Structural Redesign by Large Admissible Perturbations With Static Mode Compensation

Abstract

The method of LargE Admissible Perturbations (LEAP) solves redesign problems of complex structures without trial and error or repetitive finite element analyses. Code RESTRUCT (Redesign of STRUCTures) produces an optimal redesign of minimum structural change or minimum weight with modal dynamics and/or static displacement specifications. LEAP allows for large structural changes. First, the general perturbation equations are derived relating the original structure S1 (known) to the objective structure S2 (unknown) which is to satisfy the designer’s specifications. Next, the redesign problem is solved using an incremental prediction-correction scheme. In the past, LEAP produced accurate results even for 100–300 percent changes in redesign for modal objectives without any intermediate FEAs. Accuracy in static redesign, however, was limited to about 50 percent changes in static objectives. In this work, a new static general perturbation equation and the corresponding LEAP algorithm are developed to achieve accuracy for 100–300 percent changes in static performance as well. The new formulation includes the static deflection shape as the zeroth mode in the expansion of static properties in terms of dynamic modes. Systematic numerical applications show that high accuracy is achieved by fewer extracted modes.