In this contribution an innovative method for shape optimization with parametrizationdirectly on FE mesh is proposed. Parametrization of the design for shapeoptimization can be based on CAD models or directly on the FE mesh (CAD-freeparametrization). In CAD based design optimization, design variables arechosen among the parameters related to the underlying CAD model. Duringthe optimization process, the update of the finite element mesh is dueto changes of the CAD model. In FE based design optimization, nodal coordinatesare taken as design variables. This parametrization gives more freedomto the optimization process, since the result of the optimization problemis not restricted to the preselected CAD design space. However, there aremany technical facts which in the past made this natural choice of optimizationmodel to appear as prohibitive, as there are: the large number of designvariables, the wiggly shape and the inherent problems of FE discretization(e.g. locking) which may lead to mechanically wrong answers. This contributionpresents an innovative approach to overcome these shortcomings by a combinationof several techniques which results in a powerful and flexible tool forthe preliminary design of free form shells. From the mechanical point ofview locking-free elements (shell elements) are indispensable. The mainproblem of the FE-based design is that wiggly shapes may be obtained asoptimal designs. These wiggles are mesh dependent and obviously it is notdesirable that the optimum design depends on the coarseness of the meshused. Therefore, the aim of this research is to provide a tool to controlthe smoothness of the designs obtained as result of shape optimizationand to avoid mesh dependency. Based on the filter proposed by Sigmund [12]in to overcome checkerboard and mesh dependency problems in topology optimization,a filter for shape optimization is proposed. The optimization directlyon the FE node provides a high degree of freedom in the design process,which facilitates many applications, e.g. bead optimization based on localfilter techniques.
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In this contribution an innovative method for shape optimization with parametrizationdirectly on FE mesh is proposed. Parametrization of the design for shapeoptimization can be based on CAD models or directly on the FE mesh (CAD-freeparametrization). In CAD based design optimization, design variables arechosen among the parameters related to the underlying CAD model. Duringthe optimization process, the update of the finite element mesh is dueto changes of the CAD model. In FE based design optimi...
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