Analysis of Steel Frames with Geometric and Material Nonlinearities: MP Approach

Abstract

A very significant problem in an analysis of engineering structures is when displacements become exceedingly large. After deformation, and in addition to the well known geometric effects, a structure may remain elastic or develop plasticity. A combination of geometric and material nonlinearities needs to be accounted for. This paper presents governing equations and a systematic approach to nonlinear analysis of steel frames based on mathematical programming (MP) techniques. The basic relations of statics, kinematics and material constitutive laws are derived using the concept of fictitious forces and deformations. These formulations are then used to develop the corresponding incremental descriptions. As a result, the overall governing system can be formulated as a standard,systematic matrix format of a nonlinear complementarity problem (NCP). A special treatment is made to reformulate the NCP as a stepwise linear complementarity problem. The formulation is suitable for discretised frame structures under any combination of piecewise proportional load paths. The effect of partial-strength joint between beam and column are also incorporated in the mathematical formulation. The basic features of the computational algorithms will be briefly described for incremental analysis of structures subjected to monotonic and cyclic loading. Numerical examples are given to illustrate the application of the proposed approach. The incremental analysis steps are necessary for numerical stability especially when dealing with nonlinearities and plastic irreversibilites.