Multi-Domain Topology Optimization for Vehicle Substructure Design

2002 ◽  
Author(s):  
Zheng-Dong Ma ◽  
Noboru Kikuchi ◽  
Christophe Pierre ◽  
Basavaraju Raju
Keyword(s):  
Topology Optimization ◽  
Design Problem ◽  
Degrees Of Freedom ◽  
Optimization Technique ◽  
Synthesis Method ◽  
Material Design ◽  
Functionally Graded ◽  
Structural Domain ◽  
Management Problem ◽  
Design Problems

Topology optimization of a structure is generally considered as a problem of optimum material distribution (OMD) within a given structural domain, subject to a given amount of material and to boundary conditions and loading conditions applied to the structure. The effective design of a complex engineering structure, however, may require controllability over how the material should be distributed among the various subdomains of the structure, as well as even the use of different materials for the different subdomains. A multi-domain topology optimization technique is therefore proposed in this paper, which is based upon the homogenization method, and which employs a generalized Sequential Approximation Optimization (GSAO) algorithm. This algorithm enhances the capabilities of current topology optimization methods by using advanced updating rules and providing additional flexibility in the optimization process, thus resulting in improved convergence and higher computational efficiency. A Component Mode Synthesis method is also employed, which can significantly reduce the number of degrees of freedom associated with the subdomains whose designs are fixed at the current stage. Several example design problems are considered, including a “structure-fixture simultaneous design” problem, a “functionally graded material design” problem, a “crush energy management” problem, and a “truck frame design” problem that illustrates how the technique developed can be applied to real vehicle substructure design problems.

Multidomain Topology Optimization for Structural and Material Designs

2005 ◽  
Vol 73 (4) ◽  
pp. 565-573 ◽  
Author(s):  
Zheng-Dong Ma ◽  
Noboru Kikuchi ◽  
Christophe Pierre ◽  
Basavaraju Raju
Keyword(s):  
Topology Optimization ◽  
Engineering Design ◽  
Optimization Technique ◽  
Functionally Graded ◽  
Material Distribution ◽  
Design Problems ◽  
Linearization Methods ◽  
Engineering Design Problems ◽  
Wide Range ◽  
Multiple Materials

A multidomain topology optimization technique (MDTO) is developed, which extends the standard topology optimization method to the realm of more realistic engineering design problems. The new technique enables the effective design of a complex engineering structure by allowing the designer to control the material distribution among the subdomains during the optimal design process, to use multiple materials or composite materials in the various subdomains of the structure, and to follow a desired pattern or tendency for the material distribution. A new algorithm of Sequential Approximate Optimization (SAO) is proposed for the multidomain topology optimization, which is an enhancement and a generalization of previous SAO algorithms (including Optimality Criteria and Convex Linearization methods, etc.). An advanced substructuring method using quasi-static modes is also introduced to condense the nodal variables associated with the multidomain topology optimization problem, especially for the nondesign subdomains. The effectiveness of the new MDTO approach is demonstrated for various design problems, including one of “structure-fixture simultaneous design,” one of “functionally graded material design,” and one of “crush energy management.” These case studies demonstrate the potential significance of the new capability developed for a wide range of engineering design problems.

Optimum Material Design of Metal-Ceramic Hybrid Functionally Graded Composite

2008 ◽  
Vol 569 ◽  
pp. 121-124 ◽  
Author(s):  
Joo Hyoung Choi ◽  
Jin Rae Cho
Keyword(s):  
Volume Fraction ◽  
Optimization Technique ◽  
Material Design ◽  
Linear Interpolation ◽  
Functionally Graded ◽  
Homogeneous Material ◽  
Functionally Graded Composite ◽  
Optimum Material ◽  
Discrete Optimum ◽  
Optimum Volume

In this paper, an efficient optimum material design technique is introduced for hybrid designing of dual-phase heat-resisting functionally graded composites. The graded region is divided into a finite number of homogeneous material layers in order to reduce the total design variables. The discrete optimum volume fractions are sought by making use of the interior penalty method and the finite difference sensitivity scheme. A linear interpolation technique is adopted to make the final optimum volume fraction distribution be continuous. The validity of the proposed optimization technique is examined through the illustrative numerical experiment.

Topology-Boundary Optimization of Coupled Structural-Acoustic Systems

2009 ◽  
Author(s):  
Lei Shu ◽  
Zhengdong Ma ◽  
Zongde Fang
Keyword(s):  
Topology Optimization ◽  
Noise Reduction ◽  
Coupling Effect ◽  
Optimization Technique ◽  
Interior Noise ◽  
Structural Domain ◽  
Material Distribution ◽  
Acoustic System ◽  
Boundary Shape ◽  
Acoustic Domain

A new topology optimization technique is presented in this paper for optimal design of coupled structural-acoustic system with a current focus on interior noise reduction of automotive vehicles. The new topology optimization technique is based on an earlier published work on the analysis and sensitivity analysis of the coupled structural-acoustic system [1–2]. It is extended in this paper to consider the optimum material distribution in the structural domain as well as the optimum boundary shape between the structural and acoustic domains for the purpose of interior noise reduction. Firstly, a fixed boundary problem was considered with a focus on the material distribution in the structural domain to achieve the desired acoustic response inside the acoustic domain. The general formulation developed accounts for the full coupling effect of the structural vibration and acoustic pressure and can consider multiple (structural and acoustic) inputs and outputs over a predefined frequency domain. Secondly, optimization of the boundary shape between the structural domain and acoustic domain is considered with a focus on modifying acoustic resonant modes as well as the interaction between the structure and acoustic field. Finally, optimal material distribution and boundary determination are simultaneously considered to obtain a truly optimum structural-acoustic system for the desired performance requirements of the coupled system. Examples will be given to demonstrate the feasibility and effectiveness of the new topology optimization technique for various applications.

Modeling and free vibration analysis of rotating hub-blade assemblies reinforced with graphene nanoplatelets

2021 ◽  
pp. 030932472098690
Author(s):  
Tian Yu Zhao ◽  
Ze Yu Jiang ◽  
Zhan Zhao ◽  
Li Yang Xie ◽  
Hui Qun Yuan
Keyword(s):  
Free Vibration ◽  
Synthesis Method ◽  
Free Vibration Analysis ◽  
Material Design ◽  
Weight Fraction ◽  
Mathematic Model ◽  
Graphene Nanoplatelets ◽  
Functionally Graded ◽  
Width Ratio ◽  
Graphene Nanoplatelet

This paper presents a new theoretical model for rotating elastic hub-blade assemblies, made of functionally graded (FG) graphene nanoplatelet (GPL) reinforced nanocomposites, and their free vibration characteristics are investigated. This model is the first attempt to include two elastic components simultaneously and consider the coupled effect. The Euler-Bernoulli beam theory and the Donnell’s shell theory are employed to establish the mathematic model of the blade and hub, respectively. The effective material properties, varying continuously along the thickness of the beam and cylindrical shell, are determined via the Halpin-Tsai micromechanics model and the rule of the mixture. The Lagrange’s equation is adopted to derive the equations of motion which are then solved by employing the substructure mode synthesis method and the Galerkin method. A parametric study is conducted to examine the effects of the rotating speed, graphene nanoplatelet distribution pattern, GPL weight fraction, length-to-thickness ratio and length-to-width ratio of graphene nanoplatelets (GPLs) and blade dimension on the natural frequencies of the nanocomposite rotor system, which will significantly benefit on the structural and material design of GPL reinforced hub-blade assembly.

scholarly journals On understanding of design problem formulation for compliant mechanisms through topology optimization

2013 ◽  
Vol 4 (2) ◽  
pp. 357-369 ◽  
Author(s):  
L. Cao ◽  
A. Dolovich ◽  
W. J. Zhang
Keyword(s):  
Topology Optimization ◽  
Compliant Mechanisms ◽  
Optimization Technique ◽  
Problem Formulation ◽  
Functional Requirements ◽  
Motion Generation ◽  
Design Problems ◽  
Standard Design ◽  
Quantitative Design ◽  
Future Work

Abstract. General problems associated with the design of compliant mechanisms through the topology optimization technique are defined in this paper due to the lack of comprehensive definitions for these problems in the literature. Standard design problems associated with rigid body mechanisms, i.e. function generation, path generation and motion generation, are extended to compliant mechanisms. Functional requirements and the associated 25 formulations in the literature are comprehensively reviewed along with their limitations. Based on whether the output is controlled quantitatively or not, these formulations are categorized into two types: (1) formulations for quantitative design; and (2) formulations for qualitative design. In addition, formulations that aim to solve the point flexure problem are also discussed. Future work is identified based on the discussion of each topic.

scholarly journals Improved Efficient Projection Density Function Based on Topology Optimization

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Nouman Saeed ◽  
Kai Long ◽  
Jamshed Ahmed Ansari ◽  
Nasif Raza Jaffri ◽  
Usama Abrar
Keyword(s):  
Topology Optimization ◽  
Optimization Technique ◽  
Minimum Length ◽  
Design Problems ◽  
Manufacturing Costs ◽  
Minimum Compliance ◽  
Engineering Design Problems ◽  
Optimization Formulation ◽  
Solid Phases ◽  
Minimum Length Scale

Topology optimization is a powerful tool having capability of generating new solution to engineering design problems, while these designs enhance manufacturability and reduce manufacturing costs in a computational setting. Mesh-independent convergence and other techniques have been widely used as topology optimization technique, but they produce gray transition regions which is not a favorable condition for any material. In this article, a modified topology optimization formulation using a new function has been proposed. The suggested scheme makes use of the Heaviside Projection Method (HPM) to continuum topology optimization. Such technique is helpful to obtain the minimum length scale influence on void and solid phases. Application of this proposed approach is implemented to obtain the minimum compliance for macrostructures. Numerical remarkable examples illustrate the noteworthy value of the proposed approach.

Topology Optimization of a Vehicle’s Hood Using Evolutionary Structural Optimization

2006 ◽  
Vol 326-328 ◽  
pp. 1217-1220
Author(s):  
S.H. Choi ◽  
J.Y. Park ◽  
I.S. Shin ◽  
Seok Young Han
Keyword(s):  
Topology Optimization ◽  
Structural Optimization ◽  
Natural Frequency ◽  
Optimization Technique ◽  
Optimal Solution ◽  
Weighting Factor ◽  
Optimal Topology ◽  
Structural Domain ◽  
Static Stiffness ◽  
Evolutionary Structural Optimization

Topology optimization of the inner reinforcement for a vehicle’s hood has been performed by evolutionary structural optimization (ESO) method. The purpose of this study is to obtain optimal topology of the inner reinforcement for a vehicle’s hood considering static stiffness and natural frequency simultaneously. To do this, the multiobjective design optimization technique was implemented. From several combinations of weighting factors, a Pareto-optimal solution was obtained. Optimal topologies were obtained by the ESO method, i.e., by eliminating the elements having the lowest efficiency from the structural domain. As the weighting factor of the elastic strain efficiency goes from 1 to zero, it is found that the optimal topologies transmits from the optimal topology of static stiffness problem to that of natural frequency problem. Therefore, it was concluded that ESO method is effectively applied to topology optimization of the inner reinforcement of a vehicle’s hood.

Design of Zirconia-Aluminum Functionally Graded Material for Buckling and Vibration Characteristics Enhancement of Beam/Column Structure

2017 ◽  
Vol 735 ◽  
pp. 100-107
Author(s):  
Nabeel Alshabatat ◽  
Adnan I.O. Zaid ◽  
Safwan M. Al-Qawabah
Keyword(s):  
Functionally Graded Material ◽  
Design Problem ◽  
Design Method ◽  
Excitation Frequency ◽  
Weight Ratio ◽  
Vibration Characteristics ◽  
Functionally Graded ◽  
Design Problems ◽  
Material Tailoring ◽  
Graded Material

This paper presents a design method to optimize the material distribution of zirconia/aluminum-functionally graded material with respect to some buckling and vibration properties. The distribution of volume fractions of the FGM constituents is defined through the beam or column length by a trigonometric law. The finite element method is used for the buckling and vibration analysis, and a genetic algorithm is utilized for optimization of the chosen objective function. The efficiency of the method is demonstrated by two design problems. In the first design problem, FGM is used to maximize the buckling crical load to weight ratio. In the second design problem, the kinetic energy of a vibrating FGM beam is minimized at a specific excitation frequency. These design problems show that material tailoring of beam/column structures using FGM can result in substantial improvements of their buckling and vibration characteristics.

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