Abstract
A continuum-based shape design sensitivity analysis (DSA) method is presented for 2-D solid components with rate-independent elasto-plastic material. The material derivative of continuum mechanics is utilized to develop a continuum-based shape DSA method. The design sensitivity equation is derived using the incremental form of the equilibrium equation and increments of the static response with respect to shape design variables. The direct differentiation method is utilized to obtain the first-order variation of the performance measure explicitly in terms of variations of shape design variables. With the consistent tangent stiffness matrix employed at the end of each load step to compute the design sensitivity, the method does not require iterations to compute the design sensitivity. Numerical results are presented for a hollow cylinder model and a membrane with a hole model to validate the proposed DSA method.
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Park, Y.H., Choi, K.K. Shape design sensitivity analysis of nonlinear 2-D solids with elasto-plastic material. Structural Optimization 18, 236–246 (1999). https://doi.org/10.1007/BF01223305
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DOI: https://doi.org/10.1007/BF01223305