NONLINEAR-ANALYSIS OF SEMIRIGID FRAMES - A PARAMETRIC COMPLEMENTARITYAPPROACH

The nonlinear elastoplastic analysis of plane frames with semirigid co nnections is performed using a mathematical programming approach. A La grangian formulation suitable for any order analysis is first derived for a suitably discretized structural system through the three basic r elations of statics, kinematics, and the elastoplastic constitutive la w. Particular features of this formulation include the preservation of static-kinematic duality through the concept of fictitious forces and deformations, the use of a powerful class of piecewise linearized con stitutive laws to model plasticity conditions in general and semirigid ity in particular, and an exact governing description for the two-dime nsional case which can be specialized to any order of geometrical nonl inearity. Specific consideration is then given to a simple, essentiall y second-order case since it can model sufficiently accurately the beh aviour of most real frames. Whilst the particular mathematical program ming problem takes the form of a parametric nonlinear complementarity problem involving reversible or holonomic laws, the proposed numerical algorithm which is based on an iterative adaptation of the Wolfe-Mark owitz method can accommodate irreversible or nonholonomic phenomena. T he scheme can trace a complete skeleton equilibrium path beyond any cr itical point by capturing only events involving hinge activation or un loading. Numerical examples are presented to illustrate and validate t he accuracy of the approach.