A new density‐stiffness interpolation scheme for topology optimization of continuum structures

Abstract

If you would like to write for this, or any other Emerald publication, then please use our Emerald for Authors service information about how to choose which publication to write for and submission guidelines are available for all. Please visit www.emeraldinsight.com/authors for more information. About Emerald www.emeraldinsight.comEmerald is a global publisher linking research and practice to the benefit of society. The company manages a portfolio of more than 290 journals and over 2,350 books and book series volumes, as well as providing an extensive range of online products and additional customer resources and services.Emerald is both COUNTER 4 and TRANSFER compliant. The organization is a partner of the Committee on Publication Ethics (COPE) and also works with Portico and the LOCKSS initiative for digital archive preservation.Abstract In this paper, a new density-stiffness interpolation scheme for topology optimization of continuum structures is proposed. Based on this new scheme, not only the so-called checkerboard pattern can be eliminated from the final optimal topology, but also the boundary-smooth effect associated with the traditional sensitivity averaging approach can also be overcome. A proof of the existence of the solution of the optimization problem is also given, therefore mesh independent optimization results can be obtained. Numerical examples illustrate the effectiveness and the advantage of the proposed interpolation scheme. IntroductionTopology optimization is one of the most challenging research topics in the field of structural optimization. It has received more and more research attentions recently because of its great potential of application in many industrial areas. Topology optimization aims at determining the optimum number, positions and mutual connectivity of the structural members. Its importance lies in the fact that the appropriate topology is generally the most decisive factor for the efficiency of a product. For topology optimization of continuum structures, homogenization or variable density based approaches are often employed. In homogenization (or microstructure) based approach, the well-posedness of the topology optimization is achieved by introducing the porous materials with microstructure into the optimization model. The effective macroscopic properties of the porous materials are computed by applying some smear-out techniques. These effective properties are closely related to the microscopic geometry parameters, thus we can optimize the structural topology by adjusting these parameters. In variable density approach, a density

Morphology-based black and white filters for topology optimization

“…In order to obtain more discrete solutions than provided by the original density filter (12), Guo and Gu (2004) have suggested a modification to (10) where they multiply the filtered density with the original variable, i.e.…”

“…For density filtering methods, the vector ρ should only be seen as a mathematical design variable; the physical density distribution to be plotted is given by the filtered vectorρ. When the filtered densities are plotted for the examples from the paper by Guo and Gu (2004) many grey elements are observed, hence the basic idea of the method fails. There are two other problems with Guo and Gu's implementation.…”

A hybrid topology optimization methodology combining simulated annealing and SIMP

“…Perimeter control and gradient constraint algorithms add constraints to the optimization problem and require additional computational effort [25]. Alternatively, density filters modify the material interpolation scheme to achieve edge-preserving characteristics [36][37][38][39][40]. However, these filters require a nontrivial parameter tuning.…”

Recent development in structural design and optimization

“…[13][14][15]. Borrvall and Petersson [16] developed another method to regularize the ill-posed "black-and-white" optimal topology design problem.…”