Research of Topology Optimization of Nodal Density Based on Bilinear Interpolation

2015 ◽  
Vol 713-715 ◽  
pp. 1825-1829
Author(s):  
Yi Xian Du ◽  
Shuang Qiao Yan ◽  
Huang Hai Xie ◽  
Yan Zhang ◽  
Qi Hua Tian
Keyword(s):  
Topology Optimization ◽  
Density Field ◽  
Design Domain ◽  
Checkerboard Pattern ◽  
Bilinear Interpolation ◽  
Fixed Design ◽  
Numerical Instabilities ◽  
Nature Of Mathematics ◽  
Nodal Density ◽  
Smooth Density

With the purpose to overcome the numerical instabilities and to generate more distinct structural layouts in the topology optimization, by using bilinear interpolation function, a topology optimization model of density interpolation based on nodal density is established, smooth density field is constructed. This method can ensure that the density field in the fixed design domain owns C0 continuity, and checkerboard patterns are naturally avoided in the nature of mathematics. After adding the sensitivity filtering, the optimal structures are smoother and have lesser details, which is helpful for manufacturing. Two numerical examples show that not only checkerboard pattern can be solved by the proposed method, but also the middle density nodal can be suppressed effectively.

Domain Composition Method for Structural Optimization

2014 ◽  
Author(s):  
Wei Song ◽  
Hae Chang Gea ◽  
Bin Zheng
Keyword(s):  
Sensitivity Analysis ◽  
Topology Optimization ◽  
Structural Optimization ◽  
Design Domain ◽  
Material Distribution ◽  
Numerical Examples ◽  
Composition Method ◽  
Domain Composition ◽  
Fixed Design ◽  
Design Requirements

Conventionally, design domain of topology optimization is predefined and is not adjusted in the design optimization process since designers are required to specify the design domain in advance. However, it is difficult for a fixed design domain to satisfy design requirements such as domain sizing adjustment or boundaries change. In this paper, Domain Composition Method (DCM) for structural optimization is presented and it deals with the design domain adjustment and the material distribution optimization in one framework. Instead of treating design domain as a whole, DCM divides domain into several subdomains. Additional scaling factors and subdomain transformations are applied to describe changes between different designs. It then composites subdomains and solve it as a whole in the updated domain. Based on the domain composition, static analysis with DCM and sensitivity analysis are derived. Consequently, the design domain and the topology of the structure are optimized simultaneously. Finally, the effectiveness of the proposed DCM for structural optimization is demonstrated through different numerical examples.

Topology Optimization with a Penalty Factor in Optimality Criteria

2011 ◽  
Vol 317-319 ◽  
pp. 2466-2472 ◽  
Author(s):  
Xiu Peng Wang ◽  
Shou Wen Yao
Keyword(s):  
Topology Optimization ◽  
Design Variable ◽  
Numerical Stability ◽  
Optimality Criteria ◽  
Penalty Factor ◽  
Structural Density ◽  
Optimality Criteria Method ◽  
Numerical Instabilities ◽  
Nodal Density ◽  
Intermediate Density

Topology optimization is one of the most important methods of reducing the weight of structure. Optimality Criteria method (OC) as a heuristic way can be used to deal with this problem efficiently. Popular SIMP method implements micro-structural density as the design variable. During the process of optimization, numerical instabilities are always observed; Moreover, higher penalty factor is not better for decreasing intermediate density elements. In this paper a penalty factor is imposed in OC method, and a relation between the filtering area and elements is also obtained. Meanwhile, the nodal density is used as design variable for more smoothing boundary. The results show that numerical stability can be obtained, checkerboard patterns haven’t been observed, and the clear boundary of structure has been developed.

Topology Optimization for Steady-State Heat Transfer Problems Including Design-Dependent Effects

2008 ◽  
Author(s):  
Atsuro Iga ◽  
Shinji Nishiwaki ◽  
Kazuhiro Izui ◽  
Masataka Yoshimura
Keyword(s):  
Heat Transfer ◽  
Topology Optimization ◽  
Optimization Method ◽  
Homogenization Method ◽  
Heaviside Function ◽  
Design Domain ◽  
Transfer Coefficients ◽  
Total Potential ◽  
Fixed Design ◽  
Topology Optimization Method

In this paper, a topology optimization method is constructed for thermal problems with generic heat transfer boundaries in a fixed design domain that includes design-dependent effects. First, the topology optimization method for thermal problems is briefly explained using a homogenization method for the relaxation of the design domain, where a continuous material distribution is assumed, to suppress numerical instabilities and checkerboards. Next, a method is developed for handling heat transfer boundaries between material and void regions that appear in the fixed design domain and move during the optimization process, using the Heaviside function as a function of node-based material density to extract the boundaries of the target structure being optimized so that the heat transfer boundary conditions can be set. Shape dependencies concerning heat transfer coefficients are also considered in the topology optimization scheme. The optimization problem is formulated using the concept of total potential energy and an optimization algorithm is constructed using the Finite Element Method and Sequential Linear Programming. Finally, several numerical examples are presented to confirm the usefulness of the proposed method.

A Systematic Topology Optimization Approach for Optimal Stiffener Design

1998 ◽  
Author(s):  
Jian Hui Luo ◽  
Hae Chang Gea
Keyword(s):  
Topology Optimization ◽  
Location Problem ◽  
Eigenvalue Problems ◽  
Three Dimensional ◽  
Orthotropic Materials ◽  
Optimization Approach ◽  
Design Domain ◽  
Plate Structures ◽  
Shell Plate

Abstract A systematic topology optimization approach is developed to design the optimal stiffener of three dimensional shell/plate structures in static and eigenvalue problems. Optimal stiffener design involves the determination of the best location and orientation. In this paper, the stiffener location problem is solved by a microstructure-based design domain method and the orientation probelm is modeled as an optimal orientation problem of equivalent orthotropic materials, which is solved by a newly developed energy based method. Examples are presented to demonstrate the application of the proposed approach.

Topology Synthesis of Two-Phase Compliant Actuators

1999 ◽  
Author(s):  
Ole Sigmund
Keyword(s):  
Topology Optimization ◽  
Material Design ◽  
Optimization Method ◽  
The Other ◽  
Design Domain ◽  
Active Materials ◽  
Two Phase ◽  
Thermal Actuators ◽  
Compliant Actuators ◽  
Topology Optimization Method

Abstract This paper describes how the topology optimization method can be used as a tool for the synthesis of two-phase compliant actuators. Two materials, one or both being active materials, are distributed in a design domain such that the work performed on an elastic workpiece is maximized. The two-material design is obtained by introducing two variables per element. One variable determines the relative density of material in the element and the other variable determines the material type. Examples demonstrate the design of thermal actuators and gripping mechanisms.

Optimal Synthesis of Compliant Mechanisms Using Subdivision and Commercial FEA

2004 ◽  
Author(s):  
Patrick V. Hull ◽  
Stephen Canfield
Keyword(s):  
Topology Optimization ◽  
Mechanism Design ◽  
Compliant Mechanism ◽  
Rapid Prototype ◽  
Optimization Procedure ◽  
Design Tool ◽  
Design Parameters ◽  
Solid Model ◽  
Control Points ◽  
Numerical Instabilities

The field of distributed-compliance mechanisms has seen significant work in developing suitable topology optimization tools for their design. These optimal design tools have grown out of the techniques of structural optimization. This paper will build on the previous work in topology optimization and compliant mechanism design by proposing an alternative design space parameterization through control points and adding another step to the process, that of subdivision. The control points assist a specific design to be represented as a solid model during the optimization process. The process of subdivision creates an additional number of control points that help smooth the surface (for example a C2 continuous surface depending on the method of subdivision chosen) creating a manufacturable design free of traditional numerical instabilities. Note that these additional control points do not add to the number of design parameters. This alternative parameterization and description as a solid model effectively and completely separates the design variables from the analysis variables during the optimization procedure. The motivation behind this work is to avoid several of the numerical instabilities that occur in topology optimization and to create an automated design tool from task definition to functional prototype created on a CNC or rapid-prototype machine. This paper will describe the complaint mechanism design process including subdivision and will demonstrate the procedure on several common examples.

scholarly journals Automatic Position Information of Web-Openings of Building Using Minimized Strain Energy Topology Optimization

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Dongkyu Lee ◽  
Soomi Shin
Keyword(s):  
Topology Optimization ◽  
Building Design ◽  
Optimization Techniques ◽  
Design Parameters ◽  
Engineering Practice ◽  
Design Domain ◽  
Web Openings ◽  
Position Information ◽  
Design Information ◽  
Density Values

This study presents a new engineering practice and idea that material topology optimization results may be utilized to optimally decide the positions of web-openings of structural members in a building structure. Material topology optimization utilizes element densities as design parameters, that is, nominal constructional material, and then optimal material distributions of densities between voids (0) and solids (1) in a given design domain represent the determination of topology and shape. That means that regions with element density values become occupied by solids in a design domain, while there are only void phases in regions where no density values exist. Therefore, the void regions of topology optimization results may provide design information that decides appropriate depositions of web-opening in structure. Numerical examples demonstrate the efficiency of the present methodological design information using optimization techniques to automatically resolve the building design of proper deposition of web-openings.

Topology Optimization for Nonlinear Kirchhoff Plate Using RKPM

2011 ◽  
Vol 121-126 ◽  
pp. 545-549 ◽  
Author(s):  
Jian Ping Zhang ◽  
Yan Kun Jiang ◽  
Shu Guang Gong ◽  
Xin Liu
Keyword(s):  
Topology Optimization ◽  
Reproducing Kernel ◽  
Optimization Procedure ◽  
Particle Method ◽  
Kirchhoff Plate ◽  
Checkerboard Pattern ◽  
Reproducing Kernel Particle Method ◽  
Design Variables ◽  
Reproducing Kernel Particle ◽  
Criterion Method

In this paper, the topology optimization of nonlinear Kirchhoff plate was studied by using meshless Reproducing Kernel Particle Method (RKPM). The relative densities of nodes were chosen as design variables to eliminate the checkerboard pattern, and the visibility criterion method was used to dispose the discontinuity of RKPM approximation function in the nonlinear Kirchhoff plate. The topology optimization model of nonlinear Kirchhoff plate based on RKPM was developed, and the topology optimization procedure was given in detail. Finally, all the Matlab programs were written, and one numerical example shows the advantage of the present method.

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