Topology optimization of shell–infill structures using an erosion-based interface identification method

Abstract Topology optimization of shell–infill structures has been a hot topic in the optimization community. The crucial issue of such design problem is how to accurately describe the material interfaces, which is often regarded as a relatively difficult problem in density-based topology optimization. This paper presents an erosion-based interface identification method to handle this difficulty by defining the different parts of the original and eroded structures as interfaces. The theoretical relation for determining the erosion parameters is derived to control the interface thickness accurately. It turns out that the erosion-based method offers excellent performance even for the extreme cases where the ratios of member sizes to a prescribed thickness are small, and at the same time, it is easy to implement since we only need to consider the frequently-used filtering and projection processes in the applied erosion operation. Then, we provide an improved SIMP-based topology optimization method for shell–infill structures based on the new idea of defining interfaces. In this paper, a tweak to the existing two-step filtering/projection process is made to separate the shell and infill, and a corresponding interpolation function is developed to model the whole composite objects. Enhanced by the worst-case based robust formulation, the minimum length scale of optimized structures can be controlled. Several 2D and 3D compliance optimization examples are provided to illustrate the effectiveness of the proposed method.

[1]  Xiaoming Wang,et al.  A level set method for structural topology optimization , 2003 .

[2]  O. Sigmund,et al.  Filters in topology optimization based on Helmholtz‐type differential equations , 2011 .

[3]  Xu Guo,et al.  Explicit three dimensional topology optimization via Moving Morphable Void (MMV) approach , 2017, 1704.06060.

[4]  Michael Yu Wang,et al.  Shape and topology optimization of compliant mechanisms using a parameterization level set method , 2007, J. Comput. Phys..

[5]  Anders Clausen,et al.  Minimum Compliance Topology Optimization of Shell-Infill Composites for Additive Manufacturing , 2017 .

[6]  Zhan Kang,et al.  Integrated topology optimization of multi-component structures considering connecting interface behavior , 2018, Computer Methods in Applied Mechanics and Engineering.

[7]  Ole Sigmund,et al.  Topology optimization of piezo modal transducers with null-polarity phases , 2016 .

[8]  Ole Sigmund,et al.  Buckling strength topology optimization of 2D periodic materials based on linearized bifurcation analysis , 2018, Computer Methods in Applied Mechanics and Engineering.

[9]  Y. Xie,et al.  A simple evolutionary procedure for structural optimization , 1993 .

[10]  O. Sigmund,et al.  Topology optimization of coated structures and material interface problems , 2015 .

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

[12]  Ole Sigmund,et al.  Topological design of electromechanical actuators with robustness toward over- and under-etching , 2013 .

[13]  Ole Sigmund,et al.  Giga-voxel computational morphogenesis for structural design , 2017, Nature.

[14]  Liang Gao,et al.  Topology optimization of multi-material structures with graded interfaces , 2019, Computer Methods in Applied Mechanics and Engineering.

[15]  T. Shi,et al.  Stable hole nucleation in level set based topology optimization by using the material removal scheme of BESO , 2019, Computer Methods in Applied Mechanics and Engineering.

[16]  Georgios Michailidis,et al.  Design of thermoelastic multi-material structures with graded interfaces using topology optimization , 2017, Structural and Multidisciplinary Optimization.

[17]  Ole Sigmund,et al.  Exploiting Additive Manufacturing Infill in Topology Optimization for Improved Buckling Load , 2016 .

[18]  Ole Sigmund,et al.  Manufacturing tolerant topology optimization , 2009 .

[19]  K. Maute,et al.  Level set topology optimization of structural problems with interface cohesion , 2017 .

[20]  Gengdong Cheng,et al.  Optimum structure with homogeneous optimum truss-like material , 2008 .

[21]  Shutian Liu,et al.  A projection‐based method for topology optimization of structures with graded surfaces , 2019, International Journal for Numerical Methods in Engineering.

[22]  Liang Gao,et al.  Topology optimization of shell-infill structures using a distance regularized parametric level-set method , 2018, Structural and Multidisciplinary Optimization.

[23]  Chunlei Wu,et al.  Robust topology optimization of multi-material structures considering uncertain graded interface , 2019, Composite Structures.

[24]  K. Maute,et al.  Level set topology optimization of problems with sliding contact interfaces , 2015 .

[25]  Ole Sigmund,et al.  Topology optimization of 3D shell structures with porous infill , 2017 .

[26]  Erik Andreassen,et al.  On filter boundary conditions in topology optimization , 2017 .

[27]  G. Allaire,et al.  Structural optimization using sensitivity analysis and a level-set method , 2004 .

[28]  Xu Guo,et al.  Doing Topology Optimization Explicitly and Geometrically—A New Moving Morphable Components Based Framework , 2014 .

[29]  Y. Xie,et al.  Bi-directional evolutionary topology optimization of continuum structures with one or multiple materials , 2009 .

[30]  Zhan Kang,et al.  A level set method for shape and topology optimization of coated structures , 2018 .

[31]  Liang Gao,et al.  Design of shell-infill structures by a multiscale level set topology optimization method , 2019, Computers & Structures.

[32]  Z. Kang,et al.  Multi-material topology optimization considering interface behavior via XFEM and level set method , 2016 .

[33]  M. Bendsøe,et al.  Topology Optimization: "Theory, Methods, And Applications" , 2011 .

[34]  Grégoire Allaire,et al.  Material interface effects on the topology optimizationof multi-phase structures using a level set method , 2014 .

[35]  Ole Sigmund,et al.  On projection methods, convergence and robust formulations in topology optimization , 2011, Structural and Multidisciplinary Optimization.

[36]  G. Allaire,et al.  MULTI-PHASE STRUCTURAL OPTIMIZATION VIA A LEVEL SET METHOD ∗, ∗∗ , 2014 .

[37]  Zhan Kang,et al.  A velocity field level set method for shape and topology optimization , 2018, International Journal for Numerical Methods in Engineering.