Introduction to linear and nonlinear programming

Finite elements for structural analysis

ber of active constraints in each cycle are limited to a small subset of the total constraints. Optimal design of plate struct,ures using This subset is updated in each cycle and the the Optimality Criteria Method (OCM) is disstrategy allows the new constraints to enter cussed in this paper. The optimum designs while others leave. The OCM presented in are reached by just scaling the design variRef. 1, consisted of two basic steps and they ables to an optimum intersection of multiple are referred to as resizing and scaling. Both constraints (compound scaling algorithm). A are iterative in the design space and their purfour-noded isoparametric plate element is used pose is to search for the optimum. The resizfor modelling the structure. Sensitivity coming algorithm is used when the design is on putations and the optimization algorithm are the constraint surface with respect t o one or discussed. The optimization cost involved (exmore active constraints. I t is derived directly cluding the finite element analyses) is minimal from the optimality conditions. The scaling compared to the mathematical optimization step on the other hand is to bring the design algorithms. The procedure is demonstrated on to the constraint surface when it is away from three example problems using stress and disthe boundary. When the constraints and the placement constraints with side bounds on the objective are linear functions of the variables, design variables. the scaling to the constraint surface can be accomplished in a single step. Based on this Introduction premise the OCM method was applied to design a number of large scale aerospace strucIn the past tw'enty years OptimalitJ' critures with stress, displacement, and frequency teria (OCM) have been constraints [I-51. Because o f the perceived limapplied in the design of large scale structural itation of the scaling step, past applications of optimization problems [1-31. The success of OCM were limited to structures modelled with OCM is largely attributed to the application of membrane elements (trusses and wings). an active constraint strategy where the numGeneralization of the scaling to linear and * Associate Professor, Member AIAA nonlinear functions is the major advance in * * Graduate Research Assistant the application of OCM to a wide variety of *** WL Fellow, Member AIAA mathematical optimization problems [6]. The

Optimality criteria method for minimum weight design of plate structures

This paper presents the generalized compound scaling algorithm and its application to optimum weight design of plate structures The optimum designs are reached by simply scaling the design variables to an optimum intersection of multiple constraints A four-noded isoparametric plate element is used for modeling the structure Sensitivity computations and the optimization algorithm are discussed The optimization cost involved (excluding the finite element analyses) is very small using this algorithm The procedure is demonstrated on three example problems using stress and displacement constraints with side bounds on the design variables

Yang Tzong-Shuoh

Papers

Application of multiplier update method to the minimum weight design of elastic plates