Structural Topology Optimization Using Frame Elements Based on the Complementary Strain Energy Concept for Eigen-Frequency Maximization

2005 ◽  
Author(s):  
Akihiro Takezawa ◽  
Shinji Nishiwaki ◽  
Kazuhiro Izui ◽  
Masataka Yoshimura
Keyword(s):  
Topology Optimization ◽  
Cross Sections ◽  
Strain Energy ◽  
Optimization Procedure ◽  
Optimization Method ◽  
Structural Topology ◽  
Energy Concept ◽  
Conceptual Design Phase ◽  
Complementary Strain ◽  
Topology Optimization Method

This paper discuses a new topology optimization method using frame elements for the design of mechanical structures at the conceptual design phase. The optimal configurations are determined by maximizing multiple eigen-frequencies in order to obtain the most stable structures for dynamic problems. The optimization problem is formulated using frame elements having ellipsoidal cross-sections, as the simplest case. Construction of the optimization procedure is based on CONLIN and the complementary strain energy concept. Finally, several examples are presented to confirm that the proposed method is useful for the topology optimization method discussed here.

A Method for Determining the Optimal Direction of the Principal Moment of Inertia in Frame Element Cross-Sections

2004 ◽  
Author(s):  
Akihiro Takezawa ◽  
Shinji Nishiwaki ◽  
Kazuhiro Izui ◽  
Masataka Yoshimura
Keyword(s):  
Topology Optimization ◽  
Cross Sections ◽  
Optimization Procedure ◽  
Optimization Method ◽  
Moment Of Inertia ◽  
Structural Topology ◽  
Principal Moment ◽  
Frame Element ◽  
Optimal Direction ◽  
Conceptual Design Phase

This paper discusses a method to determine the optimal direction of the principal moment of inertia in frames element cross-sections for the design of mechanical structures at the conceptual design phase. The direction in each frame element is determined by maximizing the structural stiffness. Construction of the optimization procedure is based on the KKT-conditions and the balance of bending moments applied to each frame element. This method is implemented as an application in a structural topology optimization procedure that uses frame elements. Finally, several examples are presented to confirm that the proposed method is useful for the topology optimization method discussed here.

Analogy of Strain Energy Density Based Bone-Remodeling Algorithm and Structural Topology Optimization

2008 ◽  
Vol 131 (1) ◽  
Author(s):  
In Gwun Jang ◽  
Il Yong Kim ◽  
Byung Man Kwak
Keyword(s):  
Topology Optimization ◽  
Energy Density ◽  
Bone Remodeling ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Optimization Method ◽  
Bone Adaptation ◽  
Structural Topology Optimization ◽  
Structural Topology ◽  
Topology Optimization Method

In bone-remodeling studies, it is believed that the morphology of bone is affected by its internal mechanical loads. From the 1970s, high computing power enabled quantitative studies in the simulation of bone remodeling or bone adaptation. Among them, Huiskes et al. (1987, “Adaptive Bone Remodeling Theory Applied to Prosthetic Design Analysis,” J. Biomech. Eng., 20, pp. 1135–1150) proposed a strain energy density based approach to bone remodeling and used the apparent density for the characterization of internal bone morphology. The fundamental idea was that bone density would increase when strain (or strain energy density) is higher than a certain value and bone resorption would occur when the strain (or strain energy density) quantities are lower than the threshold. Several advanced algorithms were developed based on these studies in an attempt to more accurately simulate physiological bone-remodeling processes. As another approach, topology optimization originally devised in structural optimization has been also used in the computational simulation of the bone-remodeling process. The topology optimization method systematically and iteratively distributes material in a design domain, determining an optimal structure that minimizes an objective function. In this paper, we compared two seemingly different approaches in different fields—the strain energy density based bone-remodeling algorithm (biomechanical approach) and the compliance based structural topology optimization method (mechanical approach)—in terms of mathematical formulations, numerical difficulties, and behavior of their numerical solutions. Two numerical case studies were conducted to demonstrate their similarity and difference, and then the solution convergences were discussed quantitatively.

A CAD-oriented structural topology optimization method

2020 ◽  
Vol 239 ◽  
pp. 106324 ◽  
Author(s):  
Lipeng Jiu ◽  
Weihong Zhang ◽  
Liang Meng ◽  
Ying Zhou ◽  
Liang Chen
Keyword(s):  
Topology Optimization ◽  
Optimization Method ◽  
Structural Topology Optimization ◽  
Structural Topology ◽  
Topology Optimization Method

A Structural Topology Optimization Method Using Beam Elements : Effect of Cross-Sectional Shape of Beam

2002 ◽  
Vol 2002.5 (0) ◽  
pp. 135-140
Author(s):  
Shinji Nishiwaki ◽  
Hidekazu Nishigaki ◽  
Yasuaki Tsurumi ◽  
Yoshio Kojima ◽  
Noboru Kikuchi ◽  
...  
Keyword(s):  
Topology Optimization ◽  
Optimization Method ◽  
Structural Topology Optimization ◽  
Structural Topology ◽  
Cross Sectional ◽  
Beam Elements ◽  
Sectional Shape ◽  
Topology Optimization Method

Multi-Functional Topology Optimization of Piezoresistive Nanocomposite Beams

2015 ◽  
Author(s):  
Ryan Seifert ◽  
Mayuresh Patil ◽  
Gary Seidel ◽  
Gregory Reich
Keyword(s):  
Topology Optimization ◽  
Cross Sections ◽  
Strain Energy ◽  
Optimization Method ◽  
Design Tool ◽  
Resistance Change ◽  
Functional Topology ◽  
Minimum Strain Energy ◽  
The Individual ◽  
Multifunctional Nanocomposites

This paper presents an analysis of optimization for multifunctional nanocomposites. A carbon nanotubeepoxy composite is optimized for maximum resistance change and minimum strain energy. Analysis uses a finite element method and includes the coupled physics of mechanics, electrostatics, and piezoresistivity. The problem is solved first for minimum strain energy, then two resistance maximization problems are solved. For all optimization, sensitivities are obtained analytically. After solving the individual problems a weighted sum approach is used in the multi-objective optimization of both minimizing the strain energy and maximizing the resistance change. Comments are made as to the effect of the topology optimization method as a design tool, on the shape of the optimized cross sections, and on the possible extensions on using the coupled physics topology optimization algorithm.

Structural Topology Optimization of the Column of Form Grinding Machine

2010 ◽  
Vol 455 ◽  
pp. 397-401
Author(s):  
S.G. Yao ◽  
Hang Li
Keyword(s):  
Topology Optimization ◽  
Optimization Design ◽  
Optimization Method ◽  
Structural Topology Optimization ◽  
Structural Topology ◽  
Constraint Condition ◽  
Structural Dynamic ◽  
Structural Dynamic Model ◽  
Grinding Machine ◽  
Topology Optimization Method

Based on Topology optimization method of continuum the structural dynamic model has been built by constraint condition of volume and objective function of column natural frequency. In order to improve precision the dynamic characteristics of non-design region have been considered in optimization process. The column of structural optimization design has been done by applying topology optimization. The quality has not only reduced, but also the dynamic characteristic of the column has been improved. Thus the design effect has been reached.

Compliant Mechanism Design Using a Strain Based Topology Optimization Method

2011 ◽  
Author(s):  
Xiaobao Liu ◽  
Euihark Lee ◽  
Hae Chang Gea ◽  
Ping An Du
Keyword(s):  
Topology Optimization ◽  
Mechanism Design ◽  
Strain Energy ◽  
Compliant Mechanism ◽  
Effective Strain ◽  
Optimization Method ◽  
Structural Rigidity ◽  
Applied Forces ◽  
Compliant Mechanism Design ◽  
Topology Optimization Method

Energy based topology optimization method has been used in the design of compliant mechanisms for many years. Although many successful examples from the energy based topology optimization have been presented, optimized configurations of these designs are often very similar to their rigid linkage counterparts except using compliant joints in place of rigid links. It is obvious that these complaint joints will endure large deformations under the applied forces in order to perform the specified motions and the large deformation will produce high stress which is very undesirable in compliant mechanism design. In this paper, a strain based topology optimization method is proposed to avoid localized high deformation design which is one of the drawbacks using strain energy formulation. Therefore, instead of minimizing the strain energy for structural rigidity, a global effective strain functional is minimized in order to distribute the deformation within the entire mechanism while maximizing the structural rigidity. Furthermore, the physical programming method is adopted to accommodate both flexibility and rigidity design objectives. Comparisons of design examples from both the strain energy based topology optimization and the strain based method are presented and discussed.

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