Abstract:A general mesh independent filter as a mean to control the complexity of topology optimization designed structures is discussed. A new mesh-independent filter, applied over the move-limits of the sequential linear programming is proposed, and it is shown that its use alleviates common problems in the continuum topology optimization, like checkerboarding, mesh dependency, as well as effects associated to non-structured meshes, like numerical anisotropy. The structural optimization formulation adopted in this wo… Show more
“…The alternative methods in group 3 are mostly still in their infancy and have yet to be successfully applied to advanced problems with many constraints. There are also methods that are hybrids between categories 1 and 2 (Zhou et al, 2001;Cardoso and Fonseca, 2003). Here, the box-constraints of the optimization algorithm are modified according to a filtering scheme, resulting in local gradient controllike behavior.…”
In order to ensure manufacturability and mesh-independence in density-based topology optimization schemes it is imperative to use restriction methods. This paper introduces a new class of morphology based restriction schemes which work as density filters, i.e. the physical stiffness of an element is based on a function of the design variables of the neighboring elements. The new filters have the advantage that they eliminate grey scale transitions between solid and void regions. Using different test examples, it is shown that the schemes in general provide black and white designs with minimum length-scale constraints on either or both minimum hole sizes and minimum structural feature sizes. The new schemes are compared with methods and modified methods found in the literature.
“…The alternative methods in group 3 are mostly still in their infancy and have yet to be successfully applied to advanced problems with many constraints. There are also methods that are hybrids between categories 1 and 2 (Zhou et al, 2001;Cardoso and Fonseca, 2003). Here, the box-constraints of the optimization algorithm are modified according to a filtering scheme, resulting in local gradient controllike behavior.…”
In order to ensure manufacturability and mesh-independence in density-based topology optimization schemes it is imperative to use restriction methods. This paper introduces a new class of morphology based restriction schemes which work as density filters, i.e. the physical stiffness of an element is based on a function of the design variables of the neighboring elements. The new filters have the advantage that they eliminate grey scale transitions between solid and void regions. Using different test examples, it is shown that the schemes in general provide black and white designs with minimum length-scale constraints on either or both minimum hole sizes and minimum structural feature sizes. The new schemes are compared with methods and modified methods found in the literature.
“…Currently, there is a need of efficient engineering methodologies to design parts and structures in order to save material, time and costs [11]. Thus, in recent years, there has been increasing interest in methods that automatically obtain optimized structures from performance conditions specified by the designer [12].…”
Section: Topology Optimization Methods For Fgm Designmentioning
confidence: 99%
“…Even though these methods are useful, the number of design variables used in the optimization problem are higher than those used in the SIMP model. Additionally, homogenization models require a dependence model for the material properties with respect to the geometric parameters of the unit cell, which complicates their implementation [11].…”
Section: Basics Of the Topology Optimization Methodsmentioning
Functionally graded materials (FGMs) are a new class of bio-inspired composite materials made from different material phases, in which their volume fraction changes gradually towards a particular direction. Accordingly, continuous changes in the composition, microstructure and porosity of the graded materials results in material properties gradients; for this reason, the material properties move smoothly and continuously from one surface to another, eliminating the interface problem. Hence, with appropriate design, FGMs can develop better properties than their homogeneous counterpart due to their better designability. One potential employment of FGMs is as damper or energy absorber in dynamic applications, in which optimization techniques such as the topology optimization method (TOM) can contribute to a better performance in relation to a non-optimized design. In this chapter, functionally graded structures are designed with and without the TOM in order to explore the advantages of the FGM concept in low-velocity impact condition, which is a special case in the world of dynamic analysis, and has interest for designing machinery parts and components.
“…The procedure converges when the changes in design variables from iteration to iteration are below than 10 À3 (Rubio, 2005). Moreover, in order to avoid the traditional mesh dependency and checkerboard (regions with alternating solid and void element) problems in topology optimization (Bendsøe and Sigmund, 2003), a filter (Cardoso and Fonseca, 2003) is implemented by using a filter radius of eight neighboring elements.…”
Section: Characterization Of Electro-thermally Driven Microgrippermentioning
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