Lower Bound Limit Analysis of Plane Stress Problems by a Finite Element Method

摘要

In a recent paper, Hayes and Marcel developed a finite element method for determining upper bounds on the limit load for perfectly plastic plane stress problems. By means of a finite element technique, they constructed a parametric family of kinematically admissible velocity fields and then obtained a best upper bound by minimizing the associated load multiplier. The present paper describes a complementary method for finding the lower bound on the limit load for plane stress problems. In this case, the finite element technique is used to construct a parametric family of equilibrium stress fields. The determination of the best lower bound then becomes a problem of mathematical programming; the maximization of the objective function, the load multiplier, subject to the constraint that the yield condition not be violated. The lower bound method and an upper bound method similar to that of Hayes and Marcal were coded as FORTRAN IV programs and results were obtained for a number of problems.