Shape optimization of microstructural designs subject to local stress constraints within an XFEM-level set framework

Published on Jun 1, 2017in Structural and Multidisciplinary Optimization4.542
· DOI :10.1007/S00158-016-1642-8
Lise Noël6
Estimated H-index: 6
(University of Liège),
Pierre Duysinx21
Estimated H-index: 21
(University of Liège)
Sources
Abstract
The present paper investigates the tailoring of bimaterial microstructures minimizing their local stress field exploiting shape optimization. The problem formulation relies on the extended finite element method (XFEM) combined with a level set representation of the geometry, to deal with complex microstructures and handle large shape modifications while working on fixed meshes. The homogenization theory, allowing extracting the behavior of periodic materials built from the repetition of a representative volume element (RVE), is applied to impose macroscopic strain fields and periodic boundary conditions to the RVE. Classical numerical homogenization techniques are adapted to the selected XFEM-level set framework. Following previous works by the authors on analytical sensitivity analysis (Noel et al. (2016)), the scope of the developed approach is extended to tackle the problem of stress objective or constraint functions. Finally, the method is illustrated by revisiting 2D classical shape optimization examples: finding the optimal shapes of single or multiple inclusions in a microstructure while minimizing its local stress field.
Figures & Tables
Download
📖 Papers frequently viewed together
2020
4 Authors (Timon Rabczuk, ..., Cosmin Anitescu)
References55
Newest
#1Lise Noël (University of Liège)H-Index: 6
#2Laurent Van Miegroet (University of Liège)H-Index: 9
Last. Pierre Duysinx (University of Liège)H-Index: 21
view all 3 authors...
The present work investigates the shape optimization of bimaterial structures. The problem is formulated using a level set description of the geometry and the extended finite element method (XFEM) to enable an easy treatment of complex geometries. A key issue comes from the sensitivity analysis of the structural responses with respect to the design parameters ruling the boundaries. Even if the approach does not imply any mesh modification, the study shows that shape modifications lead to difficu...
Source
#1Ahmad R. NajafiH-Index: 13
#2Masoud SafdariH-Index: 14
Last. Philippe H. GeubelleH-Index: 53
view all 3 authors...
Source
#1Pedro CoelhoH-Index: 11
#2Rui A. ReisH-Index: 1
Last. José M. Guedes (IST: Instituto Superior Técnico)H-Index: 19
view all 3 authors...
Source
#1Ahmad R. Najafi (UIUC: University of Illinois at Urbana–Champaign)H-Index: 13
#2Masoud Safdari (UIUC: University of Illinois at Urbana–Champaign)H-Index: 14
Last. Philippe H. GeubelleH-Index: 53
view all 4 authors...
#1Ahmad R. Najafi (UIUC: University of Illinois at Urbana–Champaign)H-Index: 13
#2Masoud Safdari (UIUC: University of Illinois at Urbana–Champaign)H-Index: 14
Last. Philippe H. Geubelle (UIUC: University of Illinois at Urbana–Champaign)H-Index: 53
view all 4 authors...
Abstract A gradient-based shape optimization scheme using an Interface-enriched Generalized Finite Element Method (IGFEM) is presented wherein the design geometry is projected onto a fixed mesh and the IGFEM is used for analysis. This approach eliminates the mesh distortion present in conventional Lagrangian shape optimization methods, as well as the need for remeshing. An analytical sensitivity analysis using both the adjoint or direct approaches is presented to compute derivatives of the objec...
Source
#1Erik Andreassen (DTU: Technical University of Denmark)H-Index: 13
#2Casper Schousboe Andreasen (DTU: Technical University of Denmark)H-Index: 14
Abstract Numerical homogenization is an efficient way to determine effective macroscopic properties, such as the elasticity tensor, of a periodic composite material. In this paper an educational description of the method is provided based on a short, self-contained Matlab implementation. It is shown how the basic code, which computes the effective elasticity tensor of a two material composite, where one material could be void, is easily extended to include more materials. Furthermore, extensions...
Source
Materials with good vibration damping properties and high stiffness are of great industrial interest. In this paper the bounds for viscoelastic composites are investigated and material microstructures that realize the upper bound are obtained by topology optimization. These viscoelastic composites can be realized by additive manufacturing technologies followed by an infiltration process. Viscoelastic composites consisting of a relatively stiff elastic phase, e.g. steel, and a relatively lossy vi...
Source
Source
#1Nico P. van Dijk (Uppsala University)H-Index: 9
#2Kurt Maute (CU: University of Colorado Boulder)H-Index: 46
Last. Fred van Keulen (TU Delft: Delft University of Technology)H-Index: 20
view all 4 authors...
This review paper provides an overview of different level-set methods for structural topology optimization. Level-set methods can be categorized with respect to the level-set-function parameterization, the geometry mapping, the physical/mechanical model, the information and the procedure to update the design and the applied regularization. Different approaches for each of these interlinked components are outlined and compared. Based on this categorization, the convergence behavior of the optimiz...
Source
#1Laurent Van Miegroet (University of Liège)H-Index: 9
Cited By22
Newest
#1Jian Zhang (TU Delft: Delft University of Technology)H-Index: 5
#2Fred van Keulen (TU Delft: Delft University of Technology)H-Index: 20
Last. Alejandro M. Aragón (TU Delft: Delft University of Technology)H-Index: 15
view all 3 authors...
Abstract null null We propose a fully immersed topology optimization procedure to design structures with tailored fracture resistance under linear elastic fracture mechanics assumptions for brittle materials. We use a level set function discretized by radial basis functions to represent the topology and the Interface-enriched Generalized Finite Element Method (IGFEM) to obtain an accurate structural response. The technique assumes that cracks can nucleate at right angles from the boundary, at th...
Source
#1Ying Zhou (NPU: Northwestern Polytechnical University)H-Index: 2
#2Jihong Zhu (NPU: Northwestern Polytechnical University)H-Index: 22
Last. YuanTong Gu (QUT: Queensland University of Technology)H-Index: 52
view all 0 authors...
Abstract null null In this paper, we propose a B-Spline Offset Feature (BSOF) for feature-driven topology optimization. The feature is inspired from the geometric morphology of worms characterized by an elongated cylindrical, bilaterally symmetric, and well-segmented body along a highly deformable directrix. B-spline is used to define the directrix with its outward and inward offsets outlining the BSOF. This definition endows the BSOF with high deformability such as self-folding and self-interse...
Source
#1Subhayan De (CU: University of Colorado Boulder)H-Index: 6
#2Kurt Maute (CU: University of Colorado Boulder)H-Index: 46
Last. Alireza Doostan (CU: University of Colorado Boulder)H-Index: 27
view all 3 authors...
This paper considers the design of structures made of engineered materials, accounting for uncertainty in material properties. We present a topology optimization approach that optimizes the structural shape and topology at the macroscale assuming design-independent uncertain microstructures. The structural geometry at the macroscale is described by an explicit level set approach, and the macroscopic structural response is predicted by the eXtended Finite Element Method (XFEM). We describe the mi...
#1Ruijie Zhao (Beihang University)
#2Junpeng Zhao (Beihang University)H-Index: 9
Last. Chun Jie Wang (Beihang University)H-Index: 8
view all 3 authors...
Source
#1A. Ferrer (École Polytechnique)H-Index: 92
#2P. Geoffroy-Donders (Arts et Métiers ParisTech)H-Index: 1
Last. Grégoire Allaire (École Polytechnique)H-Index: 49
view all 3 authors...
Lattice structures are periodic porous bodies which are becoming popular since they are a good compromise between rigidity and weight and can be built by additive manufacturing techniques. Their optimization has recently attracted some attention, based on the homogenization method, mostly for compliance minimization [1], [2], [3]. The goal of the present two-part work is to extend this lattice optimization to an objective function involving stress minimization. As is well known in structural opt...
Source
#1Cong Hong Phong Nguyen (CAU: Chung-Ang University)H-Index: 4
#2Young Wook Choi (CAU: Chung-Ang University)H-Index: 30
The emergence of additive manufacturing (AM) has enabled the design of complex structures with high performance, such as functionally graded cellular structures (FGCSs). Concurrent topology optimization is commonly utilized for designing FGCSs; however, this approach suffers from an extremely high computational cost due to the complexity of the design problem. Recently, level-set-based methods, which rely on the implicit-based modeling technique, have gained increased attention and been consider...
Source
#1Pedro Coelho (NOVA: Universidade Nova de Lisboa)H-Index: 11
#2Bruno C. Barroca (Katholieke Universiteit Leuven)
Last. José M. Guedes (IST: Instituto Superior Técnico)H-Index: 19
view all 4 authors...
Strength-oriented optimization of porous periodic microstructures impacts on efficient design of load-bearing lightweight structures avoiding mechanical failure. In this work, the maximal von-Mises stress, predicted by homogenization theory on a planar representative unit-cell domain, is minimized using either shape or topology design changes. Plane stress and linear behaviour are assumed. Two benchmarks problems are revisited, bulk and shear loads. Firstly, a fully stressed design is sought on ...
Source
#1Lee Alacoque (Caltech: California Institute of Technology)H-Index: 2
#2Ryan T. Watkins (Caltech: California Institute of Technology)H-Index: 1
Last. Ali Yeilaghi Tamijani (Caltech: California Institute of Technology)H-Index: 11
view all 3 authors...
Abstract To take advantage of multi-material additive manufacturing technology using mixtures of metal alloys, a topology optimization framework is developed to synthesize high-strength spatially periodic metamaterials possessing unique thermoelastic properties. A thermal and mechanical stress analysis formulation based on homogenization theory is developed and is used in a regional scaled aggregation stress constraint method. Since specific load cases are not always known beforehand, a method o...
Source
#1Bhavik D. UpadhyayH-Index: 1
#2Sunil S. SonigraH-Index: 1
Last. Sachin D. Daxini (Gujarat Technological University)H-Index: 4
view all 3 authors...
Abstract This review presents developments in structural shape optimization post 2000 from perspective of numerical analysis techniques. Traditional shape optimization with FEM has undergone considerable transformation as developments in CAD, numerical analysis techniques and optimization algorithms have contributed significantly in improving it. Mesh dependency and inconsistent description of the geometry for design and analysis models remained major challenges in traditional FEM based shape op...
Source
#1Lei Zhao (NPU: Northwestern Polytechnical University)H-Index: 6
#2Bin Xu (NPU: Northwestern Polytechnical University)H-Index: 9
Last. Jianhua Rong (CSUST: Changsha University of Science and Technology)H-Index: 8
view all 4 authors...
Abstract This paper proposes a concurrent topology optimization method of macrostructural material distribution and periodic microstructure considering dynamic stress response under random excitations. The optimization problem is the minimization of the dynamic stress response of the macrostructure subject to volume constraints in both macrostructure and microstructure. To ensure the safety of the macrostructure, a new relaxation method is put forward to establish a relationship between the dyna...
Source
This website uses cookies.
We use cookies to improve your online experience. By continuing to use our website we assume you agree to the placement of these cookies.
To learn more, you can find in our Privacy Policy.