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1.
Tuo Zhao Adeildo S. Ramos Jr. Glaucio H. Paulino 《International journal for numerical methods in engineering》2019,118(13):804-828
This paper addresses material nonlinear topology optimization considering the von Mises criterion by means of an asymptotic analysis using a fictitious nonlinear elastic model. In this context, we consider the topology optimization problem subjected to prescribed energy, which leads to robust convergence in nonlinear problems. Two nested formulations are considered. In the first, the objective is to maximize the strain energy of the system in equilibrium, and in the second, the objective is to maximize the load factor. In both cases, a volume constraint is imposed. The sensitivity analysis is quite effective and efficient in the sense that there is no extra adjoint equation. In addition, the nonlinear structural equilibrium problem is solved using direct minimization of the structural strain energy using Newton's method with an inexact line-search strategy. Four numerical examples demonstrate the features of the proposed material nonlinear topology optimization framework for approximating standard von Mises plasticity. 相似文献
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Daisuke Murai Atsushi Kawamoto Tsuguo Kondoh 《International journal for numerical methods in engineering》2020,121(10):2246-2261
This article describes a numerical solution to the topology optimization problem using a time-evolution equation. The design variables of the topology optimization problem are defined as a mathematical scalar function in a given design domain. The scalar function is projected to the normalized density function. The adjoint variable method is used to determine the gradient defined as the ratio of the variation of the objective function or constraint function to the variation of the design variable. The variation of design variables is obtained using the solution of the time-evolution equation in which the source term and Neumann boundary condition are given as a negative gradient. The distribution of design variables yielding an optimal solution is obtained by time integration of the solution of the time-evolution equation. By solving the topology optimization problem using the proposed method, it is shown that the objective function decreases when the constraints are satisfied. Furthermore, we apply the proposed method to the thermal resistance minimization problem under the total volume constraint and the mean compliance minimization problem under the total volume constraint. 相似文献
3.
Topology optimization of continuum structures with displacement constraints based on meshless method
Xujing Yang Juan Zheng Shuyao Long 《International Journal of Mechanics and Materials in Design》2017,13(2):311-320
In this paper, the element free Galerkin method (EFG) is applied to carry out the topology optimization of continuum structures with displacement constraints. In the EFG method, the matrices in the discretized system equations are assembled based on the quadrature points. In the sense, the relative density at Gauss quadrature point is employed as design variable. Considering the minimization of weight as an objective function, the mathematical formulation of the topology optimization subjected to displacement constraints is developed using the solid isotropic microstructures with penalization interpolation scheme. Moreover, the approximate explicit function expression between topological variables and displacement constraints are derived. Sensitivity of the objective function is derived based on the adjoint method. Three numerical examples are used to demonstrate the feasibility and effectiveness of the proposed method. 相似文献
4.
This article presents a numerical approach of topology optimization with multiple materials for the heat conduction problem. The multiphase level set model is used to implicitly describe the geometric boundaries of material regions with different conductivities. The model of multi-material representation has no emergence of the intermediate density. The optimization objective is to construct the optimal heat conductive paths which improve the efficiency of heat transfer. The dissipation of thermal transport potential capacity is taken as the objective function. The sensitivity analysis is implemented by the adjoint variable method, which is the foundation of constructing the velocity field of the level set equation. The optimal result is gradually realized by the evolution of multi-material boundaries, and the topological changes are naturally handled during the optimization process. Finally, the numerical examples are presented to demonstrate the feasibility and validity of the proposed method for topology optimization of the heat conduction problem. 相似文献
5.
Robust shape and topology optimization considering geometric uncertainties with stochastic level set perturbation
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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
6.
Linyuan Shang 《工程优选》2016,48(6):1060-1079
This article investigates topology optimization of a bi-material model for acoustic–structural coupled systems. The design variables are volume fractions of inclusion material in a bi-material model constructed by the microstructure-based design domain method (MDDM). The design objective is the minimization of sound pressure level (SPL) in an interior acoustic medium. Sensitivities of SPL with respect to topological design variables are derived concretely by the adjoint method. A relaxed form of optimality criteria (OC) is developed for solving the acoustic–structural coupled optimization problem to find the optimum bi-material distribution. Based on OC and the adjoint method, a topology optimization method to deal with large calculations in acoustic–structural coupled problems is proposed. Numerical examples are given to illustrate the applications of topology optimization for a bi-material plate under a low single-frequency excitation and an aerospace structure under a low frequency-band excitation, and to prove the efficiency of the adjoint method and the relaxed form of OC. 相似文献
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Jakob S. Jensen 《International journal for numerical methods in engineering》2007,72(13):1605-1630
An efficient procedure for topology optimization of dynamics problems is proposed. The method is based on frequency responses represented by Padé approximants and analytical sensitivity analysis derived using the adjoint method. This gives an accurate approximation of the frequency response over wide frequency ranges and a formulation that allows for design sensitivities to be computed at low computational cost also for a large number of design variables. Two examples that deal with optimization of forced vibrations are included. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
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Summary The reflection, refraction and scattering of inhomogeneous plane waves of SH type by an interface crack between two dissimilar viscoelastic bodies are investigated. The singular integral equation method is used to reduce the scattering problem into the Cauchy singular integral equation of first kind by introduction of the crack dislocation density function. Then, the singular integral equation is solved numerically by Kurtz's piecewise continous function method. The crack opening displacement and dynamic stress intensity factor characterizing the scattered near-field are estimated for various incident angles, frequencies and relaxation times. The differences on crack opening displacement and stress intensity factor between elastic and viscoelastic interface crack are contrasted. And the effects of incident angle, incident frequency and relaxation time of the viscoelastic material are analyzed and explained by the features of phase lag and energy dissipation of the viscoelastic wave. 相似文献
11.
将时间反转理论与拓扑优化思想结合在一起,引入了直接声场和伴随声场的概念。通过将时间反转后的兰姆波散射信号作为伴随声场中的二次激励源,实现了信号在缺陷处的聚焦,并根据时域拓扑能量公式计算出检测区域内各点的拓扑能量值,从而对薄板内多缺陷进行表征。有限元仿真和实验表明:在多缺陷情形下,延迟叠加法(Delay and Sum,DAS)因受瑞利准则的约束而在缺陷间距小于分辨率阈值时,无法对缺陷位置进行定位;时域拓扑能量法通过兰姆波时间反转聚焦、图像融合,不仅提高了缺陷检测分辨率,还消除了多模式、有噪声环境下伪像的干扰。有效推动了兰姆波在板类结构无损检测中的应用。 相似文献
12.
Shinnosuke Nishi Takayuki Yamada Kazuhiro Izui Shinji Nishiwaki Kenjiro Terada 《International journal for numerical methods in engineering》2020,121(6):1218-1247
This study presents a level set–based topology optimization with isogeometric analysis (IGA) for controlling high-frequency electromagnetic wave propagation in a domain with periodic microstructures (unit cells). The high-frequency homogenization method is applied to characterize the macroscopic high-frequency waves in periodic heterogeneous media whose wavelength is comparative to or smaller than the representative length of a unit cell. B-spline basis functions are employed for the IGA discretization procedure to improve the performance of electromagnetic wave analysis in a unit cell and topology optimization. Also, to keep the same order of continuity on the periodic boundaries as on other element edges in the domain, we propose the extended domain approach, while incorporating Floquet periodic boundary condition (FPBC). Two types of optimization problems are taken as examples to demonstrate the effectiveness of the proposed method in comparison with the standard finite element analysis (FEA). The optimization results provide optimized topologies of unit cells qualified as anisotropic metamaterials with hyperbolic and bidirectional dispersion properties at the macroscale. 相似文献
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Dong Wang Weifeng Gao 《International journal for numerical methods in engineering》2019,120(11):1249-1272
The topology optimization problem of a continuum structure on the compliance minimization objective is investigated under consideration of the external load uncertainty in its application position with a nonprobabilistic approach. The load position is defined as the uncertain-but-bounded parameter and is represented by an interval variable with a nominal application point. The structural compliance due to the load position deviation is formulated with the quadratic Taylor series expansion. As a result, the objective gradient information to the topological variables can be evaluated efficiently in a quadratic expression. Based on the maximum design sensitivity value, which corresponds to the most sensitive compliance to the uncertain loading position, a single-level optimization approach is suggested by using a popular gradient-based optimality criteria method. The proposed optimization scheme is performed to gain the robust topology optimizations of three benchmark examples, and the final configuration designs are compared comprehensively with the conventional topology optimizations under the loading point fixation. It can be observed that the present method can provide remarkably different material layouts with auxiliary components to accommodate the load position disturbances. The numerical results of the representative examples also show that the structural performances of the robust topology optimizations appear less sensitive to the load position perturbations than the traditional designs. 相似文献
14.
Robust optimal Robin boundary control for the transient heat equation with random input data
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J. Martínez‐Frutos M. Kessler A. Münch F. Periago 《International journal for numerical methods in engineering》2016,108(2):116-135
The problem of robust optimal Robin boundary control for a parabolic partial differential equation with uncertain input data is considered. As a measure of robustness, the variance of the random system response is included in two different cost functionals. Uncertainties in both the underlying state equation and the control variable are quantified through random fields. The paper is mainly concerned with the numerical resolution of the problem. To this end, a gradient‐based method is proposed considering different functional costs to achieve the robustness of the system. An adaptive anisotropic sparse grid stochastic collocation method is used for the numerical resolution of the associated state and adjoint state equations. The different functional costs are analysed in terms of computational efficiency and its capability to provide robust solutions. Two numerical experiments illustrate the performance of the algorithm. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
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Satoshi Kitayama Koetsu Yamazaki 《International Journal of Mechanics and Materials in Design》2014,10(3):313-328
This paper proposes a sequential approximate robust design optimization (SARDO) with the radial basis function (RBF) network. In RDO, the mean and the standard deviation of objective should be minimized simultaneously. Therefore, the RDO is generally formulated as bi-objective design optimization. Our goal is to find a robust optimal solution with a small number of function evaluations, not identifying a set of Pareto-optimal solution using Multi-Objective Evolutionary Algorithms. The weighted sum is often used to find a robust optimal solution. In contrast, the weighted lp norm method is used in this paper. Through illustrative examples, some validations of the weighted lp norm method to the RDO are clarified. Next, SARDO with the RBF network is discussed. In general, the standard deviation of functions is obtained by using the finite difference method. Thus, in order to obtain the standard deviation of functions, the finite difference method is directly applied to the response surface. High accuracy of the finite difference method will leads to highly accurate robust optimal solution. In order to avoid the inaccurate numerical calculation, the standard deviation is expressed by only the Gaussian kernel. As the result, it is expected that a highly accurate robust optimal solution can be found with a small number of function evaluations. Through numerical examples, the validity of the proposed approach is examined. Finally, the variable blank holder force trajectory for reducing springback is examined. 相似文献
17.
S. Kanaun 《International Journal of Engineering Science》2008,46(4):352-373
The work is dedicated to the analysis of acoustical and optical branches of longitudinal elastic wave propagation in the medium with a random set of spherical inclusions. The effective field method and quasicrystalline approximation are used for the construction of the dispersion equation for the wave number of the mean (coherent) wave field propagating in the composite. This dispersion equation serves for all frequencies of the incident field, properties and volume concentrations of inclusions. Different branches of the solutions of this equation are obtained and analyzed. Each of these branches may be interpreted as a specific mode of wave propagation, and its input in the mean (coherent) wave field is essential only in a certain frequency region. The predictions of the method are compared with some experimental data existing in the literature. 相似文献
18.
Robust topology optimization of phononic crystals with random field uncertainty 总被引:1,自引:0,他引:1
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Xiaopeng Zhang Jingjie He Akihiro Takezawa Zhan Kang 《International journal for numerical methods in engineering》2018,115(9):1154-1173
The uncertain spatial variation of material properties can remarkably affect the band gap characteristics of phononic crystals (PnCs). It is necessary to consider this issue when designing and manufacturing PnC materials/structures. This paper investigates a robust topology optimization method for designing the microstructures of PnCs by considering random‐field material properties. Herein, the spatial distribution of the material properties is first represented by a random field and then discretized into uncorrelated stochastic variables with the expansion optimal linear estimation method; stochastic band gap analysis is then conducted with polynomial chaos expansion. Furthermore, a robust topology optimization formulation of PnCs is proposed on the basis of the relative elemental density, where a weighted objective function handles the compromise of the mean value and standard deviation of the PnC band gap. The band gap response is analyzed, employing the finite element method for each sample of polynomial chaos expansion. In this context, the sensitivities of the stochastic band gap behaviors to the design variables are also derived. Numerical examples demonstrate that the proposed method can generate meaningful optimal topologies of PnCs with a relatively large width and less sensitive band gap. Additionally, the effects of the weight factors in the objective function and the variation coefficient of material properties are discussed. 相似文献
19.
André Jacomel Torii Antonio André Novotny Renatha Batista dos Santos 《International journal for numerical methods in engineering》2016,106(11):889-903
In this paper, we present an approach for robust compliance topology optimization under volume constraint. The compliance is evaluated considering a point‐wise worst‐case scenario. Analogously to sequential optimization and reliability assessment, the resulting robust optimization problem can be decoupled into a deterministic topology optimization step and a reliability analysis step. This procedure allows us to use topology optimization algorithms already developed with only small modifications. Here, the deterministic topology optimization problem is addressed with an efficient algorithm based on the topological derivative concept and a level‐set domain representation method. The reliability analysis step is handled as in the performance measure approach. Several numerical examples are presented showing the effectiveness of the proposed approach. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献