Topology optimization using polytopes
Autor: | Ivan F. M. Menezes, Leonardo S. Duarte, Glaucio H. Paulino, Arun L. Gain |
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Rok vydání: | 2015 |
Předmět: |
Discretization
Mechanical Engineering Topology optimization Computational Mechanics General Physics and Astronomy Polytope Numerical Analysis (math.NA) Degrees of freedom (mechanics) Finite element method Computer Science Applications Optimization and Control (math.OC) Mechanics of Materials Convergence (routing) FOS: Mathematics Polygon mesh Mathematics - Numerical Analysis Mathematics - Optimization and Control Algorithm ComputingMethodologies_COMPUTERGRAPHICS Mathematics Stiffness matrix |
Zdroj: | Computer Methods in Applied Mechanics and Engineering. 293:411-430 |
ISSN: | 0045-7825 |
Popis: | Meshing complex engineering domains is a challenging task. Arbitrary polyhedral meshes can provide the much needed flexibility in automated discretization of such domains. The geometric property of the polyhedral meshes such as the unstructured nature and the facial connectivity between elements makes them specially attractive for topology optimization applications. Numerical anomalies in designs such as the single node connections and checkerboard pattern, which are difficult to manufacture physically, are naturally alleviated with polyhedrons. Special interpolants such as Wachspress, mean value coordinates, maximum entropy shape functions are available to handle arbitrary shaped elements. But the finite elements approaches based on these shape functions face some challenges such as accurate and efficient computation of the shape functions and their derivatives for the numerical evaluation of the weak form integrals. In the current work, we solve the governing three-dimensional elasticity state equation using a Virtual Element Method (VEM) approach. The main characteristic difference between VEM and standard finite element methods (FEM) is that in VEM the canonical basis functions are not constructed explicitly. Rather the stiffness matrix is computed directly utilizing a projection map which extracts the linear component of the deformation. Such a construction guarantees the satisfaction of the patch test (used by engineers as an indicator of optimal convergence of numerical solutions under mesh refinement). Finally, the computations reduce to the evaluation of matrices which contain purely geometric surface facet quantities. The present work focuses on the first-order VEM in which the degrees of freedom associated with the vertices. Utilizing polyhedral elements for topology optimization, we show that the mesh bias in the member orientation is alleviated. |
Databáze: | OpenAIRE |
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