Isogeometric shape design optimization of nanoscale structures using continuum-based shell theory considering surface effects

Considering surface effects on nanoscale structures, an isogeometric shape optimization method is developed for curved structures using Naghdi's shell formulation. Since the curved structures are very sensitive to geometrical changes, the geometric exactness of isogeometric approach successfully prevents the loss of higher-order geometric information in design sensitivity analysis (DSA). A direct differentiation method is employed for the DSA, where the control points are selected as the design variables and describe the flexible modeling of free-form shell surfaces. Through numerical examples, we verified the accuracy of isogeometric analysis whose framework shows better convergence rate than finite element analysis due to the exact geometry and the higher order geometric information in the DSA formulation. The surface Lame constants turns out to alter the ratio between the portion of membrane and bending energies. Also, the optimal shape is dependent on the residual surface stress that affects its stress state.