A homogenization method for shape and topology optimization

Suzuki, Katsuyuki; Kikuchi, Noboru

doi:10.1016/0045-7825(91)90245-2

Cited by 769 publications

(285 citation statements)

References 19 publications

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“…Ever since the first time Bendsøe [1], Suzuki and Kikuchi [2] used homogenization based approach to solve structural topology optimization problems, many scholars had focused their attention on this appealing filed of structure optimization. The latter researches proposed the solid isotropic material with penalization (SIMP) method [3][4][5] which made it possible to gain practical structure design through topology optimization, the ESO method [6], and the level set method [7], etc.…”

Section: Introductionmentioning

confidence: 99%

Backbone cup – a structure design competition based on topology optimization and 3D printing

Zhu

Yang

Zhang

2016

Int. J. Simul. Multisci. Des. Optim.

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-This paper addresses a structure design competition based on topology optimization and 3D Printing, and proposes an experimental approach to efficiently and quickly measure the mechanical performance of the structures designed using topology optimization. Since the topology optimized structure designs are prone to be geometrically complex, it is extremely inconvenient to fabricate these designs with traditional machining. In this study, we not only fabricated the topology optimized structure designs using one kind of 3D Printing technology known as stereolithography (SLA), but also tested the mechanical performance of the produced prototype parts. The finite element method is used to analyze the structure responses, and the consistent results of the numerical simulations and structure experiments prove the validity of this new structure testing approach. This new approach will not only provide a rapid access to topology optimized structure designs verifying, but also cut the turnaround time of structure design significantly.

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Section: Introductionmentioning

confidence: 99%

Backbone cup – a structure design competition based on topology optimization and 3D printing

Zhu

Yang

Zhang

2016

Int. J. Simul. Multisci. Des. Optim.

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“…The underlying assumption of AH is the periodicity of RVE and field quantities at macro and microscopic scales. AH method has been widely used in multiscale analysis of composite materials (Kalamkarov et al, 2009;Kanouté et al, 2009), topology optimization (Bendsøe and Kikuchi, 1988;Bendsøe and Sigmund, 2003;Díaaz and Kikuchi, 1992;Guedes and Kikuchi, 1990;Hassani and Hinton, 1998;Suzuki and Kikuchi, 1991), and hierarchical design of materials and structures (Coelho et al, 2008;Coelho et al, 2011;Gonçalves Coelho et al, 2011;Rodrigues et al, 2002).…”

Section: Fatigue Analysis Of Cellular Materialsmentioning

confidence: 99%

Fatigue design of a mechanically biocompatible lattice for a proof-of-concept femoral stem

Khanoki

Pasini

2013

Journal of the Mechanical Behavior of Biomedical Materials

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A methodology is proposed to design a spatially periodic microarchitectured material for a twodimensional femoral implant under walking gait conditions. The material is composed of a graded lattice with controlled property distribution that minimizes concurrently bone resorption and interface failure. The periodic microstructure of the material is designed for fatigue fracture caused by cyclic loadings on the hip joint as a result of walking. The bulk material of the lattice is Ti6AL4V and its microstructure is assumed free of defects. The Soderberg diagram is used for the fatigue design under multiaxial loadings. Two cell topologies, square and Kagome, are chosen to obtain optimized property gradients for a two-dimensional implant. Asymptotic homogenization (AH) theory is used to address the multiscale mechanics of the implant as well as to capture the stress and strain distribution at both the macro and the microscale. The microstress distribution found with AH is also compared with that obtained from a detailed finite element analysis. For the maximum value of the von Mises stress, we observe a deviation of 18.6 % in unit cells close to the implant boundary, where the AH assumption of spatial periodicity of the fluctuating fields ceases to hold. In the second part of the paper, the metrics of bone resorption and interface shear stress are used to benchmark the graded cellular implant with existing prostheses made of fully dense titanium implant.The results show that the amount of initial postoperative bone loss for square and kagome lattice implants decreases, respectively, by 53.8% and 58%. In addition, the maximum shear interface failure at the distal end is significantly reduced by about 79%.A set of proof-of-concepts of planar implants have been fabricated via Electron Beam Melting (EBM) to demonstrate the manufacturability of Ti6AL4V into graded lattices with alternative cell size. Optical microscopy has been used to measure the morphological parameters of the cellular microstructure, including cell wall thickness and pore size, and compared them with the nominal values. No sign of fracture or incomplete cell walls was observed, an assessment that shows the satisfactory metallurgical bond of cell walls and the structural integrity of the implants.

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“…The concept of composite media not only comes directly from the physical world but also provides a theoretically sound means for relaxation of variational problems -the problem of optimum topology design (see [5], [22], [12], [2] or [14]) in the first rank of importance. It is a classical result of the homogenization theory that composites can be replaced by a macroscopically homogeneous medium whose material constants -the so called effective constants or effective moduli -depend on the microgeometry in which the (*) Manuscrit received March 10, 94.…”

Section: Abstract -The Microstructure Identification Problem Is Treamentioning

confidence: 99%

“…Since the single inclusion microgeometries belong to the « reasonable » (meaning : more or less manufacturable) classes» it is interesting to see how well they manage to cover the full G o -closure sets. Specifically, in [5] and [22], one uses only sub-optimal microstructures -rectangular inclusions -for relaxation of the optimum shape design problem. We study how big are the différences among the rectangular inclusion composites, the single inclusion composites, and the full G o -closure sets.…”

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confidence: 99%

Optimum composite material design

Haslinger¹,

Dvořák²

1995

ESAIM: M2AN

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A homogenization method for shape and topology optimization

Abstract: Shape and topology optimization of a linearly elastic structure is discussed using a modification of the homogenization method introduced by Bendsoe and Kikuchi together with various examples which may justify validity and strength of the present approach for plane structures.

Cited by 769 publications

References 19 publications

Backbone cup – a structure design competition based on topology optimization and 3D printing

Backbone cup – a structure design competition based on topology optimization and 3D printing

Fatigue design of a mechanically biocompatible lattice for a proof-of-concept femoral stem

Optimum composite material design

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