Minimax Finite Element Method

The minimax method is applied to boundary value problems of structural mechanics. This is a weighted residual method in which the absolute value of a residual is minimized. It is similar to collocation-based finite elements. Computational implementation is achieved using linear programming. Since inequality constraints are acceptable to linear programming, the minimax method can bm used to solve problems formulated using inequality relationships. For example, the minimax finite element method can perform limit analyses or can be applied to such contact problems as offset supports. The proposed approach is formulated in some detail. It is then applied to some elasticity stress analysis problems and to the limit analysis of a beam. The method appears to be relatively easy to set up and gives satisfactory results.