Numerical Analysis of Nonholonomic Elastoplastic Frames by Mathematical Programming

Abstract

The strength as well as the ductility of a structure may be estimated by performing an elastoplastic analysis. In such an analysis structural loading is incre- mentally applied through a proportional loading factor in accordance to a predefined loading pattern. During this process we have continuous plasticizations of various parts of the structure. For a more accurate description of the physical process, pos- sible deplasticizations should also be taken into account. Thus a nonholonomic ma- terial behavior should be followed. In this work such an analysis is performed in an efficient way. The basis of the approach is the formulation of the incremental prob- lem as a convex parametric quadratic programming (PQP) problem between two successive plastic hinges. The solution of this problem is done by assuming a ficti- tious load factor which establishes a search direction for the next plasticization. The true load factor is established when the plastic hinge that is closest to open really opens. An example of application, which serves as benchmark, is also included.