening; Combined stresses; Ultimate load; Structural design; Holonomic system; Stress strain relation; Frames; Ultimate load; Strain softening; Combined stresses; Elastoplastic analysis; Complementarity problem; Modeling; Frame structure; Holonomic behavior; Complementarity; Example; Elastoplastic analysis; Structural analysis
• ISSN: 0141-0296; 1873-7323
• DOI: 10.1016/j.engstruct.2007.05.014

This paper presents a method for carrying out, in a single step, an elastoplastic analysis to obtain simultaneously both the ultimate load and corresponding deformation of a strain softening structure. The effect of combined bending moment and axial force is also accounted for in the piecewise linearized softening yield condition. However, a monotonic loading process is assumed within a small displacement framework. We propose a mathematical programming approach to tackle this problem. In particular, the formulation leads to an instance of the challenging class of a so-called “mathematical program with equilibrium constraints” (MPEC). Various nonlinear programming based algorithms are proposed to solve the MPEC. Numerical examples are provided to illustrate the described analysis and also to highlight the effects of constitutive local softening instability and of axial forces on the overall structural behavior of the frames.