Isogeometric shape design sensitivity analysis of elasticity problems using boundary integral equations

Using boundary integral equations and isogeometric approach, a shape design sensitivity analysis (DSA) method is developed for two dimensional elastic structures. In the isogeometric approach, NURBS basis functions in CAD systems are directly utilized in response analysis, which enables a seamless incorporation of exact geometry and higher continuity into computational framework. To enhance the accuracy of shape design sensitivity, the CAD-based higher-order geometric information such as curvature, normal, and tangential vector is exactly embedded in the sensitivity expressions. In boundary integral formulation, shape design velocity field is decomposed into normal and tangential components, which significantly affect the accuracy of shape design sensitivity. Also, the proposed boundary-based method does not require the tedious design parameterization of internal domain. Through the numerical examples, the developed shape DSA method turns out to be more accurate than conventional finite element based one.