Abstract
The benefit of adaptive meshing strategies for a recently introduced thermodynamic topology optimization is presented. Employing an elementwise gradient penalization, stability is obtained and checkerboarding prevented while very fine structures can be resolved sharply using adaptive meshing at material-void interfaces. The usage of coarse elements and thereby smaller design space does not restrict the obtainable structures if a proper adaptive remeshing is considered during the optimization. Qualitatively equal structures and quantitatively the same stiffness as for uniform meshing are obtained with less degrees of freedom, memory requirement and overall optimization runtime. In addition, the adaptivity can be used to zoom into coarse global structures to better resolve details of interesting spots such as truss nodes.
Highlights
Topology optimization has been introduced several decades ago and it has been established as a powerful tool during engineering design processes
We provide a detailed study for the behavior of the thermodynamic topology optimization method in conjunction with adaptive meshing employing the symmetrically reduced Messerschmidt-Bolkow-Blohm (MBB) beam as a running example
Only very small deviations are observed, but in this case the evolutionary thermodynamic topology optimization finds a different local minimum for the adaptive case compared with full mesh refinement
Summary
Topology optimization has been introduced several decades ago and it has been established as a powerful tool during engineering design processes. It is obvious that accounting for the correct (non-linear) material behavior allows for using the potentials of design space and material at its best In this regard, the so-called thermodynamic topology optimization has been introduced (Junker and Hackl 2015; Jantos et al 2018). Stainko (2006) employs an adaptive multilevel approach refining towards the material-void interface and a multigrid method to efficiently solve the elasticity problem. The employment of the multigrid method (Hackbusch 1985) can considerably reduce the computational cost to solve the finite element analysis This is in particular of interest since adaptive mesh refinement can be directly employed to create a nested mesh hierarchy that is used for the multigrid algorithm (Bramble et al 1991; Bastian and Wittum 1994). Four different test cases are considered and results in terms of obtained stiffness, stability and runtime presented
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