Force Method Optimization

Book excerpt: To overcome problems arising from the rigorous representation of stress constraints in structural optimization, the use of the force method is demonstrated. The force method of finite element analysis is used to transform a stress-constrained redundant structure into a stress and displacement constrained determinate structure for the purposes of optimization. The resulting problem is non-linear, but the use of a linear programming stage is effective in providing a rapid convergence on the optimum design in many cases. Problems which hitherto required many iterations to converge are now solvable in only one or two steps. The rate of constraint numbers versus numbers of variables is investigated analytically using a 22-bar truss problem as an example. The vital key in optimization technology is identified as the identification of active constraints. The incorporation of displacement constraints into the optimization program is also presented. Examples of problems solved by this approach are included. Discussion of difficulties encountered in the development work also provides indicators for future areas of research. (Author).