scholarly journals Three-Dimensional Dynamic Topology Optimization with Frequency Constraints Using Composite Exponential Function and ICM Method

2015 ◽  
Vol 2015 ◽  
pp. 1-10
Author(s):  
Hongling Ye ◽  
Ning Chen ◽  
Yunkang Sui ◽  
Jun Tie
Keyword(s):  
Topology Optimization ◽  
Exponential Function ◽  
Three Dimensional ◽  
Continuous Mapping ◽  
Taylor Series Expansion ◽  
Optimal Model ◽  
Filter Function ◽  
Frequency Constraints ◽  
Design Variables ◽  
Dynamic Topology

The dynamic topology optimization of three-dimensional continuum structures subject to frequency constraints is investigated using Independent Continuous Mapping (ICM) design variable fields. The composite exponential function (CEF) is selected to be a filter function which recognizes the design variables and to implement the changing process of design variables from “discrete” to “continuous” and back to “discrete.” Explicit formulations of frequency constraints are given based on filter functions, first-order Taylor series expansion. And an improved optimal model is formulated using CEF and the explicit frequency constraints. Dual sequential quadratic programming (DSQP) algorithm is used to solve the optimal model. The program is developed on the platform of MSC Patran & Nastran. Finally, numerical examples are given to demonstrate the validity and applicability of the proposed method.

scholarly journals Topology Optimization Using Parabolic Aggregation Function with Independent-Continuous-Mapping Method

2013 ◽  
Vol 2013 ◽  
pp. 1-18
Author(s):  
Tie Jun ◽  
Sui Yun-kang
Keyword(s):  
Topology Optimization ◽  
Strain Energy ◽  
Stress Singularity ◽  
Continuous Mapping ◽  
Stress Constraints ◽  
Aggregation Function ◽  
Sensitivity Analyses ◽  
Stress Concentrations ◽  
Filter Function ◽  
Design Variables

This paper concentrates on finding the optimal distribution for continuum structure such that the structural weight with stress constraints is minimized where the physical design domain is discretized by finite elements. A novel Independent-Continuous-Mapping (ICM) method is proposed to convert equivalently the binary design variables which is used to indicate material or void in the various elements to independent continuous design variables. Moreover, three smooth mappings about weight, stiffness, and stress of the structural elements are introduced to formulate the objective function based on the so-called concepts of polish function and weighting filter function. A new general continuous approach for topology optimization is given which can eliminate the stress singularity phenomena more efficiently than the traditionalε-relaxation method, and an alternative strain energy method for the stress constraints is proposed to overcome the difficulty in stress sensitivity analyses. Mathematically, by means of a generalized aggregation KS-like function defined as the parabolic aggregation function, a topology optimization model is formulated with the weight objective and single parabolic global strain energy constraints. The numerical examples demonstrate that the proposed methods effectively remove the stress concentrations and generate black-and-white designs for practically sized problems.

Structural Dynamic Topology Optimization of the Transmission Housing

2011 ◽  
Vol 308-310 ◽  
pp. 368-372
Author(s):  
Shou Wen Yao ◽  
Jian Li Lv ◽  
Qing Dong Peng
Keyword(s):  
Topology Optimization ◽  
Dynamic Performance ◽  
Cad Model ◽  
Mass Reduction ◽  
Element Analysis ◽  
Structural Dynamic ◽  
Design Variables ◽  
The Finite Element Analysis ◽  
Dynamic Topology ◽  
Topology Model

Dynamic performance is one of the most important factors in the product’s life. Transmission housing is one of the important components in vehicle, which has direct influence on the vehicle’s powertrain performance. Dynamic topology optimization can improve the product’s performance. The dynamic topology model is built, in which the density of elements are the design variables, the displacement of frequency response and volume are the constraints, and the objective is to maximize the first natural frequency of the housing. According to the result of optimization, the CAD model of housing is rebuilt and the finite element analysis of the new housing is done.The results show that both the static and dynamic performance are improved besides the mass reduction, namely, dynamic topology optimization can significantly improve the product’s performance.

The Research of Optimization Algorithm of Dynamic Topology Optimization Model of Continuum Structure Based on the ICM Method

2013 ◽  
Vol 380-384 ◽  
pp. 1804-1807
Author(s):  
Yan Ming Zhang ◽  
Hong Ling Ye ◽  
Yao Ming Li ◽  
Yun Kang Sui
Keyword(s):  
Optimization Model ◽  
Optimization Algorithms ◽  
Mapping Method ◽  
Optimal Model ◽  
Filter Function ◽  
Continuum Structures ◽  
Dynamic Topology ◽  
Convergent Method ◽  
Continuum Structure ◽  
Moving Asymptotes

In this paper, we mainly focus on the structural optimal design of dynamics for continuum structures, and aim at constructing the topological optimal formulation by using the ICM (Independent, Continuum and Mapping) method, which is considering weight as objective function and fundamental eigenfrequency as constraint. The local model is removed by selecting suitable filter function. And two algorithms, dual sequential quadratic programming (DSQP) and global convergent method of moving asymptotes (GCMMA) algorithm, were used to solve the mathematic optimal model. Finally, numerical example is provided to demonstrate the validity and effectiveness of the ICM method and compare the optimization results of two optimization algorithms. The results show that both optimization algorithms can solve the mathematics optimization model effectively.

Research on Three-Dimensional Topology Optimization for the Bed of NC Gear Shaper

2013 ◽  
Vol 690-693 ◽  
pp. 2821-2825
Author(s):  
Qi Hua Tian ◽  
Ran Tao ◽  
Yi Xian Du
Keyword(s):  
Topology Optimization ◽  
Optimization Design ◽  
Interpolation Method ◽  
Geometric Model ◽  
Three Dimensional ◽  
Optimality Criteria ◽  
Material Distribution ◽  
Design Variables ◽  
Three Dimensional Finite Element ◽  
Bed Material

Taking minimum compliance of the bed of YKS5120B-3 NC gear shaper as the optimization objective, and the three-dimensional finite element relative density as design variables, the three-dimensional topology optimization mathematical model is established based on the interpolation method of solid isotropic material. The optimality criteria algorithm is used to update design variables. Topology optimization design of loaded bed is conducted and the optimal bed material distribution in the design domain is obtained. The new geometric model of the bed is reconstructed according to the optimal bed material distribution. Comparing the static analyses results of original model of the bed with reconstructed model of the bed, the correctness and the validity of the proposed method is verified.

Analysis and Optimization of Dismantling Machine Shear Head Based on ANSYS Workbench

2014 ◽  
Vol 945-949 ◽  
pp. 653-657
Author(s):  
Wan Peng Du ◽  
Yong Jian Zhang ◽  
Chen Quan Zhou ◽  
Ai Hui Zhang ◽  
Ji Yu ◽  
...  
Keyword(s):  
Topology Optimization ◽  
Shear Force ◽  
Equivalent Stress ◽  
Three Dimensional ◽  
Total Deformation ◽  
Design Variables ◽  
Maximum Shear Force ◽  
Maximum Equivalent Stress ◽  
Three Dimensional Models ◽  
Ansys Workbench

The object is dismantling machine shear head with 500kN’s maximum shear force. The three-dimensional models, static analysis, topology optimization were done in the ANSYS Workbench. And the goal driven optimization was done which based on topology optimization. The maximum total deformation, maximum equivalent stress and geometry mass were selected as objective parameters and the distance of two connecting holes, diameter of long hole and length of blade as design variables. At last, the optimized structure was checked. The strength and rigidity meet the requirements and the mass decreased.

Natural Frequency Optimization of Variable-Density Additive Manufactured Lattice Structure: Theory and Experimental Validation

2018 ◽  
Vol 140 (10) ◽  
Author(s):  
Lin Cheng ◽  
Xuan Liang ◽  
Eric Belski ◽  
Xue Wang ◽  
Jennifer M. Sietins ◽  
...  
Keyword(s):  
Topology Optimization ◽  
Density Distribution ◽  
Lattice Structure ◽  
Design Method ◽  
Three Dimensional ◽  
Continuous Mapping ◽  
Variable Density ◽  
Structure Theory ◽  
Mapping Technique ◽  
Optimal Density

Additive manufacturing (AM) is now capable of fabricating geometrically complex geometries such as a variable-density lattice structure. This ability to handle geometric complexity provides the designer an opportunity to rethink the design method. In this work, a novel topology optimization algorithm is proposed to design variable-density lattice infill to maximize the first eigenfrequency of the structure. To make the method efficient, the lattice infill is treated as a continuum material with equivalent elastic properties obtained from asymptotic homogenization (AH), and the topology optimization is employed to find the optimum density distribution of the lattice structure. Specifically, the AH method is employed to calculate the effective mechanical properties of a predefined lattice structure as a function of its relative densities. Once the optimal density distribution is obtained, a continuous mapping technique is used to convert the optimal density distribution into variable-density lattice structured design. Two three-dimensional (3D) examples are used to validate the proposed method, where the designs are printed by the EOS direct metal laser sintering (DMLS) process in Ti6Al4V. Experimental results obtained from dynamical testing of the printed samples and detailed simulation results are in good agreement with the homogenized model results, which demonstrates the accuracy and efficiency of the proposed method.

scholarly journals Topology optimization accounting for surface layer effects

2020 ◽  
Vol 62 (6) ◽  
pp. 3009-3019
Author(s):  
Shyam Suresh ◽  
Carl-Johan Thore ◽  
Bo Torstenfelt ◽  
Anders Klarbring
Keyword(s):  
Surface Layer ◽  
Topology Optimization ◽  
Three Dimensional ◽  
Optimization Method ◽  
Structural Members ◽  
Stiffness Optimization ◽  
Direct Extension ◽  
Design Variables ◽  
Domain Extension ◽  
Standard Density

AbstractMetal AM (additive manufacturing) components are generally inhomogeneous and have different microstructure in the bulk compared with (contour) regions near the surface. This, as well as rough as-built surfaces, affects mechanical properties. In this paper, we develop a topology optimization method that considers such inhomogeneities. The method is a direct extension of standard density-based methods using linear filtering for regularization, and a second filtering of the design variables is used to identify a surface layer, the thickness of which is given by the filter radius. Domain extension is used in order to properly identify such layers at the boundary of the design domain. The method is generally applicable but is demonstrated for stiffness optimization. Both two- and three-dimensional problems are treated. A general property of the method is that the topological complexity is reduced, i.e. the optimized designs get fewer and thicker structural members as the width of the surface layer is increased.

Finite Element Modeling for Steel Cord Analysis in Radial Tires

2013 ◽  
Vol 41 (1) ◽  
pp. 60-79 ◽  
Author(s):  
Wei Yintao ◽  
Luo Yiwen ◽  
Miao Yiming ◽  
Chai Delong ◽  
Feng Xijin
Keyword(s):  
Finite Element ◽  
High Efficiency ◽  
Force Measurement ◽  
Three Dimensional ◽  
Local Stress ◽  
Tension Force ◽  
Center Line ◽  
Element Analysis ◽  
Design Variables ◽  
Steel Cord

ABSTRACT: This article focuses on steel cord deformation and force investigation within heavy-duty radial tires. Typical bending deformation and tension force distributions of steel reinforcement within a truck bus radial (TBR) tire have been obtained, and they provide useful input for the local scale modeling of the steel cord. The three-dimensional carpet plots of the cord force distribution within a TBR tire are presented. The carcass-bending curvature is derived from the deformation of the carcass center line. A high-efficiency modeling approach for layered multistrand cord structures has been developed that uses cord design variables such as lay angle, lay length, and radius of the strand center line as input. Several types of steel cord have been modeled using the developed method as an example. The pure tension for two cords and the combined tension bending under various loading conditions relevant to tire deformation have been simulated by a finite element analysis (FEA). Good agreement has been found between experimental and FEA-determined tension force-displacement curves, and the characteristic structural and plastic deformation phases have been revealed by the FE simulation. Furthermore, some interesting local stress and deformation patterns under combined tension and bending are found that have not been previously reported. In addition, an experimental cord force measurement approach is included in this article.

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