Generating optimal topologies in structural design using a homogenization method
Computer Methods in Applied Mechanics and Engineering
On various aspects of evolutionary structural optimization for problems with stiffness constraints
Finite Elements in Analysis and Design
Structural boundary design via level set and immersed interface methods
Journal of Computational Physics
Curves and surfaces for CAGD: a practical guide
Curves and surfaces for CAGD: a practical guide
Geometric modeling for shape and topology optimization
Selected and Expanded Papers from the IFIP TC5/WG5.2 Working Conference on Geometric Modeling for Product Realization
On the solution of the checkerboard problem in mixed-FEM topology optimization
Computers and Structures
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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.