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.

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.

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.

An Evolutionary Soft-Add Topology Optimization Method for Synthesis of Compliant Mechanisms With Maximum Output Displacement

2017 ◽  
Vol 9 (5) ◽  
Author(s):  
Chih-Hsing Liu ◽  
Guo-Feng Huang ◽  
Ta-Lun Chen
Keyword(s):  
Topology Optimization ◽  
Compliant Mechanisms ◽  
Volume Fraction ◽  
Compliant Mechanism ◽  
Optimization Method ◽  
Computational Time ◽  
Maximum Output ◽  
Spring Stiffness ◽  
Output Displacement ◽  
Topology Optimization Method

This paper presents an evolutionary soft-add topology optimization method for synthesis of compliant mechanisms. Unlike the traditional hard-kill or soft-kill approaches, a soft-add scheme is proposed in this study where the elements are equivalent to be numerically added into the analysis domain through the proposed approach. The objective function in this study is to maximize the output displacement of the analyzed compliant mechanism. Three numerical examples are provided to demonstrate the effectiveness of the proposed method. The results show that the optimal topologies of the analyzed compliant mechanisms are in good agreement with previous studies. In addition, the computational time can be greatly reduced by using the proposed soft-add method in the analysis cases. As the target volume fraction in topology optimization for the analyzed compliant mechanism is usually below 30% of the design domain, the traditional methods which remove unnecessary elements from 100% turn into inefficient. The effect of spring stiffness on the optimized topology has also been investigated. It shows that higher stiffness values of the springs can obtain a clearer layout and minimize the one-node hinge problem for two-dimensional cases. The effect of spring stiffness is not significant for the three-dimensional case.

Evolutionary Topology Optimization for compliant mechanism design

2016 ◽  
Author(s):  
Claudia Marcela Pérez Madrid ◽  
Renato Pavanello ◽  
William Martins Vicente ◽  
Renato Picelli
Keyword(s):  
Topology Optimization ◽  
Mechanism Design ◽  
Compliant Mechanism ◽  
Compliant Mechanism Design

A simple evolutionary topology optimization procedure for compliant mechanism design

2007 ◽  
Vol 44 (1-2) ◽  
pp. 53-62 ◽  
Author(s):  
Rubén Ansola ◽  
Estrella Veguería ◽  
Javier Canales ◽  
José A. Tárrago
Keyword(s):  
Topology Optimization ◽  
Mechanism Design ◽  
Compliant Mechanism ◽  
Optimization Procedure ◽  
Compliant Mechanism Design
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