Multiscale topology optimization with direct \(\mathrm{FE}^2\). (English) Zbl 1536.74204
Summary: Together with the rapid development in manufacturing technology, multiscale structural topology optimization presents opportunities for the design of components at both the structural and sub-structural scales. A few works on topological optimization based on \(\mathrm{FE}^2\) computational homogenization to concurrently evolve the structure and sub-structure have been reported. However, significant expertise and coding are required in the conventional implementation of \(\mathrm{FE}^2\). It is shown that multiscale \(\mathrm{FE}^2\) optimization can be readily implemented on commercial finite element codes using the Direct \(\mathrm{FE}^2\) approach. The multiscale analysis is carried out as a single topology optimization job on commercial FE software. Numerical example problems are solved using ABAQUS to demonstrate the proposed method for stiffness optimization. It is shown that Direct \(\mathrm{FE}^2\) optimization takes only a fraction of the computational time required for optimization with a fine mesh and yet gives comparable optimized stiffness.
MSC:
| 74P15 | Topological methods for optimization problems in solid mechanics |
| 74S05 | Finite element methods applied to problems in solid mechanics |
Keywords:
topology optimization; multiscale analysis; direct \(\mathrm{FE}^2\); SIMP; computational homogenizationReferences:
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