Minimum Weight Design with Stability Constraint

The problem of minimum weight design of structures composed of finite elements each having a finite number of degrees of freedom and subject to a critical buckling load constraint is formulated as in nonlinear programming. Employing the accelerated cutting plane method of Wolfe, all constraints except the general buckling load constraint are expressed by linear inequalities. A method for the solution of this problem is developed which differs from the projected gradient method only in the way the direction of motion is selected once the nonlinear constraint is encountered. The method involves first moving in the direction of the projected gradient, and then returning to this region on the hyperplane of constant weight along the projection of the buckling-constraint gradient. The method is applied to the minimum weight design of a built-up column of varying width.