engleski

Evolutionary topology optimization using parameterized b-spline surface

In solid mechanics, the topology optimization process involves two separate fields: displacement fields as well as density fields (material distribution). The level set topology op-timization method is based on implicit functions whose iso-lines describe the respective ge-ometry. The traditional level set method is performed by using the Hamilton-Jacobi transport equation, which implies the use of gradient optimization methods that are prone to getting stuck in local extremes. Furthermore, resulting optimal shapes are strongly dependent on the initial guess. In order to provide a robust topology optimization method insensitive to local optima, param-eterized level set functions and evolutionary optimization methods (genetic algorithms) are used. Using B-spline parameterized level set functions enables the number of variables to be reduced and the use of genetic algorithms possible. The method is presented on a simple 2D cantilever plate. The objective function is minimum of compliance in one case and minimum of volume in the second case. Due the geometric change, the finite element method requires remeshing. To avoid remeshing, the “Ersatz material” technique is applied. It changes the material properties by setting Young's module of elasticity to zero for elements of the FE mesh where the material should be removed. The proposed method of topology optimization using genetic algorithms is feasible, but a very time-consuming process. For more complex problems, the proposed procedure with a smaller number of generations can be used as a generator of the initial solutions for subsequent faster procedures.

Topology optimization; parameterization; structural mechanics; topology description function – Level set function

nije evidentirano