Towards the stabilization of the low density elements in topology optimization with large deformation

• Published in: Computational mechanics Vol. 52; no. 4; pp. 779 - 797
• Main Authors: Lahuerta, Ricardo Doll, Simões, Eduardo T., Campello, Eduardo M. B., Pimenta, Paulo M., Silva, Emilio C. N.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2013; Springer; Springer Nature B.V
• Subjects: Analysis; Asymptotes; Classical and Continuum Physics; Computational Science and Engineering; Constitutive models; Deformation; Density; Design optimization; Elasticity; Engineering; Finite element method; Internal forces; Kinematics; Mathematical analysis; Mathematical models; Nonlinear programming; Nonlinearity; Original Paper; Plane strain; Plane stress; Stability; Stiffness matrix; Theoretical and Applied Mechanics; Topology optimization; Voids; Structural topology optimization method; Finite element method; Geometric nonlinearities; Nonlinear elasticity; Method of moving asymptotes; Large deformations
• ISSN: 0178-7675; 1432-0924
• DOI: 10.1007/s00466-013-0843-x

This work addresses the treatment of lower density regions of structures undergoing large deformations during the design process by the topology optimization method (TOM) based on the finite element method. During the design process the nonlinear elastic behavior of the structure is based on exact kinematics. The material model applied in the TOM is based on the solid isotropic microstructure with penalization approach. No void elements are deleted and all internal forces of the nodes surrounding the void elements are considered during the nonlinear equilibrium solution. The distribution of design variables is solved through the method of moving asymptotes, in which the sensitivity of the objective function is obtained directly. In addition, a continuation function and a nonlinear projection function are invoked to obtain a checkerboard free and mesh independent design. 2D examples with both plane strain and plane stress conditions hypothesis are presented and compared. The problem of instability is overcome by adopting a polyconvex constitutive model in conjunction with a suggested relaxation function to stabilize the excessive distorted elements. The exact tangent stiffness matrix is used. The optimal topology results are compared to the results obtained by using the classical Saint Venant–Kirchhoff constitutive law, and strong differences are found.