A force method for elastic-plastic analysis of frames by quadratic optimization (Q1094211)

A numerical method for the analysis of elastoplastic planar frames is developed on the basis of a minimum principle in finite increments of stresses and plastic factors. Local elastic unloading and plastic admissibility of final stresses are considered in this theoretical formulation, avoiding additional iterative procedures. Since all possible stress distributions can be represented exactly, only an interpolation of plastic multiplier fields is required to transform the formulation in the functional space into a problem with a finite number of variables. Plastic admissibility for any section along a beam element is substituted by a finite number of contraints. The interpretation of this approximation is used to choose appropriate interpolation bases. The resulting discrete version of the principle is a quadratic optimization problem solved in this work by dualization, condensation to a problem in plastic factors only, and application of Lemke's algorithm. The advantages of the force method when compared with kinematical approaches for planar frames are discussed and demonstrated by examples.