Elastic-Plastic Torsion of Multiply-Connected Cylinders by Quadratic Programming

摘要

A numerical method for solving the problem of elastic/perfectly-plastic torsion of a cylinder of general shape is presented. The method applies finite elements and a minimum rate principle of plasticity to provide a complete history of stress function during a quasi-static, monotonically increasing angle of twist. In particular, the method exhibits the plastic unloading phenomenon which occurs for some hollow cylinders. For the chosen finite element representation, the minimum principle reduces to a problem in quadratic programming. Results are presented for both simply and multiply-connected cylinders and are compared to other available results. It is shown that for the problems which were analyzed plastic unloading occurs in areas of high stress concentration only after the value of the stress function on the inside boundary has essentially reached its maximum. (Author)