Linear programming solution of masonry arch stability

A pier Jack arch, and segmental arch will be analyzed using a minimization of potential energy procedure. The method involves creating an energy equation that describes the structure in terms of local displacements. The energy equation will be set up in a linear form so that it can utilize linear programming methods of minimization. The minimization routine will be subject to a number of constraints used to enforce the end conditions of the arch at the abutments and constraints against interpenetration and sliding of adjacent blocks, and then solved for both the primal and dual solutions. The normal forces which are necessary to determine the frictional energy dissipated due to a sliding failure will be derived from the slack of the dual solution. The primal solution will result in either an unbounded solution, indicating an unstable structure, or a solution of zero, indicating a stable structure. This information will be used to solve for a critical value of stability for a particular unknown.