Multi-objective shape optimization for maximizing stiffness in thermo-elastic fields

Katamine, Eiji; Arai, Yuto

doi:10.1299/transjsme.16-00490

Cited by 3 publications

(3 citation statements)

References 14 publications

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“…However, since the purpose of this study is to maximize the stiffness, not the strength, it is unavoidable. In fact, the similar results can be seen in other studies (Azegami, 2020, Katamine andArai, 2017) on shape optimization for stiffness maximization based on minimizing mean compliance.…”

Section: Structure On Cavity Flowsupporting

confidence: 89%

“…On the other hand, the authors have proposed solutions to fundamental shape optimization problems for maximizing the stiffness of the linear thermoelastic bodies (Katamine and Arai, 2017) and for minimizing the dissipative energy in viscous flow fields (Katamine et al 2005), and demonstrated their validity. These solutions use the H 1 gradient method…”

Section: Introductionmentioning

confidence: 99%

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Shape optimization for stiffness maximization of geometrically nonlinear structure by considering fluid-structure-interaction

Katamine

Kawai

Takahashi

2021

Mechanical Engineering Letters

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This paper presents numerical solution to a shape optimization for stationary fluid structure interactive fields. In the fluid structure interactive analysis, a weak coupled analysis is used to alternately analyze the governing equations of the flow field domain and the structural field considering geometrically nonlinear. A mean compliance minimization problem is formulated in order to achieve stiffness maximization on the structural field. Shape derivative, which means the sensitivity in the shape optimization problem, is derived theoretically by using the Lagrange multiplier method and adjoint variable method, and the formulae of the shape derivative with respect to domain variation of the distribution function. Reshaping is carried out by the H 1 gradient method proposed as an approach to solving shape optimization problems. Numerical analysis program for the problem is developed by using FreeFEM, and validity of proposed method is confirmed by numerical results of 2D problems.

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Section: Structure On Cavity Flowsupporting

confidence: 89%

Section: Introductionmentioning

confidence: 99%

Shape optimization for stiffness maximization of geometrically nonlinear structure by considering fluid-structure-interaction

Katamine

Kawai

Takahashi

2021

Mechanical Engineering Letters

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“…The performance function shown in Eq. ( 1), which is expressed by the linear relaxation techniques that are often employed in multi-objective optimization, is used (Katamine and Arai, 2017;Mohamad et al, 2023). The performance function J is a performance index that weights the performance function J 1 to achieve minimal strain energy as shown in Eq.…”

Section: Topology Optimization For Multi-objective Optimization Problemsmentioning

confidence: 99%

Development of a novel non-positive definite correspondence modified optimality criteria method for multi-objective density-based topology optimization

KISHIDA,

KURAHASHI

2023

Mechanical Engineering Journal

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The aim of this study is to propose a new modified optimality criteria method for non-positive definiteness in multi-objective density-based topology optimization problems. Our proposed modified optimality criteria method is a density update method that was developed by incorporating the concept of Newton's method into the conventional optimality criteria method. Topology optimization for strain energy minimization and von Mises stress minimization problems were performed separately, and actual experiments revealed the characteristics of each. Each optimization problem setting has its individual advantages: strain energy minimization is computationally stable, whereas von Mises stress minimization obtains a higher-strength structure. Therefore, in this study, to take advantage of both, we performed multi-objective optimization using the modified optimality criteria method. Since updating was not possible with the previously proposed modified optimality criteria method in multi-objective optimization problems, we propose incorporating mapping to enable it to be updated. As a numerical example problem, topology optimization was performed on the MBB beam model and gripper model for a robotic arm using the conventional optimality criteria method and our proposed mapping-based modified optimality criteria method to compare the update methods. Numerical example of the MBB beam model demonstrate that the mapping-based modified optimality criteria method is independent of the move-limit and can be updated. The mapping-based modified optimality criteria method also has a small number of arbitrary parameter settings that can cause problems for engineers because the weighting factor in the optimality criteria method is set in each element. Numerical example of the gripper model are used here to investigate the speed of updating the mapping-based modified optimality criteria method and guidelines for setting the appropriate weight coefficients of performance function to create a design.

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Shape optimization analysis considering a rotational body in a flow field based on the adjoint variable and the finite element methods

Kurahashi

Ozeki

Katamine

2019

JFST

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Multi-objective shape optimization for maximizing stiffness in thermo-elastic fields

Cited by 3 publications

References 14 publications

Shape optimization for stiffness maximization of geometrically nonlinear structure by considering fluid-structure-interaction

Shape optimization for stiffness maximization of geometrically nonlinear structure by considering fluid-structure-interaction

Development of a novel non-positive definite correspondence modified optimality criteria method for multi-objective density-based topology optimization

Shape optimization analysis considering a rotational body in a flow field based on the adjoint variable and the finite element methods

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