scholarly journals Multi-Objective Topology Optimization of Multi-Functional Components in a Multibody Dynamics System

2012 ◽  
Author(s):  
Zheng-Dong Ma ◽  
Guang Dong
Keyword(s):  
Topology Optimization ◽  
Multibody Dynamics ◽  
Multi Objective ◽  
Functional Components

Topology Optimization for the Natural Frequency of Multibody Dynamics Systems With Multi-Functional Components

2015 ◽  
Author(s):  
Guang Dong
Keyword(s):  
Topology Optimization ◽  
Natural Frequency ◽  
Multibody Dynamics ◽  
Design Problem ◽  
Optimization Method ◽  
Layout Design ◽  
Dynamic Responses ◽  
Interactive System ◽  
Static Responses ◽  
Functional Components

The multi-functional components layout design problem, which may have various options associated with it, including passive, active, and reactive components in given multibody dynamics systems, is defined in this study. The defined layout design problem is able to address the objective functions that are related to the dynamic responses of multibody dynamics systems, rather than static responses. The target of the multi-functional components layout design problem in given multibody dynamics systems is to seek the optimal interactive system layout between given multiple multibody dynamics system in order to maximize or minimize the dynamic objective function. The governing equations for the interactive system and the given multibody dynamics systems are derived first. The optimization objective is the first order natural frequency of the multibody dynamics system with multi-functional components in this study. The sensitivity analysis was then implemented based on the system eigen equation. Two numerical examples are presented in this study, it shows that the topology optimization method can be applied to the multibody dynamics system natural frequency optimization successfully.

scholarly journals NODAL COSINE SINE MATERIAL INTERPOLATION IN MULTI OBJECTIVE TOPOLOGY OPTIMIZATION WITH THE GLOBAL CRITERIA METHOD FOR LINEAR ELASTO STATIC, HEAT TRANSFER, POTENTIAL FLOW AND BINARY CROSS ENTROPY SHARPENING

2021 ◽  
Vol 1 ◽  
pp. 2247-2256
Author(s):  
Martin Denk ◽  
Klemens Rother ◽  
Mario Zinßer ◽  
Christoph Petroll ◽  
Kristin Paetzold
Keyword(s):  
Heat Transfer ◽  
Topology Optimization ◽  
Potential Flow ◽  
Cross Entropy ◽  
Objective Criterion ◽  
Multi Objective ◽  
Material Interpolation ◽  
Continuous Material ◽  
Mean Compliance ◽  
Transfer Potential

AbstractTopology optimization is typically used for suitable design suggestions for objectives like mean compliance, mean temperature, or model analysis. Some modern modeling technics in topology optimization require a nodal based material interpolation. Therefore this article is referred to a continuous material interpolation in topology optimization. To cover a smooth and differentiable density field, we address trigonometric shape functions which are infinitely differentiable. Furthermore, we extend a so-known global criteria method with a sharpening function based on binary cross-entropy, so that sharper solutions results. The proposed material interpolation is applied to different applications such as heat transfer, elasto static, and potential flow. Furthermore, these different objectives are together optimized using a multi-objective criterion.

Efficient Sensitivity Analysis for Multibody Dynamics Systems Using an Iterative Steps Method With Application in Topology Optimization

2011 ◽  
Author(s):  
Guang Dong ◽  
Zheng-Dong Ma ◽  
Gregory Hulbert ◽  
Noboru Kikuchi ◽  
Sudhakar Arepally ◽  
...  
Keyword(s):  
Sensitivity Analysis ◽  
Topology Optimization ◽  
Multibody Dynamics ◽  
Optimization Problem ◽  
Finite Difference Methods ◽  
Analysis Method ◽  
Topology Optimization Problem ◽  
Design Variables ◽  
Sensitivity Analysis Method ◽  
Rotational Motions

Efficient and reliable sensitivity analyses are critical for topology optimization, especially for multibody dynamics systems, because of the large number of design variables and the complexities and expense in solving the state equations. This research addresses a general and efficient sensitivity analysis method for topology optimization with design objectives associated with time dependent dynamics responses of multibody dynamics systems that include nonlinear geometric effects associated with large translational and rotational motions. An iterative sensitivity analysis relation is proposed, based on typical finite difference methods for the differential algebraic equations (DAEs). These iterative equations can be simplified for specific cases to obtain more efficient sensitivity analysis methods. Since finite difference methods are general and widely used, the iterative sensitivity analysis is also applicable to various numerical solution approaches. The proposed sensitivity analysis method is demonstrated using a truss structure topology optimization problem with consideration of the dynamic response including large translational and rotational motions. The topology optimization problem of the general truss structure is formulated using the SIMP (Simply Isotropic Material with Penalization) assumption for the design variables associated with each truss member. It is shown that the proposed iterative steps sensitivity analysis method is both reliable and efficient.

Time Integration Incorporated Sensitivity Analysis With Generalized-α Method for Multibody Dynamics Systems

2011 ◽  
Author(s):  
Guang Dong ◽  
Zheng-Dong Ma ◽  
Gregory Hulbert ◽  
Noboru Kikuchi
Keyword(s):  
Sensitivity Analysis ◽  
Topology Optimization ◽  
Dynamic Loading ◽  
Multibody Dynamics ◽  
Equations Of Motion ◽  
Time Integration ◽  
Optimization Method ◽  
Sensitivity Analysis Method ◽  
System Equations ◽  
Consecutive Time

The topology optimization method is extended for the optimization of geometrically nonlinear, time-dependent multibody dynamics systems undergoing nonlinear responses. In particular, this paper focuses on sensitivity analysis methods for topology optimization of general multibody dynamics systems, which include large displacements and rotations and dynamic loading. The generalized-α method is employed to solve the multibody dynamics system equations of motion. The developed time integration incorporated sensitivity analysis method is based on a linear approximation of two consecutive time steps, such that the generalized-α method is only applied once in the time integration of the equations of motion. This approach significantly reduces the computational costs associated with sensitivity analysis. To show the effectiveness of the developed procedures, topology optimization of a ground structure embedded in a planar multibody dynamics system under dynamic loading is presented.

An Evolutionary Multi-Objective Optimization Approach to the Topology Optimization of Auxetic Structures

2002 ◽  
Author(s):  
Ashraf O. Nassef
Keyword(s):  
Topology Optimization ◽  
Elastic Modulus ◽  
Finite Elements ◽  
Multiobjective Optimization ◽  
Poisson Ratio ◽  
Optimization Approach ◽  
Multi Objective Optimization ◽  
Finite Elements Analysis ◽  
Multi Objective ◽  
Auxetic Structures

Auxetic structures are ones, which exhibit an in-plane negative Poisson ratio behavior. Such structures can be obtained by specially designed honeycombs or by specially designed composites. The design of such honeycombs and composites has been tackled using a combination of optimization and finite elements analysis. Since, there is a tradeoff between the Poisson ratio of such structures and their elastic modulus, it might not be possible to attain a desired value for both properties simultaneously. The presented work approaches the problem using evolutionary multiobjective optimization to produce several designs rather than one. The algorithm provides the designs that lie on the tradeoff frontier between both properties.

Multi-Objective Topological Optimization of Support Frame for High-Speed and Heavy-Load Triangle Track Wheel Based on Analytic Hierarchy Process

2018 ◽  
Author(s):  
Fenghe Wu ◽  
Zhaohua Wang ◽  
Yinxu Sun ◽  
Yulin Yang ◽  
Yongxin Li ◽  
...  
Keyword(s):  
Topology Optimization ◽  
High Speed ◽  
Working Condition ◽  
Average Frequency ◽  
Frequency Method ◽  
Analytic Hierarchy ◽  
Heavy Load ◽  
Multi Objective ◽  
Support Frame ◽  
Hierarchy Process

The high-speed, heavy-load and changeable triangle track wheel is a motion device that can carry out interchange between the track wheel and tire in an ordinary vehicle. The topology optimization for the support frame can reduce weight and improve the maneuverability of the vehicle. However, it is difficult to consider simultaneously its weight, stiffness and modal in the process of the structure optimization. Thus, a topology optimization method for multi-objective and multi-working-condition is proposed based on the AHP (analytic hierarchy process) and average frequency method. Firstly, considering the static multi-stiffness target and dynamic vibration frequency target, using the compromise programming method and average frequency method, the objective function of the multi-objective and multi-working-condition topology optimization is established. Then, based on the optimization target, design criteria and indexes, the lightweight hierarchical structure model of the support frame consisting of three levels and eight weight factors is established. Values of 8 weight coefficients of the multi-objective topology optimization are determined through solving the weight factor judgment matrix. Finally, considering the multi-working-condition, taking the minimum objective function of the static and dynamic characteristics as target, and the volume ratio is 50% as boundary, the mathematical model of the topology optimization is established. Simulation results show that the stiffness and strength of the support frame are improved respectively by 74.3% and 1.3% while its weight is reduced by 16.3%. This method also provides a new way to the lightweight design for other large, heavy and multi-condition equipment.

Multi-Objective Topology Optimization for Bevel Gear and Geometrical Reconstruction

2013 ◽  
Vol 278-280 ◽  
pp. 139-142
Author(s):  
Xiang Bian ◽  
Zong De Fang ◽  
Kun Qin ◽  
Lifei Lian ◽  
Bao Yu Zhang
Keyword(s):  
Topology Optimization ◽  
Optimization Method ◽  
Tooth Root ◽  
Multi Objective Optimization ◽  
Direct Optimization ◽  
Multi Objective ◽  
Gear Modification ◽  
Parametric Cad ◽  
Straight Lines ◽  
Root Stress

Usually the gear modification is a main measure to reduce the vibration and noise of the gears, but in view of the complexity of the gear modification, topology optimization method was used to optimize the structure of the gear. The minimum volume was set as the direct optimization goal. To achieve the target of reducing contact stress, tooth root bending stress and improving flexibility, the upper bound of the stress and lower bound of the flexibility were set appropriately, thus realizing multi-objective optimization indirectly. A method for converting topology result into parametric CAD model which can be modified was presented, by fitting the topology result with simple straight lines and arcs, the model can be smoothed automatically, after further regulating, the geometry reconstruction was finished. After topology optimization, the resulting structure and properties of the gear are consistent with cavity gear. While reducing the weight of the gear, the noise can be reduced and its life would be extended through increasing flexibility and reducing tooth root stress.

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