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1.
Il Yong Kim Byung Man Kwak 《International journal for numerical methods in engineering》2002,53(8):1979-2002
A generalized optimization problem in which design space is also a design to be found is defined and a numerical implementation method is proposed. In conventional optimization, only a portion of structural parameters is designated as design variables while the remaining set of other parameters related to the design space are often taken for granted. A design space is specified by the number of design variables, and the layout or configuration. To solve this type of design space problems, a simple initial design space is selected and gradually improved while the usual design variables are being optimized. To make the design space evolve into a better one, one may increase the number of design variables, but, in this transition, there are discontinuities in the objective and constraint functions. Accordingly, the sensitivity analysis methods based on continuity will not apply to this discontinuous stage. To overcome the difficulties, a numerical continuation scheme is proposed based on a new concept of a pivot phase design space. Two new categories of structural optimization problems are formulated and concrete examples shown. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
2.
Jiaqin Chen Vadim Shapiro Krishnan Suresh Igor Tsukanov 《International journal for numerical methods in engineering》2007,71(3):313-346
Recent advances in shape optimization rely on free-form implicit representations, such as level sets, to support boundary deformations and topological changes. By contrast, parametric shape optimization is formulated directly in terms of meaningful geometric design variables, but usually does not support free-form boundary and topological changes. We propose a novel approach to shape optimization that combines and retains the advantages of the earlier optimization techniques. The shapes in the design space are represented implicitly as level sets of a higher-dimensional function that is constructed using B-splines (to allow free-form deformations), and parameterized primitives combined with R-functions (to support desired parametric changes). Our approach to shape design and optimization offers great flexibility because it provides explicit parametric control of geometry and topology within a large space of free-form shapes. The resulting method is also general in that it subsumes most other types of shape optimization as special cases. We describe an implementation of the proposed technique with attractive numerical properties. The explicit construction of an implicit representation supports straightforward sensitivity analysis that can be used with most gradient-based optimization methods. Furthermore, our implementation does not require any error-prone polygonization or approximation of level sets (isocurves and isosurfaces). The effectiveness of the method is demonstrated by several numerical examples. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
3.
When geometric uncertainties arising from manufacturing errors are comparable with the characteristic length or the product responses are sensitive to such uncertainties, the products of deterministic design cannot perform robustly. This paper presents a new level set‐based framework for robust shape and topology optimization against geometric uncertainties. We first propose a stochastic level set perturbation model of uncertain topology/shape to characterize manufacturing errors in conjunction with Karhunen–Loève (K–L) expansion. We then utilize polynomial chaos expansion to implement the stochastic response analysis. In this context, the mathematical formulation of the considered robust shape and topology optimization problem is developed, and the adjoint‐variable shape sensitivity scheme is derived. An advantage of this method is that relatively large shape variations and even topological changes can be accounted for with desired accuracy and efficiency. Numerical examples are given to demonstrate the validity of the present formulation and numerical techniques. In particular, this method is justified by the observations in minimum compliance problems, where slender bars vanish when the manufacturing errors become comparable with the characteristic length of the structures. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
4.
A series of techniques is presented for overcoming some of the numerical instabilities associated with SIMP materials. These techniques are combined to create a robust topology optimization algorithm designed to be able to accommodate a large suite of problems that more closely resemble those found in industry applications. A variant of the Kreisselmeier–Steinhauser (KS) function in which the aggregation parameter is dynamically increased over the course of the optimization is used to handle multi-load problems. Results from this method are compared with those obtained using the bound formulation. It is shown that the KS aggregation method produces results superior to those of the bound formulation, which can be highly susceptible to local minima. Adaptive mesh-refinement is presented as a means of addressing the mesh-dependency problem. It is shown that successive mesh-refinement cycles can generate smooth, well-defined structures, and when used in combination with nine-node elements, virtually eliminate checkerboarding and flexural hinges. 相似文献
5.
Abstract This paper combines previously developed techniques for image‐preprocessing and characteristic image‐interpreting together with a newly proposed automated shape‐optimization modeling technique into an integrated topology‐optimization and shape‐optimization system. As a result, structure designers are provided with an efficient and reliable automated structural optimization system (ASOS). The automated shape‐optimization modeling technique, the key technique in ASOS, uses hole‐expanding strategy, interference analysis, and hole shape‐adjusting strategy to automatically define the design variables and side constraints needed for shape optimization. This technique not only eliminates the need to manually define design variables and side constraints for shape optimization, but during the process of shape optimization also prevents interference between the interior holes and the exterior boundary. The ASOS is tested in three different structural configuration design examples. 相似文献
6.
Francesco Mezzadri Xiaoping Qian 《International journal for numerical methods in engineering》2022,123(2):465-504
In topology optimization, the finite-element analysis of the problem is generally the most computationally demanding task of the solution process. In order to improve the efficiency of this phase, in this article we propose to represent regions with zero density gradient by a coarser analysis mesh. The design is instead represented in a uniform mesh. We motivate the density gradient-based adaptive refinement by discussing the topological meaning of the density gradient and how it can help avoid loss of information during projections or interpolations between design and analysis meshes. We also study the adaptiveness of the mesh and its ability to detect the topology change of the design. An a posteriori error analysis is performed as well. Furthermore, we provide theoretical and numerical considerations on the reduction of the number of degrees of freedoms of the adaptive analysis mesh with respect to the uniform case. This translates into a faster solution of the analysis, as we show numerically. Finally, we solve several test problems, including large 3D problems that we solve in parallel on computer cluster, demonstrating the applicability of our procedure in large scale computing and with iterative solvers. 相似文献
7.
F. J. FUENMAYOR J. L. OLIVER J. J. R
DENAS 《International journal for numerical methods in engineering》1997,40(8):1413-1433
The application of the Zienkiewicz–Zhu estimator was extended to the estimation of the discretization error arising from shape sensitivity analysis using the finite element method. The sensitivity error was quantified from the sensitivity of the energy norm by using an estimator specially developed for this purpose. Sensitivity analyses were carried out using the discrete analytical approach, which introduced no additional errors other than the discretization error. In this work, direct nodal averaging was used for linear triangular elements and the SPR technique for quadratic elements in order to obtain the smoothed stress and sensitivities fields. Two examples with an exact solution are used to analyse the effectivity of the proposed estimator and its convergence with the h-adaptive refinement. © 1997 by John Wiley & Sons, Ltd. 相似文献
8.
James K. Guest Lindsey C. Smith Genut 《International journal for numerical methods in engineering》2010,81(8):1019-1045
Topology optimization methodologies typically use the same discretization for the design variable and analysis meshes. Analysis accuracy and expense are thus directly tied to design dimensionality and optimization expense. This paper proposes leveraging properties of the Heaviside projection method (HPM) to separate the design variable field from the analysis mesh in continuum topology optimization. HPM projects independent design variables onto element space over a prescribed length scale. A single design variable therefore influences several elements, creating a redundancy within the design that can be exploited to reduce the number of independent design variables without significantly restricting the design space. The algorithm begins with sparse design variable fields and adapts these fields as the optimization progresses. The technique is demonstrated on minimum compliance (maximum stiffness) problems solved using continuous optimization and genetic algorithms. For the former, the proposed algorithm typically identifies solutions having objective functions within 1% of those found using full design variable fields. Computational savings are minor to moderate for the minimum compliance formulation with a single constraint, and are substantial for formulations having many local constraints. When using genetic algorithms, solutions are consistently obtained on mesh resolutions that were previously considered intractable. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
9.
H. Nguyen‐Xuan 《International journal for numerical methods in engineering》2017,110(10):972-1000
10.
Min Kyu Oh Dok Soo Lee Jeonghoon Yoo 《International journal for numerical methods in engineering》2022,123(2):339-365
This study presents a topological optimization method simultaneously considering the stress constraint and the uncertainty of the load positions for practical applications. The phase field design method is used to derive the topologically optimal structure shape. The stress penalization function, which makes intermediate design variable values disproportionately expensive, is employed to ensure numerical stability and avoid the singularity during the optimization process. The adaptive mesh refinement and a modified P-norm stress with correction factor are also employed to reduce the computational cost. As numerical examples, cantilever beam, L-shaped, and MBB-beam are presented to verify the proposed design method. The open-source code FreeFEM++ is used for the finite element analysis and the design process. 相似文献
11.
This article investigates multi-objective optimization under reliability constraints with applications in vehicle structural design. To improve computational efficiency, an improved multi-objective system reliability-based design optimization (MOSRBDO) method is developed, and used to explore the lightweight and high-performance design of a concept car body under uncertainty. A parametric model knowledge base is established, followed by the construction of a fully parametric concept car body of a multi-purpose vehicle (FPCCB-MPV) based on the knowledge base. The structural shape, gauge and topology optimization are then designed on the basis of FPCCB-MPV. The numerical implementation of MOSRBDO employs the double-loop method with design optimization in the outer loop and system reliability analysis in the inner loop. Multi-objective particle swarm optimization is used as the outer loop optimization solver. An improved multi-modal radial-based importance sampling (MRBIS) method is utilized as the system reliability solver for multi-constraint analysis in the inner loop. The accuracy and efficiency of the MRBIS method are demonstrated on three widely used test problems. In conclusion, MOSRBDO has been successfully applied for the design of a full parametric concept car body. The results show that the improved MOSRBDO method is more effective and efficient than the traditional MOSRBDO while achieving the same accuracy, and that the optimized body-in-white structure signifies a noticeable improvement from the baseline model. 相似文献
12.
This article introduces the element-propagating method to structural shape and topology optimization. Structural optimization based on the conventional level-set method needs to solve several partial differential equations. By the insertion and deletion of basic material elements around the geometric boundary, the element-propagating method can avoid solving the partial differential equations and realize the dynamic updating of the material region. This approach also places no restrictions on the signed distance function and the Courant–Friedrichs–Lewy condition for numerical stability. At the same time, in order to suppress the dependence on the design initialization for the 2D structural optimization problem, the strain energy density is taken as a criterion to generate new holes in the material region. The coupled algorithm of the element-propagating method and the method for generating new holes makes the structural optimization more robust. Numerical examples demonstrate that the proposed approach greatly improves numerical efficiency, compared with the conventional level-set method for structural topology optimization. 相似文献
13.
程长征;杨博;王选;刘培硕 《工程力学》2025,42(6):11-19
强度和刚度作为衡量工程结构的力学性能的重要指标,一直是工程优化领域重点关注的对象。另外,工程结构在服役过程中存在的不确定性因素对结构性能也影响较大。鉴于此,针对不确定载荷下同时考虑应力和柔度可靠性要求的结构设计问题,该文提出一种基于多项式混沌展开式代理模型的可靠性拓扑优化方法。利用Kieisselmeier-Steinhauser函数聚合最大应力和柔度,构建结构的极限状态函数。引进多项式混沌展开式,建立极限状态函数关于载荷随机变量的显式的代理模型,简化可靠性分析目标性能函数对随机变量的求导过程。详细推导了目标性能函数关于设计变量的导数,采用移动渐进线算法进行设计变量的更新,最后采用2个典型算例及蒙特卡洛仿真模拟验证了所提方法的准确性和有效性,数值结果表明所提方法可以给出同时满足应力和柔度可靠性要求的设计。 相似文献
14.
15.
Wei-Hong Zhang Pierre Beckers Claude Fleury 《International journal for numerical methods in engineering》1995,38(13):2283-2292
This paper presents a general parametric design approach for 2-D shape optimization problems. This approach has been achieved by integrating practical design methodologies into numerical procedures. It is characterized by three features: (i) automatic selection of a minimum number of shape design variables based on the CAD geometric model; (ii) integration of sequential convex programming algorithms to solve equality constrained optimization problems; (iii) efficient sensitivity analysis by means of the improved semi-analytical method. It is shown that shape design variables can be either manually or systematically identified with the help of equality constraints describing the relationship between geometric entities. Numerical solutions are performed to demonstrate the applicability of the proposed approach. A discussion of the results is also given: 相似文献
16.
Stergios Topouris 《工程优选》2013,45(10):1710-1726
This article focuses on generating a monobloc fingered hub (top-hat) disc design, aiming at reducing disc mass but maintaining rotor thermal capacity, while also improving heat dissipation characteristics. The analyses and tests demonstrated that such a design is possible to achieve, with mass reduction of just over 9%. The activities included research into cast iron modelling, which gave very important insights into the limits of mechanical performance under bending. Initial finite element analyses enabled considerable progress to be made towards establishing a baseline design, but only through shape optimization and topology optimization procedures was the full potential of the design accomplished. Shape optimization facilitated the reduction of maximum principal stress by 32%, considerably improving disc torsional strength with practically no increase in mass. The safety factor in torsion achieved a value of 3.57. Topology optimization provided further, although small, mass reduction (1.5%) while maintaining low stress levels. 相似文献
17.
Combining Shape Optimization (SO) with Adaptive Mesh Refinement (AMR) potentially offers a higher accuracy and higher computational efficiency, especially if the applied target error for AMR is reduced in the course of the optimization process. The disadvantage of that approach is that the rate of convergence of the corresponding optimization processes can be significantly lower as compared to processes which apply a fixed target error for AMR. In the present paper the so-called Multipoint Approximation Method (MAM) is used as a basis for SO in conjunction with AMR. Several techniques for improvement of the rates of convergence are presented and investigated. Firstly, alternative algorithms for determining the approximation functions using a weighted least squares method are investigated. The focus is on weights which depend on the discretization errors. Secondly, different strategies for moving and resizing the search sub-regions in the space of design variables are presented. The proposed methods are illustrated by means of several optimization problems in which the effect of AMR with changing discretization errors is modelled by artificially introduced numerical noise. 相似文献
18.
Eckhard Kirchner Rainer Immel 《International journal for numerical methods in engineering》2000,48(2):185-209
A novel approach towards fully stressed designs in hyperelasticity is discussed leading to closed‐form expressions for the sensitivities of the objective and displacements with respect to design variations. The key idea is the modification of the classical approach coupled with a so‐called design element method offering a lot of parallelism to standard finite element methods. We bypass implicit constraints on dependent quantities and derive an explicit linearly constrained optimization problem solved by means of first‐order procedures. The results obtained with the proposed method are adequate from an engineering point of view though being computed with a simple method. Copyright © 2000 John Wiley & Sons, Ltd. 相似文献
19.
Vlad Florea Manish Pamwar Balbir Sangha Il Yong Kim 《International journal for numerical methods in engineering》2020,121(7):1558-1594
As the aerospace and automotive industries continue to strive for efficient lightweight structures, topology optimization (TO) has become an important tool in this design process. However, one ever-present criticism of TO, and especially of multimaterial (MM) optimization, is that neither method can produce structures that are practical to manufacture. Optimal joint design is one of the main requirements for manufacturability. This article proposes a new density-based methodology for performing simultaneous MMTO and multijoint TO. This algorithm can simultaneously determine the optimum selection and placement of structural materials, as well as the optimum selection and placement of joints at material interfaces. In order to achieve this, a new solid isotropic material with penalization-based interpolation scheme is proposed. A process for identifying dissimilar material interfaces based on spatial gradients is also discussed. The capabilities of the algorithm are demonstrated using four case studies. Through these case studies, the coupling between the optimal structural material design and the optimal joint design is investigated. Total joint cost is considered as both an objective and a constraint in the optimization problem statement. Using the biobjective problem statement, the tradeoff between total joint cost and structural compliance is explored. Finally, a method for enforcing tooling accessibility constraints in joint design is presented. 相似文献
20.
工程结构优化设计发展综述 总被引：49，自引：5，他引：44
着重评述了工程结构优化设计研究领域从最初的尺寸优化发展到形状优化、拓扑优化的基本历程及其相关特点,并对优化设计选用的优化算法进行了归类,提出了这一领域今后仍然有待于发展的主要方面． 相似文献