Continuum Shape Sensitivity with Spatial Gradient Reconstruction of Built-up Structures

Accurate and efficient computation of sensitivities are critical to the success of implementing gradient based optimization algorithms for large-scale, multi-disciplinary design problems. Traditional methods for computing design sensitivities, such as the finite difference, complex step, discrete semi-analytic, and discrete analytic methods often yield unsatisfactory results. Presented here is a local continuum shape sensitivity method with spatial gradient reconstruction. This method is accurate, efficient, and easy to implement. Most importantly, it is formulated as a general approach to sensitivity analysis, which makes it amenable to use with black box analyses. The method has previously been implemented for beam models, and here it is implemented for linear static bending of rectangular stiffened plate models. Among the examples presented are rectangular plates analysed with a variety of pressure loads, boundary conditions, plate theories, and finite element formulations. The final implementation is for a beam-stiffened rectangular plate, which is representative of a built-up structure. The local continuum sensitivity solutions are compared to either analytically derived sensitivities or finite difference sensitivities.