ON THE USE OF MIXED FINITE ELEMENTS IN TOPOLOGY OPTIMIZATION

The paper deals with a topology optimization formulation that uses mixed-finite elements. The discretization scheme adopts not only displacements (as usual) but also stresses as primary variables. Two dual variational formulations based on the HellingerReissner variational principle are presented in continuous and discrete form. The use of this technique and the choice of nodal densities as optimization variables are the main features of the topology optimization problem here formulated and solved by the method of moving asymptotes (MMA) [21]. Numerical examples are performed to test the capabilities of the presented method and to introduce the ongoing research concerning the presence of stress constraints and the optimization of incompressible media.

[1]  K. Svanberg.  The method of moving asymptotes—a new method for structural optimization , 1987 .

[2]  T. E. Bruns,et al.  Numerical methods for the topology optimization of structures that exhibit snap‐through , 2002 .

[3]  M. Bendsøe,et al.  Material interpolation schemes in topology optimization , 1999 .

[4]  J. Petersson,et al.  Numerical instabilities in topology optimization: A survey on procedures dealing with checkerboards, mesh-dependencies and local minima , 1998 .

[5]  Niels Olhoff,et al.  Topology optimization of continuum structures: A review* , 2001 .

[6]  T. E. Bruns,et al.  Topology optimization of non-linear elastic structures and compliant mechanisms , 2001 .

[7]  M. Bendsøe,et al.  Generating optimal topologies in structural design using a homogenization method , 1988 .

[8]  Noboru Kikuchi,et al.  Topology optimization with design-dependent loads , 2001 .

[9]  Claes Johnson,et al.  Some equilibrium finite element methods for two-dimensional elasticity problems , 1978 .

[10]  N. Kikuchi,et al.  Solutions to shape and topology eigenvalue optimization problems using a homogenization method , 1992 .

[11]  Michel Fortin,et al.  Mixed and Hybrid Finite Element Methods , 2011, Springer Series in Computational Mathematics.

[12]  Anders Klarbring,et al.  Topology optimization of flow networks , 2003 .

[13]  Claude Fleury,et al.  CONLIN: An efficient dual optimizer based on convex approximation concepts , 1989 .

[14]  M. Bendsøe,et al.  Topology optimization of continuum structures with local stress constraints , 1998 .

[15]  Dongwoo Sheen,et al.  Checkerboard‐free topology optimization using non‐conforming finite elements , 2003 .

[16]  O. Sigmund.  A new class of extremal composites , 2000 .

[17]  E. Ramm,et al.  Topology and shape optimization for elastoplastic structural response , 2001 .

[18]  J. Petersson.  Some convergence results in perimeter-controlled topology optimization , 1999 .