Integrated optimal design of structures subjected to alternate loads using geometric programming

A parallel decomposition for two or more alternative loading conditions in the integrated optimum structural design is investigated. The method developed, called move coordination, consists of formulating the large optimization problem in the form of smaller subproblems based on the load conditions. This is accomplished by allowing the structural design variables to differ from one load condition to another. The objective function of the global optimization problem for all load conditions is rewritten in separately additive form of several terms, each of which is considered as the objective function of one subproblem. The structural optimization is performed for each load condition separately in a parallel cyclic iterative way. The coupling among the load conditions is accomplished by the introduction of some coordinating constraints in the solution of each subproblem. These constraints have the effect of penalty-relaxation on the subproblems, and they ensure that the final design is the same for all subproblems at the end of the optimization process. The coordinating constraints are updated dynamically in each cycle. In contrast to other multilevel decomposition techniques where optimization problems are solved in two levels, in this method no optimization problem is solved in the second level. Two algorithms are proposed to get the numerical solution by the move coordination method where the second algorithm is an improvement over the first one, thus accelerating convergence. This is accomplished by restricting the move of the coordinating constraints.;The method developed is illustrated by the solution of some planar and space truss optimization problems. The generalized geometric programming with equality and inequality constraints is used to get the solution of the integrated optimum structural design formulation. A computer generation of the variables, equality and inequality constraints is obtained automatically from the structural layout. The method of decomposition developed presents an advantage of reducing the size of the large optimization problem. The algorithm is suitable for implementation on computers using parallel processing.