Stress Constraints and Screening for Optimality Criteria Design

Procedures that emphasize the processing of stress constraints within optimality criteria designs for low structural weight with stress and compliance constraints are described. Prescreening criteria are used to partition stress constraints into either potentially active primary sets or passive secondary sets that require minimal processing. Side-constraint boundaries for passive constraints are derived by projections from design histories to modify conventional stress-ratio boundaries. Other procedures described apply partial structural modification reanalysis to correct stress constraint violations of unfeasible designs. Sample problem results show effective design convergence and, in particular, advantages for reanalysis in obtaining lower feasible design weights. HERE have been many significant developments1 during the past two decades in the structural-design optimization procedures that select member-size design variables to achieve low structure weight subject to constraints on displacement compliances and member stresses. For this type of problem, the difficulties of satisfying the stress constraints are usually more severe than those associated with the compliance constraints. Stress constraints are more troublesome because they are direct functions of strains; displacement constraints, however, are integral functions that benefit from the smoothing of local strain variations. This paper concentrates on the processing of stress constraints to expedite com- putations and to produce effective designs within optimality criteria methods. These are indirect design methods for which the solution space is equal to the number of active constraints and is typically smaller than the number of design variables. On the other hand, the solution space for direct design methods is equal in size to the number of design variables. Consequently, optimality criteria methods have the ad- vantages of larger problem-size potential and smaller com- putational effort. Optimality criteria solution methods determine Lagrange multipliers for the active constraints and then use these within the criteria to determine the design variables. The procedures to determine the Lagrange multipliers employ sensitivity (or flexibility) coefficients that are assumed not to depend upon the design variables. Nevertheless, the extent of structural redundancy weakens this assumption, and for the typically redundant structure it is necessary to develop the design through a number of iterative cycles. In each cycle: 1) the structure is reanalyzed to update the coefficients so that they are consistent with the current stage of design; 2) candidate active constraints are screened; 3) design space algorithms are applied to construct the active set of constraints and to determine the associated multipliers; and 4) the optimality criteria are applied to determine the design variables for the next cycle. Nonlinear mathematical programming techniques are used to determine the Lagrange multipliers2 for the set of active constraints. Methods for constructing this set apply hier- archical strategies in which constraints from a candidate set are assembled, added, or deleted. The determination of the multipliers and the construction of the sets of active con-