Volume Adjustable Topology Optimization with Multiple Displacement Constraints

2017 ◽  
Vol 34 (6) ◽  
pp. 759-770
Author(s):  
C. W. Huang ◽  
K. W. Chou
Keyword(s):  
Topology Optimization ◽  
Volume Ratio ◽  
Optimization Methods ◽  
Optimal Topology ◽  
Volume Constraint ◽  
Functional Constraints ◽  
Topology Optimization Problem ◽  
Finite Element Software ◽  
Minimum Compliance ◽  
Displacement Constraints

AbstractMost topology optimization methods seek optimal topologies that satisfy a minimum compliance with a pre-specified volume constraint in the design domain. However, practical designs often include various functional constraints and the optimal solid volume ratios are unknown a priori, which implies a gap between topology optimization methods and practical designs in industries. This paper studies the performance-based topology optimization (PTO) problem that searches for the optimal topology with minimum compliance to satisfy the pre-specified functional constraints without a pre-specified volume constraint. A novel element-based evolutionary switching method (ESM), which can automatically adjust solid volume ratio and material distribution, is developed and implemented using the commercial finite element software ABAQUS. The effects of displacement constraints on the optimal topologies are investigated, and the differences between PTO problems and the topology optimization problem which has a volume constraint are discussed. Numerical examples demonstrate that the optimal topologies are mainly determined by the load pattern and locally changed with respect to the location of the active displacement constraints. In addition, the displacement constraints to a large extent control the solid volume ratio of optimal topologies according to the allowable displacements in PTO problems. Finally, the proposed ESM could provide conservative solutions to the topology optimization with multiple displacement constraints problems.

A NEW ELEMENT-BASED METHOD FOR SOLVING STRUCTURAL TOPOLOGY OPTIMIZATION PROBLEMS WITH NON-UNIFORM MESHES

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Kuang-Wu Chou ◽  
Chang-Wei Huang
Keyword(s):  
Topology Optimization ◽  
Optimization Problems ◽  
Optimization Method ◽  
Optimal Topology ◽  
Evolutionary Stage ◽  
Structural Topology Optimization ◽  
Volume Constraint ◽  
Structural Topology ◽  
Exchange Method ◽  
Python Scripting

This study proposes a new element-based method to solve structural topology optimization problems with non-uniform meshes. The objective function is to minimize the compliance of a structure, subject to a volume constraint. For a structure of a fixed volume, the method is intended to find a topology that could almost conform to the compliance minimum. The method is refined from the evolutionary switching method, whose policy of exchanging elements is improved by replacing some empirical decisions with ones according to optimization theories. The method has the evolutionary stage and the element exchange stage to conduct topology optimization. The evolutionary stage uses the evolutionary structural optimization method to remove inefficient elements until the volume constraint is satisfied. The element exchange stage performs a procedure refined from the element exchange method. Notably, the procedures of both stages are refined to conduct non-uniform finite element meshes. The proposed method was implemented to use the Abaqus Python scripting interface to call the services of Abaqus such as running analysis and retrieving the output database of an analysis. Numerical examples demonstrate that the proposed optimization method could determine the optimal topology of a structure that is subject to a volume constraint and whose mesh is non-uniform.

Topology Optimization for Work Flat of Tower-Belt under Multi-Loading Cases

2012 ◽  
Vol 197 ◽  
pp. 614-618
Author(s):  
Yi Xian Du ◽  
Jin Run Hu ◽  
Zi Fan Fang ◽  
Qi Hua Tian
Keyword(s):  
Topology Optimization ◽  
Static Analysis ◽  
Geometric Model ◽  
Mathematical Optimization ◽  
Structural Models ◽  
Optimal Topology ◽  
Multiple Objective ◽  
Objective Functions ◽  
Minimum Compliance ◽  
Mathematical Optimization Model

Taking minimum compliance of the whole structure as the objective, the mathematical optimization model of multi-loading cases topology optimization is constructed by using the weight compromise programming method to coordinate the multiple objective functions. The optimal topology of the work flat is obtained using Hyperworks/Optistruct software and geometric model is reconstructed. The static analysis of original and reconstructed structural models of the work flat show that the optimized structure can not only decrease the weight, but also improve the stiffness and reduce the stress. The work flat will be more safe and reliable than before.

Topology Optimization Design of Bars Structure Based on SKO Method

2013 ◽  
Vol 394 ◽  
pp. 515-520 ◽  
Author(s):  
Wen Jun Li ◽  
Qi Cai Zhou ◽  
Xu Hui Zhang ◽  
Xiao Lei Xiong ◽  
Jiong Zhao
Keyword(s):  
Global Optimization ◽  
Topology Optimization ◽  
Optimization Design ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Optimization Methods ◽  
Topology Optimization Problem ◽  
Proposed Model ◽  
Continuum Structure ◽  
The Impact

There are less topology optimization methods for bars structure than those for continuum structure. Bionic intelligent method is a powerful way to solve the topology optimization problems of bars structure since it is of good global optimization capacity and convenient for numerical calculation. This article presents a SKO topology optimization model for bars structure based on SKO (Soft Kill Option) method derived from adaptive growth rules of trees, bones, etc. The model has been applied to solve the topology optimization problem of a space frame. It uses three optimization strategies, which are constant, decreasing and increasing material removed rate. The impact on the optimization processes and results of different strategies are discussed, and the validity of the proposed model is proved.

scholarly journals SOLUTION OF THE LARGE MINIMUM COMPLIANCE PROBLEM USING BILEVEL OPTIMIZATION

2016 ◽  
Vol 12 (2) ◽  
pp. 5928-5937
Author(s):  
Makrizi Abdelilah ◽  
Bouchaïb Radi
Keyword(s):  
Topology Optimization ◽  
Optimality Conditions ◽  
Optimization Problem ◽  
Bilevel Optimization ◽  
Numerical Results ◽  
Topology Optimization Problem ◽  
Single Level ◽  
Minimum Compliance ◽  
Bilevel Problem ◽  
Compliance Problem

The topology optimization problem have a great industrial interest. Using the subdomains method, we have formulated the decomposed topology optimization problem as a bilevel one. In this paper, we reformulate our bilevel problem as a single level optimization problem by replacing the lower level optimization problem with its KKT optimality conditions, we give also a new algorithm and numerical results.

scholarly journals An Efficient Topology Description Function Method Based on Modified Sigmoid Function

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Xingfa Yang ◽  
Jie Liu ◽  
Yin Yang ◽  
Qixiang Qing ◽  
Guilin Wen
Keyword(s):  
Topology Optimization ◽  
Function Method ◽  
Optimization Problem ◽  
Optimization Methods ◽  
Heaviside Function ◽  
Sigmoid Function ◽  
Topology Optimization Problem ◽  
Linear Elastic ◽  
Topology Description Function ◽  
Structural Compliance

Optimal geometries extracted from traditional element-based topology optimization outcomes usually have zigzag boundaries, leading to being difficult to fabricate. In this study, a fairly accurate and efficient topology description function method (TDFM) for topology optimization of linear elastic structures is developed. By employing the modified sigmoid function, a simple yet efficient strategy is presented to tackle the computational difficulties because of the nonsmoothness of Heaviside function in topology optimization problem. The optimization problem is to minimize the structural compliance, with highest stiffness, while satisfying the volume constraint. The design problem is solved by a Sequential Linear Programming method. Convergent, crisp, and smooth final layouts are obtained, which can be fabricated without postprocessing, demonstrated by a series of numerical examples. Further, the proposed method has a rather higher accuracy and efficiency compared with traditional TDFM, when the classical topology optimization methods, such as bidirectional evolutionary structural optimization (BESO) and solid isotropic material with penalization (SIMP) method, are taken as benchmark.

Systematic Design Optimization of the Metamaterial Shear Beam of a Nonpneumatic Wheel for Low Rolling Resistance

2015 ◽  
Vol 137 (4) ◽  
Author(s):  
Christopher Czech ◽  
Paolo Guarneri ◽  
Niranjan Thyagaraja ◽  
Georges Fadel
Keyword(s):  
Topology Optimization ◽  
Shear Layer ◽  
Mechanical Design ◽  
Pure Shear ◽  
Rolling Resistance ◽  
Optimization Methods ◽  
Topology Optimization Problem ◽  
Mesoscale Structure ◽  
Shear Beam ◽  
Level Design

Systematic engineering of components that employ metamaterials has expanded the mechanical design field in recent years. Yet, topology optimization remains a burdensome tool to utilize within a systematic engineering paradigm. In this work, the design of a metamaterial shear beam for a nonpneumatic wheel using a systematic, two-level design approach is discussed. A top-level design process is used to determine the geometric and effective material properties of the shear beam, and linking functions are established and validated for the design of a shear layer mesoscale structure. At the metamaterial design level, innovative homogenization and topology optimization methods are employed to determine a set of locally optimal geometric designs for the shear layer. One geometry, the auxetic honeycomb, is shown to be an optimum to the minimum volume topology optimization problem for materials subjected to pure shear boundary conditions. As such, this geometry is identified as a candidate for the shear layer.

scholarly journals An efficient approach to reliability-based topology optimization for the structural lightweight design of planar continuum structures

2021 ◽  
Vol 37 ◽  
pp. 270-281
Author(s):  
Fangfang Yin ◽  
Kaifang Dang ◽  
Weimin Yang ◽  
Yumei Ding ◽  
Pengcheng Xie
Keyword(s):  
Topology Optimization ◽  
Lightweight Design ◽  
Integrated Design ◽  
Optimization Methods ◽  
Filter Function ◽  
Continuum Structures ◽  
Performance Indexes ◽  
Reliability Method ◽  
Economic Indexes ◽  
The Impact

Abstract In order to solve the application restrictions of deterministic-based topology optimization methods arising from the omission of uncertainty factors in practice, and to realize the calculation cost control of reliability-based topology optimization. In consideration of the current reliability-based topology optimization methods of continuum structures mainly based on performance indexes model with a power filter function. An efficient probabilistic reliability-based topology optimization model that regards mass and displacement as an objective function and constraint is established based on the first-order reliability method and a modified economic indexes model with a composite exponential filter function in this study. The topology optimization results obtained by different models are discussed in relation to optimal structure and convergence efficiency. Through numerical examples, it can be seen that the optimal layouts obtained by reliability-based models have an increased amount of material and more support structures, which reveals the necessity of considering uncertainty in lightweight design. In addition, the reliability-based modified model not only can obtain lighter optimal structures compared with traditional economic indexes models in most circumstances, but also has a significant advantage in convergence efficiency, with an average increase of 44.59% and 64.76% compared with the other two reliability-based models. Furthermore, the impact of the reliability index on the results is explored, which verifies the validity of the established model. This study provides a theoretical reference for lightweight or innovative feature-integrated design in engineering applications.

scholarly journals A Comprehensive Review of Isogeometric Topology Optimization: Methods, Applications and Prospects

2020 ◽  
Vol 33 (1) ◽  
Author(s):  
Jie Gao ◽  
Mi Xiao ◽  
Yan Zhang ◽  
Liang Gao
Keyword(s):  
Topology Optimization ◽  
Computer Aided Design ◽  
Numerical Technique ◽  
Optimization Methods ◽  
Negative Influence ◽  
Comprehensive Overview ◽  
Promising Alternative ◽  
Computer Aided ◽  
Optimal Material ◽  
Material Layout

AbstractTopology Optimization (TO) is a powerful numerical technique to determine the optimal material layout in a design domain, which has accepted considerable developments in recent years. The classic Finite Element Method (FEM) is applied to compute the unknown structural responses in TO. However, several numerical deficiencies of the FEM significantly influence the effectiveness and efficiency of TO. In order to eliminate the negative influence of the FEM on TO, IsoGeometric Analysis (IGA) has become a promising alternative due to its unique feature that the Computer-Aided Design (CAD) model and Computer-Aided Engineering (CAE) model can be unified into a same mathematical model. In the paper, the main intention is to provide a comprehensive overview for the developments of Isogeometric Topology Optimization (ITO) in methods and applications. Finally, some prospects for the developments of ITO in the future are also presented.

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.

Topology Optimization Using Node-Based Smoothed Finite Element Method

2015 ◽  
Vol 07 (06) ◽  
pp. 1550085 ◽  
Author(s):  
Z. C. He ◽  
G. Y. Zhang ◽  
L. Deng ◽  
Eric Li ◽  
G. R. Liu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Topology Optimization ◽  
Optimization Design ◽  
Solid Mechanics ◽  
Optimality Criteria ◽  
Topology Optimization Problem ◽  
Design Variables ◽  
Smoothed Finite Element Method ◽  
Element Method

The node-based smoothed finite element method (NS-FEM) proposed recently has shown very good properties in solid mechanics, such as providing much better gradient solutions. In this paper, the topology optimization design of the continuum structures under static load is formulated on the basis of NS-FEM. As the node-based smoothing domain is the sub-unit of assembling stiffness matrix in the NS-FEM, the relative density of node-based smoothing domains serves as design variables. In this formulation, the compliance minimization is considered as an objective function, and the topology optimization model is developed using the solid isotropic material with penalization (SIMP) interpolation scheme. The topology optimization problem is then solved by the optimality criteria (OC) method. Finally, the feasibility and efficiency of the proposed method are illustrated with both 2D and 3D examples that are widely used in the topology optimization design.

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