Topology optimization using B-spline finite elements

Topology optimization algorithms using traditional elements often do not yield well-defined smooth boundaries. The computed optimal material distributions have problems such as “checkerboard” pattern formation unless special techniques, such as filtering, are used to suppress them. Even when the contours of a continuous density function are defined as the boundary, the solution can still have shape irregularities. The ability of B-spline elements to mitigate these problems are studied here by using these elements to both represent the density function as well as to perform structural analysis. B-spline elements can represent the density function and the displacement field as tangent and curvature continuous functions. Therefore, stresses and strains computed using these elements is continuous between elements. Furthermore, fewer quadratic and cubic B-spline elements are needed to obtain acceptable solutions. Results obtained by B-spline elements are compared with traditional elements using compliance as objective function augmented by a density smoothing scheme that eliminates mesh dependence of the solutions while promoting smoother shapes.