Yield Point Load for Plates (Limit Analysis, Collapse).

Abstract

The determination of upper bounds on the yield point loads of thin plates is considered. The basic equations based on the assumptions of the conventional thin plate engineering theory are presented together with a yield criterion based on the Frobenius norm of a matrix. The field equations are classified according to the admissibility of discontinuities in the field quantities. A variational principle producing lower and upper bound formulations for the yield point load for plates is discussed with careful consideration of the boundary conditions. Least upper bounds are searched by utilizing a series representation of the velocity field. An iterative algorithm for the minimization problem is applied in connection with a special scheme of subspace iteration. The procedure is successfully tested on a beam and various circular plate problems. New solutions for simply supported and clamped rectangular plates are presented both for plates obeying the new yield criterion and the von Mises yield criterion.