A new topology optimization approach based on Moving Morphable Components (MMC) and the ersatz material model

Zhang, Weisheng; Yuan, Jie; Zhang, Jian; Guo, Xu

doi:10.1007/s00158-015-1372-3

Cited by 402 publications

(158 citation statements)

References 36 publications

Supporting

Mentioning

157

Contrasting

Order By: Relevance

“…Discussion on the similarities and differences of these approaches has recently been reported in Sigmund and Maute (2013). We note also another recently proposed topology optimization approach using moving morphable components (Guo et al 2014;Zhang et al 2015Zhang et al , 2016.…”

Section: Introductionmentioning

confidence: 99%

Evolutionary topology optimization of elastoplastic structures

Xia

Fritzen

Breitkopf

2016

Struct Multidisc Optim

View full text Add to dashboard Cite

We have recently proposed in (Fritzen et al., Int J Numer Methods Eng 106 (6): 2016) an evolutionary topology optimization model for the design of multiscale elastoplastic structures, which is in general independent of the applied material law. Facing the variability of the final design for minor parameter changes when dealing with plastic structural designs, we further improve the robustness and the effectiveness of the BESO optimization procedure in this work by introducing a damping scheme on sensitivity numbers and by progressively reducing the sensitivity filtering radius. The damping scheme constraining the variance of the sensitivity numbers stabilizes the topological evolution process in particular for dissipative structural designs. By setting initially a large filter radius value and reducing it gradually, the emergence of the redundant structural branches, which are to be eliminated afterwards and Liang Xia are the main reasons deteriorating the design process, could be avoided. The robustness and the effectiveness of the improved model has been validated by means of benchmark numerical examples of conventional homogeneous structures.

show abstract

Section: Introductionmentioning

confidence: 99%

Evolutionary topology optimization of elastoplastic structures

Xia

Fritzen

Breitkopf

2016

Struct Multidisc Optim

View full text Add to dashboard Cite

show abstract

“…As in most topology optimization methods, the finite element method (FEM) with structured four‐node bilinear elements is employed in the displacement analysis. To enhance the computational efficiency, the ersatz material model is adopted for FEM analysis . Therefore, the elasticity tensor D e of the e th element is given by

D_{e} = \sum_{i}^{N} ((), \frac{1}{A_{e}} \int_{{normalΩ}_{e}} ρ_{i} ((), Φ) d normalΩ) D_{i}, e = 1, 2, ⋯, N_{e},

where A e is the area of the e th element and the N e is the total number of the elements.…”

Section: Numerical Implementationmentioning

confidence: 99%

A level set–based method for stress‐constrained multimaterial topology optimization of minimizing a global measure of stress

Chu

Xiao

Gao

et al. 2018

Numerical Meth Engineering

View full text Add to dashboard Cite

Summary In multimaterial topology optimization of minimizing a global measure of stress, the maximum stresses in different materials may not satisfy the strength design requirements simultaneously if stress constraints for different materials are not considered. In this paper, a level set–based method is presented to handle the stress‐constrained multimaterial topology optimization of minimizing a global stress measure. Specifically, a multimaterial level set model is adopted to describe the structural topology, and a stress interpolation scheme is introduced for stress evaluation. Then, a stress penalty‐based topology optimization model is presented. Meanwhile, an adaptive adjusting scheme of the stress penalty factor is employed to improve the control of the local stress level. To solve the stress‐constrained multimaterial topology optimization problem minimizing the global measure of stress, the parametric level set method is employed, and the sensitivity analysis is carried out. Numerical examples are provided to demonstrate the effectiveness of the presented method. Results indicate that multimaterial structures with optimized global stress can be gained, and stress constraints for different materials can be satisfied simultaneously.

show abstract

“…Among the methods listed in Table 1, two methods represent the structure as the union of primitive-shaped geometric components with fixed shape but variable dimensions and position: the moving morphable components method (Guo et al 2014a(Guo et al , 2016Zhang et al 2016b;2017b), and the geometry projection method (Bell et al 2012;Norato et al 2015;Zhang et al 2016a). The former method performs the topology optimization of a) 2d-structures, by employing as geometric components rectangles, approximated via superellipses, and quadrilateral shapes with two opposite sides described by polynomial and trigonometric curves; and b) 3d-structures, by using cuboids.…”

Section: Introductionmentioning

confidence: 99%

“…Section 3 describes the projection of the supershapes onto a density field for the analysis. The computation of the signed distance to (Bell et al 2012(Norato et al 2015, 2016 (Zhang et al 2016a) Union of rectangular bars with straight (Bell et al 2012) or semicircular (Norato et al 2015) (Guo et al 2014b), 2016a (Zhang et al 2016b), 2016b (Guo et al 2016), 2017(Zhang et al 2017b Union of rectangles approximated as superellipses (Guo et al 2014b), or curved quadrilaterals with polynomial or trigonometric sides (Zhang et al 2016b;Guo et al 2016) Positions and orientation of discrete elements, dimensions (Guo et al 2014b) and curve parameters (Zhang et al 2016b;Guo et al 2016) Maximum of Heaviside function of individual geometric components XFEM to follow level set (Guo et al 2014b;Zhang et al 2016b), ersatz material from average of nodal smooth Heaviside (Guo et al 2016) Through union of Heavisides (bars merge, separate and are engulfed in other bars); no component insertion XFEM (Guo et al 2014b;…”

Section: Introductionmentioning

confidence: 99%

Topology optimization with supershapes

Norato

2018

Struct Multidisc Optim

View full text Add to dashboard Cite

This work presents a method for the continuum-based topology optimization of structures whereby the structure is represented by the union of supershapes. Supershapes are an extension of superellipses that can exhibit variable symmetry as well as asymmetry and that can describe through a single equation, the so-called superformula, a wide variety of shapes, including geometric primitives. As demonstrated by the author and his collaborators and by others in previous work, the availability of a feature-based description of the geometry opens the possibility to impose geometric constraints that are otherwise difficult to impose in density-based or level set-based approaches. Moreover, such description lends itself to direct translation to computer aided design systems. This work is an extension of the author's group previous work, where it was desired for the discrete geometric elements that describe the structure to have a fixed shape (but variable dimensions) in order to design structures made of stock material, such as bars and plates. The use of supershapes provides a more general geometry description that, using a single formulation, can render a structure made exclusively of the union of geometric primitives. It is also desirable to retain hallmark advantages of existing methods, namely the ability to employ a fixed grid for the analysis to circumvent re-meshing and the availability of sensitivities to use robust and efficient gradient-based optimization methods. The conduit between the geometric representation of the supershapes and the fixed analysis discretization is, as in previous work, a differentiable geometry projection that maps the supershapes parameters onto a density field. The proposed approach is demonstrated on classical problems of 2-dimensional compliance-based topology optimization.

show abstract

A new topology optimization approach based on Moving Morphable Components (MMC) and the ersatz material model

Cited by 402 publications

References 36 publications

Evolutionary topology optimization of elastoplastic structures

Evolutionary topology optimization of elastoplastic structures

A level set–based method for stress‐constrained multimaterial topology optimization of minimizing a global measure of stress

Topology optimization with supershapes

Contact Info

Product

Resources

About