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1.
    
This work presents a level set framework to solve the compliance topology optimization problem considering design‐dependent pressure loads. One of the major technical difficulties related to this class of problem is the adequate association between the moving boundary and the pressure acting on it. This difficulty is easily overcome by the level set method that allows for a clear tracking of the boundary along the optimization process. In the present approach, a reaction‐diffusion equation substitutes the classical Hamilton‐Jacobi equation to control the level set evolution. This choice has the advantages of allowing the nucleation of holes inside the domain and the elimination of the undesirable reinitialization steps. Moreover, the proposed algorithm allows merging pressurized (wet) boundaries with traction‐free boundaries during level set movements. This last property, allied to the simplicity of the level set representation and successful combination with the reaction‐diffusion based evolution applied to a design‐dependent pressure load problem, represents the main contribution of this paper. Numerical examples provide successful results, many of which comparable with others found in the literature and solved with different techniques.  相似文献   

2.
    
This paper presents a level‐set‐based topology optimization method based on numerically consistent sensitivity analysis. The proposed method uses a direct steepest‐descent update of the design variables in a level‐set method; the level‐set nodal values. An exact Heaviside formulation is used to relate the level‐set function to element densities. The level‐set function is not required to be a signed‐distance function, and reinitialization is not necessary. Using this approach, level‐set‐based topology optimization problems can be solved consistently and multiple constraints treated simultaneously. The proposed method leads to more insight in the nature of level‐set‐based topology optimization problems. The level‐set‐based design parametrization can describe gray areas and numerical hinges. Consistency causes results to contain these numerical artifacts. We demonstrate that alternative parameterizations, level‐set‐based or density‐based regularization can be used to avoid artifacts in the final results. The effectiveness of the proposed method is demonstrated using several benchmark problems. The capability to treat multiple constraints shows the potential of the method. Furthermore, due to the consistency, the optimizer can run into local minima; a fundamental difficulty of level‐set‐based topology optimization. More advanced optimization strategies and more efficient optimizers may increase the performance in the future. Copyright © 2012 John Wiley & Sons, Ltd.  相似文献   

3.
    
An enriched partition of unity FEM is developed to solve time‐dependent diffusion problems. In the present formulation, multiple exponential functions describing the spatial and temporal diffusion decay are embedded in the finite element approximation space. The resulting enrichment is in the form of a local asymptotic expansion. Unlike previous works in this area where the enrichment must be updated at each time step, here, the temporal decay in the solution is embedded in the asymptotic expansion. Thus, the system matrix that is evaluated at the first time step may be decomposed and retained for every next time step by just updating the right‐hand side of the linear system of equations. The advantage is a significant saving in the computational effort where, previously, the linear system must be reevaluated and resolved at every time step. In comparison with the traditional finite element analysis with p‐version refinements, the present approach is much simpler, more efficient, and yields more accurate solutions for a prescribed number of DoFs. Numerical results are presented for a transient diffusion equation with known analytical solution. The performance of the method is analyzed on two applications: the transient heat equation with a single source and the transient heat equation with multiple sources. The aim of such a method compared with the classical FEM is to solve time‐dependent diffusion applications efficiently and with an appropriate level of accuracy. Copyright © 2012 John Wiley & Sons, Ltd.  相似文献   

4.
    
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   

5.
    
The paper introduces an approach to stress‐constrained topology optimization through Heaviside projection–based constraint aggregation. The aggregation is calculated by integrating Heaviside projected local stresses over the design domain, and then, it is normalized over the total material volume. Effectively, the normalized integral measures the volume fraction of the material that has violated the stress constraint. Hence, with the Heaviside aggregated constraint, we can remove the stress failed material from the final design by constraining the integral to a threshold value near zero. An adaptive strategy is developed to select the threshold value for ensuring that the optimized design is conservative. By adding a stress penalty factor to the integrand, the Heaviside aggregated constraint can further penalize high stresses and becomes more stable and less sensitive to the selection of the threshold value. Our two‐dimensional and three‐dimensional numerical experiments demonstrate that the single Heaviside aggregated stress constraint can efficiently control the local stress level. Compared with the traditional approaches based on the Kreisselmeier‐Steinhauser and p‐norm aggregations, the Heaviside aggregation–based single constraint can substantially reduce computational cost on sensitivity analysis. These advantages make it possible to apply the proposed approach to large‐scale stress‐constrained problems.  相似文献   

6.
    
Motivated by key advances in manufacturing techniques, the tailoring of materials to achieve novel properties such as energy dissipation properties has been the focus of active research in engineering and materials science over the past decade. The goal of material design is to determine the optimal spatial layout to achieve a desired macroscopic constitutive response. However, the manufacturing abilities are the key factors to constrain the feasible design space, eg, minimum length and geometry complexity. Traditional density-based method, where each element works as a variable, always results in complicated geometry with large number of small intricate features. To address the aforementioned challenges, a new density field representation technique, named, Heaviside function-based geometric representation algorithm, is proposed in this paper, where density field is represented by truss-like components. Truss-like components have less control parameters and easier to handle for sensitivities derivation, especially for distance sensitivities. Using bar components to explicitly represent density field can explore design space effectively and generate simple structures without any intricate small features at borders. Furthermore, this density representation method is mesh independent and design variables are reduced significantly so that optimization problem can be solved efficiently using small-scale optimization algorithm, eg, sequential quadratic programming. However, finding a reasonable initial component distribution is critical to avoid optimization failure. To overcome this difficulty, a jump-start method is proposed by solving inverse subproblem. The overall optimization progress is divided into three stages, ie, the first stage is obtaining coarse snap-through material configuration based on traditional density-based method; the second stage is an inverse optimization problem to fit the geometry component to the solution obtained in stage I; and the stage III is maximizing the energy dissipation capacity. To demonstrate the powerful ability in design buckling-induced mechanism of the proposed density representation algorithm, buckling-induced energy dissipation mechanism with snap-through behavior to achieve the desired energy dissipation capacity considering failure constraint is demonstrated through four numerical examples.  相似文献   

7.
Abstract

A time‐partition method is used to obtain the analytical solutions of delay‐differential equations by the Laplace transformation technique with a special matrix inversion algorithm.  相似文献   

8.
拓扑优化方法经过几十年的发展,已成功应用于机械工程、航空航天、电磁等领域的构型设计中。然而,由于制造工艺的限制,拓扑优化结果通常无法直接应用,需根据工艺要求进行修改,因此在拓扑优化模型中考虑制造约束成为重要的研究方向。其中,尺寸控制广泛存在于大部分制造工艺中,主要包括最小尺寸控制与最大尺寸控制。该文提出了一种基于映射的拓扑优化最大尺寸控制方法,构造了一种新的映射模型,对结构中不满足最大尺寸约束的中心单元密度进行惩罚,在不引入任何约束条件的情况下实现了对结构最大尺寸的控制。此外,该文将该方法中的惩罚转变为一个全局约束条件后与具有最小尺寸控制功能的拓扑优化鲁棒列式相结合,实现了对构件的最大最小尺寸协同控制。数值算例表明了该方法的有效性。  相似文献   

9.
    
A transient finite strain viscoplastic model is implemented in a gradient‐based topology optimization framework to design impact mitigating structures. The model's kinematics relies on the multiplicative split of the deformation gradient, and the constitutive response is based on isotropic hardening viscoplasticity. To solve the mechanical balance laws, the implicit Newmark‐beta method is used together with a total Lagrangian finite element formulation. The optimization problem is regularized using a partial differential equation filter and solved using the method of moving asymptotes. Sensitivities required to solve the optimization problem are derived using the adjoint method. To demonstrate the capability of the algorithm, several protective systems are designed, in which the absorbed viscoplastic energy is maximized. The numerical examples demonstrate that transient finite strain viscoplastic effects can successfully be combined with topology optimization.  相似文献   

10.
    
The inclusion of non‐linear elastic analyses into the topology optimization problem is necessary to capture the finite deformation response, e.g. the geometric non‐linear response of compliant mechanisms. In previous work, the non‐linear response is computed by standard non‐linear elastic finite element analysis. Here, we incorporate a load–displacement constraint method to traverse non‐linear equilibrium paths with limit points to design structures that exhibit snap‐through behaviour. To accomplish this, we modify the basic arc length algorithm and embed this analysis into the topology optimization problem. Copyright © 2002 John Wiley & Sons, Ltd.  相似文献   

11.
    
This article presents a detailed study on the potential and limitations of performing higher‐order multi‐resolution topology optimization with the finite cell method. To circumvent stiffness overestimation in high‐contrast topologies, a length‐scale is applied on the solution using filter methods. The relations between stiffness overestimation, the analysis system, and the applied length‐scale are examined, while a high‐resolution topology is maintained. The computational cost associated with nested topology optimization is reduced significantly compared with the use of first‐order finite elements. This reduction is caused by exploiting the decoupling of density and analysis mesh, and by condensing the higher‐order modes out of the stiffness matrix. Copyright © 2016 John Wiley & Sons, Ltd.  相似文献   

12.
    
This work is concerned with the development of different domain‐BEM (D‐BEM) approaches to the solution of two‐dimensional diffusion problems. In the first approach, the process of time marching is accomplished with a combination of the finite difference and the Houbolt methods. The second approach starts by weighting, with respect to time, the basic D‐BEM equation, under the assumption of linear and constant time variation for the temperature and for the heat flux, respectively. A constant time weighting function is adopted. The time integration reduces the order of the time derivative that appears in the domain integral; as a consequence, the initial conditions are directly taken into account. Four examples are presented to verify the applicability of the proposed approaches, and the D‐BEM results are compared with the corresponding analytical solutions.Copyright © 2011 John Wiley & Sons, Ltd.  相似文献   

13.
    
A rigorous method for stabilizing projection‐based linear reduced‐order models without significantly affecting their accuracy is proposed. Unlike alternative approaches, this method is computationally efficient. It requires primarily the solution of a small‐scale convex optimization problem. Furthermore, it is nonintrusive in the sense that it operates directly on readily available reduced‐order operators. These can be precomputed using any data compression technique including balanced truncation, balanced proper orthogonal decomposition, proper orthogonal decomposition, or moment matching. The proposed method is illustrated with three applications: the stabilization of the reduction of the Computational Fluid Dynamics‐based model of a linearized unsteady supersonic flow, the reduction of a Computational Structural Dynamics system, and the stabilization of the reduction of a coupled Computational Fluid Dynamics–Computational Structural Dynamics model of a linearized aeroelastic system in the transonic flow regime. Copyright © 2012 John Wiley & Sons, Ltd.  相似文献   

14.
为了满足制造工艺和静强度要求,提出一种综合考虑最小尺寸控制和应力约束的柔顺机构混合约束拓扑优化设计方法。采用改进的固体各向同性材料插值模型描述材料分布,利用多相映射方法同时控制实相和空相材料结构的最小尺寸,采用最大近似函数P范数求解机构的最大应力,以机构的输出位移最大化作为目标函数,综合考虑最小特征尺寸控制和应力约束建立柔顺机构混合约束拓扑优化数学模型,利用移动渐近算法求解柔顺机构混合约束拓扑优化问题。数值算例结果表明,混合约束拓扑优化获得的柔顺机构能够同时满足最小尺寸制造约束和静强度要求,机构的von Mises等效应力分布更加均匀。  相似文献   

15.
为了满足制造工艺和静强度要求,提出一种综合考虑最小尺寸控制和应力约束的柔顺机构混合约束拓扑优化设计方法。采用改进的固体各向同性材料插值模型描述材料分布,利用多相映射方法同时控制实相和空相材料结构的最小尺寸,采用最大近似函数P范数求解机构的最大应力,以机构的输出位移最大化作为目标函数,综合考虑最小特征尺寸控制和应力约束建立柔顺机构混合约束拓扑优化数学模型,利用移动渐近算法求解柔顺机构混合约束拓扑优化问题。数值算例结果表明,混合约束拓扑优化获得的柔顺机构能够同时满足最小尺寸制造约束和静强度要求,机构的von Mises等效应力分布更加均匀。  相似文献   

16.
    
We develop rate‐dependent regularization approaches for three‐dimensional frictional contact constraints based on the Kelvin and Maxwell viscoelastic constitutive models. With the present regularization schemes, we aim to provide a basis to better model friction and to stabilize the contact analysis while keeping the contact model as simple as possible. The key feature of the regularization approaches, implemented using an implicit time integrator, is that one can recover in the limit the widely used rate‐independent elastoplastic regularization framework without encountering numerical difficulties. Intermediate contact tractions are defined in terms of the relative displacement, the relative velocity, and the regularization parameters. The projection operators operate on the intermediate tractions and yield contact tractions that satisfy all the discretized contact constraints. The use of projection operators allows a systematic implementation of the present regularization schemes. Through numerical simulations, we observed that the Maxwell‐type regularization effectively avoids convergence problems, even for relatively large time step sizes, while the Kelvin‐type regularization does not. Copyright © 2003 John Wiley & Sons, Ltd.  相似文献   

17.
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18.
    
In this paper, we propose a three‐dimensional (3D) grayscale‐free topology optimization method using a conforming mesh to the structural boundary, which is represented by the level‐set method. The conforming mesh is generated in an r‐refinement manner; that is, it is generated by moving the nodes of the Eulerian mesh that maintains the level‐set function. Although the r‐refinement approach for the conforming mesh generation has many benefits from an implementation aspect, it has been considered as a difficult task to stably generate 3D conforming meshes in the r‐refinement manner. To resolve this task, we propose a new level‐set based r‐refinement method. Its main novelty is a procedure for minimizing the number of the collapsed elements whose nodes are moved to the structural boundary in the conforming mesh; in addition, we propose a new procedure for improving the quality of the conforming mesh, which is inspired by Laplacian smoothing. Because of these novelties, the proposed r‐refinement method can generate 3D conforming meshes at a satisfactory level, and 3D grayscale‐free topology optimization is realized. The usefulness of the proposed 3D grayscale‐free topology optimization method is confirmed through several numerical examples. Copyright © 2017 John Wiley & Sons, Ltd.  相似文献   

19.
Abstract

Several new stability criteria for the linear time‐delay system represented by some simple closed regions in the complex plane are proposed. In these criteria, the system's stability can be easily determined by examining the locations of the eigenvalues of the system matrix A 0 or its delay matrix Ad . In other words, we do not need to solve any complicated characteristic equation of the system.  相似文献   

20.
    
The present paper is concerned with the layout optimization of resonating actuators using topology optimization techniques. The goal of the optimization is a maximization of the magnitude of steady‐state vibrations for a given excitation frequency. The problem formulation includes an external viscous damper at the output port which models a working load on the structure. Copyright © 2002 John Wiley & Sons, Ltd.  相似文献   

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