Generalized Lagrange Multipliers in Elastoplastic Torsion

The Linear Nonconvex Generalized Gradient and Lagrange Multipliers

A Lagrange multiplierrules that uses small generalized gradients is introduced. It includes both inequality and set constraints. The generalized gradient is the linear generalized gradient. It is smaller than the generalized gradients of Clarke and Mordukhovich but retains much of their nice calculus. Its convex hull is the generalized gradient of Michel and Penot if a function is Lipschitz. Th...

Substructuring by Lagrange Multipliers

Lagrange Multipliers and Optimality

Lagrange multipliers used to be viewed as auxiliary variables introduced in a problem of constrained minimization in order to write first-order optimality conditions formally as a system of equations. Modern applications, with their emphasis on numerical methods and more complicated side conditions than equations, have demanded deeper understanding of the concept and how it fits into a larger t...

Elastoplastic Torsion by Quadratic Programming

A fItrite element scheme (together with a conjugate gradient algorithmj is demonstrated to be a very effective method for analyzing general elastoplastic torsion of prismatic bars posed as quadratic programming problems. Solutions for bars with elliptical and Sokolovsky’s oval cross-sections are presented. The solutions for the elliptical bars agree with the existing elastic and limit plastic s...

Elastoplastic Torsion : Twist and Stress

stresses in the rod. If the force we apply is small enough, the rod behaves as an elastic body: when we release it, it will return to its original state. But if we apply a lot of twisting force, we will eventually change the rod’s structure: some portion of it will behave plastically and will be permanently changed. If the whole rod behaves elastically, or if it all behaves plastically, then mo...