A mass constraint formulation for structural topology optimization with multiphase materials

Abstract

This work is focused on the topology optimization of lightweight structures consisting of multiphase materials. Instead of adopting the common idea of using volume constraint, a new problem formulation with mass constraint is proposed. Meanwhile, recursive multiphase materials interpolation (RMMI) and uniform multiphase materials interpolation (UMMI) schemes are discussed and compared based on numerical tests and theoretical analysis. It is indicated that the nonlinearity of the mass constraint introduced by RMMI brings numerical difficulties to attain the global optimum of the optimization problem. On the contrary, the UMMI-2 scheme makes it possible to formulate the mass constraint in a linear form with separable design variables. One such formulation favors very much the problem resolution by means of mathematical programming approaches, especially the convex programming methods. Moreover, numerical analysis indicates that fully uniform initial weighting is beneficial to seek the global optimum when UMMI-2 scheme is used. Besides, the relationship between the volume constraint and mass constraint is theoretically revealed. The filtering technique is adapted to avoid the checkerboard pattern related to the problem with multiphase materials. Numerical examples show that the UMMI-2 scheme with fully uniform initial weighting is reliable and efficient to deal with the structural topology optimization with multiphase materials and mass constraint. Meanwhile, the mass constraint formulation is evidently more significant than the volume constraint formulation.

Stress constrained shape and topology optimization with fixed mesh: A B-spline finite cell method combined with level set function

“…Finally, three representative examples show that optimization problems with and without stress constraints can successfully be solved within the FCM/LSF design framework. Further developments can be made by extending the current method to structural shape and topology optimization of multiphase materials [51], multi-component systems [21] as well as curved shell structures with openings [52].…”

Layout optimization of multi-material continuum structures with the isolines topology design method

“…Currently, the most used techniques for topology design of continuum structures using heterogeneous or multiple materials are: 1) Material interpolation schemes (Yin and Ananthasuresh 2001, Huang and Xie 2009, Gao et al 2010, Luo et al 2012, Blasques and Stolpe 2012; 2) Level-set models (Yulin and Xiaoming 2004, Zhuang et al 2007; and 3) Phase-field schemes (Bourdin and Chambolle 2000, Jung and Gea 2006, Zhou and Wang 2007.…”

Structural optimization in ESAC: annals 2011

“…This work is focused on the topology optimization of lightweight structures consisting of multiphase materials [1,2]. Instead of adopting the common idea of using volume constraint, a new problem formulation with mass constraint is firstly proposed, which is a significant breakthrough of the topology optimization with multiphase materials.…”