NURBS-based isogeometric shape and material optimization of curvilinearly stiffened plates with FGMs

In this paper, the shape and material optimization problems of the curvilinearly stiffened plates are solved by using the non-uniform rational B-splines (NURBS) based isogeometric analysis (IGA) method. The analytical formulas for calculating the sensitivity of plates and stiffeners are given and applied to shape optimization problems successfully. By designing the coordinates of the control points of the stiffener, the shape of the stiffener can be determined to minimize its flexibility under a certain volume constraint. Then, functionally graded materials (FGMs) are used for curvilinearly stiffened plates. The volume fraction of the constituent materials of FGMs is expressed in the form of polynomial expansions. By designing the coefficients of these polynomial expansions to determine the material distribution, the total volume fraction of some constituent materials under certain displacement and stress constraints is minimized.