Isogeometric Shape Design Optimization of Geometrically Nonlinear Structures

Using the isogeometric approach, the variational formulation of both response and sensitivity analyses for geometrically nonlinear structures is derived using the total Lagrangian formulation. The geometric properties of design are embedded in the nonuniform rational B-splines basis functions and control points whose perturbation naturally results in shape changes. Thus, exact geometric models can be utilized in both response and sensitivity analyses. The normal vector and curvature are continuous in the whole design space so that enhanced shape sensitivity can be expected. Refinements and design changes during the shape optimization are easily implemented within the isogeometric framework, which maintains exact geometry without subsequent communication with computer-aided design description. Through numerical examples, the developed isogeometric sensitivity is verified to demonstrate excellent agreement with finite difference sensitivity. Also, the proposed method works very well in various shape optimization problems.