A semianalytical formulation that combines the implicit differentiation of the discretized boundary integral equations and a univariate perturbation, forward-difference approximation technique is developed for the computation of structural design sensitivities. Two-dimensional plane and axisymmetric elastic continua, including body forces of the gravity and centrifugal types, are considered. As a result of the forward-difference approximation employed, the numerical integration of a new class of fundamental solution sensitivity kernels is avoided; and no special treatment is required for the evaluation of singular integrals for the diagonal entries in the boundary-element sensitivity system matrices. Because of the implicit-differentiation step, the factorization of the perturbed system matrices is avoided. Numerical data are presented for the study of the effect of the design variable perturbation size on the accuracy of the solution. Timings and accuracy results for test problems, including both plane and axisymmetric designs, are given and compared to the corresponding results obtained from a full-analytical sensitivity analysis. The present semianalytical method is computationally more efficient compared to the full-analytical implicit-differentiation approach for the same order of accuracy, for appropriate choices of design variable perturbation step sizes.
All Science Journal Classification (ASJC) codes
- Aerospace Engineering