Nonsmooth model for plastic limit analysis and its smoothing algorithm.

Jian-yu Li; Shao-hua Pan; Xing-si Li

By means of Lagrange duality theory of the convex program, a dual problem of Hill’s maximum plastic work principle under Mises’ yield condition has been derived and whereby a non-differentiable convex optimization model for the limit analysis is developed. With this model, it is not necessary to linearize the yield condition and its discrete form becomes a minimization problem of the sum of Euclidean norms subject to linear constraints. Aimed at resolving the non-differentiability of Euclidean norms, a smoothing algorithm for the limit analysis of perfect-plastic continuum media is proposed. Its efficiency is demonstrated by computing the limit load factor and the collapse state for some plane stress and plain strain problems.

LAGRANGE equations; CONVEX programming; MATHEMATICAL optimization; EUCLIDEAN algorithm; DUALITY theory (Mathematics)

Applied Mathematics & Mechanics, 2006, Vol 27, Issue 8, p1081

0253-4827

Academic Journal

10.1007/s10483-006-0808-z