Elasto-plastic Shape Optimization Using the Level Set Method

Maury, Aymeric; Allaire, Grégoire; Jouve, François

doi:10.1137/17m1128940

Cited by 23 publications

(19 citation statements)

References 57 publications

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“…Li et al [194] employed kinematic hardening model based on von Mises plasticity to capture the well-known Bauschinger effect under cyclic loads. Recently, a elastoplastic shape optimization was explored via the level-set method by Maury et al [195].…”

Section: Nonlinear (Multi-material) Topology Optimizationmentioning

confidence: 99%

Current and future trends in topology optimization for additive manufacturing

Liu

Gaynor

Chen

et al. 2018

Struct Multidisc Optim

634

249

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Manufacturing-oriented topology optimization has been extensively studied the past two decades, in particular for the conventional manufacturing methods, e.g., machining and injection molding or casting. Both design and manufacturing engineers have benefited from these efforts because of the close-tooptimal and friendly-to-manufacture design solutions. Recently, additive manufacturing (AM) has received significant attention from both academia and industry. AM is characterized by producing geometrically complex components layer-by-layer, and greatly reduces the geometric complexity restrictions imposed on topology optimization by conventional manufacturing. In other words, AM can make near-full use of the freeform structural evolution of topology optimization. Even so, new rules and restrictions emerge due to the diverse and intricate AM processes, which should be carefully addressed when developing the AM-specific topology optimization algorithms. Therefore, the motivation of this perspective paper is to summarize the state-of-art topology optimization methods for a variety of AM topics. At the same time, this paper also expresses the authors' perspectives on the challenges and opportunities in these topics. The hope is to inspire both researchers and engineers to meet these challenges with innovative solutions.

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Section: Nonlinear (Multi-material) Topology Optimizationmentioning

confidence: 99%

Current and future trends in topology optimization for additive manufacturing

Liu

Gaynor

Chen

et al. 2018

Struct Multidisc Optim

634

249

View full text Add to dashboard Cite

show abstract

“…On the boundary of the cone K called the yield surface, where ϕ(σ, χ) = 0, the plastic strain can be nonzero. The evolution of the plastic strain ε p and the internal variable ξ is governed by the associative flow rule [7,10] stating that the rates of plastic strain and the internal variable belong to the normal cone N K to the set K at a point (σ, χ).…”

Section: Elasto-plastic Contactmentioning

confidence: 99%

“…Structural optimization of elasto-plastic structures has been investigated, among others, in [1,8,10,11,16]. A major difficulty in shape or topology optimization of elasto-plastic problems as the pathdependent problems is the sensitivity analysis [10]. Therefore the original structural optimization problem has to be regularized either using the filter technique or different penalization techniques.…”

Section: Introductionmentioning

confidence: 99%

Topology Optimization of Elasto-Plastic Structures in Contact

Myśliński¹

2021

14th WCCM-ECCOMAS Congress

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This paper is concerned with the analysis as well as the numerical solution of the structural optimization problem for bilateral frictional contact problem where the static elasto-plastic material model with linear kinematic hardening rather than elastic material model is assumed. The displacement and stress of the bodies in elasto-plastic contact with a given friction are governed by the system of the coupled variational inequalities. In these problems usually very high stress appear along the surfaces in contact. It leads to wear or fatigue of the contacting surfaces. Therefore the aim of the topological optimization is to find such distribution of the material filling the body in contact to minimize the contact stress. Using von Mises yield function as well as the regularization and penalization techniques the original system of variational inequalities is transformed into the system of coupled nonlinear equations. The derivative of the cost functional with respect to the perturbation of the domain occupied by the body in contact is calculated using the material derivative method. Finite element method is used as the discretization method. In the numerical computations generalized Newton method is used to solve this contact problem. The level set method is used to describe and govern the evolution of the domain shape in the design space where the direction of the evolution is determined based on the calculated shape derivative. The results of computation are provided and discussed.

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“…Optimal control of elasto-plastic deformation has been considered from a mathematical perspective in various articles, in particular concerning the static case, see e.g. [10,14] and the references therein. When it comes to the (physically much more reasonable) quasi-static case however, the literature becomes rather scarce.…”

mentioning

confidence: 99%

“…The smoothing parameter δ of the max-function in (14) is set to 10 −8 . During the numerical experiments, it turned out that this parameter appears to have only little influence on the results and the performance of the algorithm so that we simply fix it to this value.…”

mentioning

confidence: 99%

Optimal control of perfect plasticity part I: Stress tracking

Meyer¹,

Walther²

2022

MCRF

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The paper is concerned with an optimal control problem governed by the rate-independent system of quasi-static perfect elasto-plasticity. The objective is to optimize the stress field by controlling the displacement at prescribed parts of the boundary. The control thus enters the system in the Dirichlet boundary conditions. Therefore, the safe load condition is automatically fulfilled so that the system admits a solution, whose stress field is unique. This gives rise to a well defined control-to-state operator, which is continuous but not Gâteaux differentiable. The control-to-state map is therefore regularized, first by means of the Yosida regularization resp. viscous approximation and then by a second smoothing in order to obtain a smooth problem. The approximation of global minimizers of the original non-smooth optimal control problem is shown and optimality conditions for the regularized problem are established. A numerical example illustrates the feasibility of the smoothing approach.

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Elasto-plastic Shape Optimization Using the Level Set Method

Cited by 23 publications

References 57 publications

Current and future trends in topology optimization for additive manufacturing

Current and future trends in topology optimization for additive manufacturing

Topology Optimization of Elasto-Plastic Structures in Contact

Optimal control of perfect plasticity part I: Stress tracking

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