scholarly journals Level set-based BEM topology optimization method for maximizing total potential energy of thermal problems

2022 ◽  
Vol 182 ◽  
pp. 121921
Author(s):  
Guoxian Jing ◽  
Jiao Jia ◽  
Jiawei Xiang
Keyword(s):  
Topology Optimization ◽  
Potential Energy ◽  
Level Set ◽  
Optimization Method ◽  
Total Potential Energy ◽  
Total Potential ◽  
Topology Optimization Method

Level Set-Based Topology Optimization Method for Thermal Problems Considering Design-Dependent Boundary Effects

2009 ◽  
Author(s):  
Takayuki Yamada ◽  
Shinji Nishiwaki ◽  
Atsuro Iga ◽  
Kazuhiro Izui ◽  
Masataka Yoshimura
Keyword(s):  
Field Theory ◽  
Topology Optimization ◽  
Level Set ◽  
Phase Field ◽  
Three Dimensional ◽  
Optimization Method ◽  
Interface Energy ◽  
Total Potential ◽  
Level Set Function ◽  
Topology Optimization Method

This paper proposes a new level set-based topology optimization method for thermal problems that deal with generic heat transfer boundaries including design-dependent boundary conditions, based on the level set method and the concept of the phase field theory. First, a topology optimization method using a level set model incorporating a fictitious interface energy derived from the concept of the phase field theory is briefly discussed. Next, a generic optimization problem for thermal problems is formulated based on the concept of total potential energy. An optimization algorithm that uses the Finite Element Method when solving the equilibrium equation and updating the level set function is then constructed. Finally, several three-dimensional numerical examples are provided to confirm the utility and validity of the proposed topology optimization method.

A Level Set-Based Topology Optimization Method for Maximizing Thermal Diffusivity in Problems Including Design-Dependent Effects

2011 ◽  
Vol 133 (3) ◽  
Author(s):  
Takayuki Yamada ◽  
Kazuhiro Izui ◽  
Shinji Nishiwaki
Keyword(s):  
Topology Optimization ◽  
Thermal Diffusivity ◽  
Level Set ◽  
Design Method ◽  
Optimization Method ◽  
Interface Energy ◽  
Total Potential ◽  
Level Set Function ◽  
Set Function ◽  
Topology Optimization Method

This paper proposes an optimum design method, based on our level set-based topology optimization method, for maximizing thermal diffusivity in problems dealing with generic heat transfer boundaries that include design-dependent boundary conditions. First, a topology optimization method using a level set model incorporating a fictitious interface energy for regularizing the topology optimization is briefly discussed. Next, an optimization method for maximizing thermal diffusivity is formulated based on the concept of total potential energy. An optimization algorithm that uses the finite element method when solving the equilibrium equation and updating the level set function is then constructed. Finally, several numerical examples are provided to confirm the utility and validity of the proposed topology optimization method.

An Optimization Method for the Static Balancing of Manipulators Using Springs

2020 ◽  
Author(s):  
Jieyu Wang ◽  
Xianwen Kong
Keyword(s):  
Potential Energy ◽  
Objective Function ◽  
Multiple Solutions ◽  
Optimization Method ◽  
Total Potential Energy ◽  
Static Balancing ◽  
Attachment Point ◽  
Total Potential

Abstract This paper discusses a novel optimization method to design statically balanced manipulators. Only springs are used to balance the manipulators composed of revolute (R) joints. Since the total potential energy of the system is constant when statically balanced, the sum of squared differences between the two potential energy when giving different random values of joint variables is set as the objective function. Then the optimization tool of MATLAB is used to obtain the spring attachment points. The results show that for a 1-link manipulator mounted on an R joint, in addition to attaching the spring right above the R joint, the attachment point can have offset. It also indicates that an arbitrary spatial manipulator with n link, whose weight cannot be neglected, can be balanced using n springs. Using this method, the static balancing can be readily achieved, with multiple solutions.

Displacement and Stress Constrained Topology Optimization

2013 ◽  
Author(s):  
Meisam Takalloozadeh ◽  
Krishnan Suresh
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Topology Optimization ◽  
Level Set ◽  
Numerical Experiments ◽  
Optimization Method ◽  
Stress Constraints ◽  
Element Analysis ◽  
The Finite Element Analysis ◽  
Topology Optimization Method

The objective of this paper is to demonstrate a topology optimization method subject to displacement and stress constraints. The method does not rely on pseudo-densities; instead it exploits the concept of topological level-set where ‘partial’ elements are avoided. Consequently: (1) the stresses are well-defined at all points within the evolving topology, and (2) the finite-element analysis is robust and efficient. Further, in the proposed method, a series of topologies of decreasing volume fractions are generated in a single optimization run. The method is illustrated through numerical experiments in 2D.

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