Abstract
A new approach for performing FE-shape design sensitivity analyses (DSA) of structural models with both linear elastic and elastoplastic material behaviour is presented. In the formulation of the method the derivation of the FE equilibrium equations is performed analytically leading to various terms. The differentiation of some parts of these terms is determined numerically, therefore the method is semianalytical. The formulation is particularized for isoparametric finite elements for which “exact” numerical differentiation can be obtained (exact up to round-off error). Examples of some plane stress problems testify that the results of the new method are not dependent either on the size of perturbation of the design variables or on the FE mesh refinement among other factors.
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Vaz, L.E., Hinton, E. FE-shape sensitivity of elastoplastic response. Structural Optimization 10, 231–238 (1995). https://doi.org/10.1007/BF01742597
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DOI: https://doi.org/10.1007/BF01742597