Structural optimization with pseudo-load approach exploiting design length scales.

Abstract

Numerical optimization techniques are lagging in acceptance by the engineering community. One of the most serious problems is the high computational cost associated with repeated evaluation of constraint functions and their derivatives. Structural analysis and sensitivity analysis often require finite element analysis in structural optimization. Repeated analyses of large scale finite element models are very time consuming and prohibitive. To reduce cost, an approximate method exploiting design length scales is devised and built into the analysis and optimization programs. This approach is called the pseudo-load approach. Most practical structures are divided into naturally occurring regions by manufacturers and engineers. Design variable linking is used for variables in each region. Pseudo loads are applied on each region; the response to these loads provides certain mode shapes, called pseudo-load modes. These are used to approximate the behavior of the modified structures by a Rayleigh-Ritz technique. The modes reflect local design changes and bring in design length scales to the solution of a modified structure. The Rayleigh-Ritz technique (a reduced basis method) alleviates the cost of repeated structural analysis by reducing the number of degrees of freedom. A structural synthesis program has been developed by coupling the numerical optimization program ADS to the widely used finite element program MSC/NASTRAN. The pseudo-load method is compared with other methods by solving physical problems. Thermal-load modes (response to thermal loads applied on each of design regions) and a truncated set of natural eigenvectors served as alternative basis vectors. The component mode method is employed in the analysis of intermediate designs and compared with the pseudo-load approach. Numerical results have proven that the pseudo-load approach provides accurate results and leads to fast convergence. The method should be particularly useful on very large problems.