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1.
A truss topology optimization problem under stress constraints is formulated as a Mixed Integer Programming (MIP) problem with variables indicating the existence of nodes and members. The local constraints on nodal stability and intersection of members are considered, and a moderately large lower bound is given for the cross-sectional area of an existing member. A lower-bound objective value is found by neglecting the compatibility conditions, where linear programming problems are successively solved based on a branch-and-bound method. An upper-bound solution is obtained as a solution of a Nonlinear Programming (NLP) problem for the topology satisfying the local constraints. It is shown in the examples that upper- and lower-bound solutions with a small gap in the objective value can be found by the branch-and-bound method, and the computational cost can be reduced by using the local constraints. 相似文献
2.
Ismail Farajpour 《Advances in Engineering Software》2011,42(3):64-75
The main objective of the structure optimization is to reduce the manufacturing cost of the structure. However, economical design should not deviate from engineering restrictions and laws. Based on this concept, various methods have been invented to optimize structures. In this research, some variations in one of the very simple and primary methods called “coordinate descent” or “successive coordinate search” is used for geometry optimization of the trusses. In order to increase the optimization speed and decrease the solution time of the problem, fast matrix analysis methods has been employed leading to reduction of the time required for calculating of the objective function. Furthermore, an optimized solution seeking algorithm has been introduced. In this algorithm, some factors have been defined by which the relation between the optimization time and these factors have been calculated, both experimentally and mathematically and the appropriate values of these factors are obtained to reduce the optimization time. Moreover, the effect of increasing the accuracy of the optimum solution on the number of analyses has been studied. Analysis of the presented method shows that regardless of its simplicity, it can be utilized as a fast method for optimizing variety of structures. 相似文献
3.
A method to minimize the compliance of structures subject to multiple load cases is presented. Firstly, the material distribution
in design domain is optimized to form a truss-like continuum. The anisotropic composite is employed as the material model
to simulate the constitutive relation of the truss-like continuum. The member densities and orientations at the nodes are
taken as design variables. The member densities and orientations at any point in an element vary continuously. Then, parts
of members, which are formed according to the member distribution field, are chosen to form the nearly optimum discrete structure.
Lastly, the positions of the nodes and the cross-sectional areas of the members are optimized. In the above process, numerical
instabilities such as checkerboard and mesh dependencies disappear without any additional technique. The sensitivities of
the compliance are derived. Examples are presented to demonstrate the capability of the proposed method. 相似文献
4.
A dilemma in the foaming of inner polyurethane (PU) pieces for household refrigerators is that of keeping the production costs down without adversely affecting the dimension precision. One way to do this is to reduce the electric power consumption spent running the polyurethane foaming line in which a number of heavy foaming jigs are continuously circulating, by optimally designing the reinforcement structure of the jig. In this paper, topology optimization and parameter optimization utilizing the response surface method (RSM) are applied for the optimum design of the jig reinforcement structure, in order to minimize the total jig weight while securing the dimension precision of the foamed urethane case. Both the reliability of the approximated response surfaces and the validity of the proposed optimization procedure are verified through illustrative optimization experiments. In addition, it is confirmed that the proposed procedure provides us with an optimum reinforcement structure which remarkably reduces the total jig weight. 相似文献
5.
Georg Pingen Anton Evgrafov Kurt Maute 《Structural and Multidisciplinary Optimization》2007,34(6):507-524
We consider the optimal design of two- (2D) and three-dimensional (3D) flow domains using the lattice Boltzmann method (LBM)
as an approximation of Navier-Stokes (NS) flows. The problem is solved by a topology optimization approach varying the effective
porosity of a fictitious material. The boundaries of the flow domain are represented by potentially discontinuous material
distributions. NS flows are traditionally approximated by finite element and finite volume methods. These schemes, while well
established as high-fidelity simulation tools using body-fitted meshes, are effected in their accuracy and robustness when
regular meshes with zero-velocity constraints along the surface and in the interior of obstacles are used, as is common in
topology optimization. Therefore, we study the potential of the LBM for approximating low Mach number incompressible viscous
flows for topology optimization. In the LBM the geometry of flow domains is defined in a discontinuous manner, similar to
the approach used in material-based topology optimization. In addition, this non-traditional discretization method features
parallel scalability and allows for high-resolution, regular fluid meshes. In this paper, we show how the variation of the
porosity can be used in conjunction with the LBM for the optimal design of fluid domains, making the LBM an interesting alternative
to NS solvers for topology optimization problems. The potential of our topology optimization approach will be illustrated
by 2D and 3D numerical examples. 相似文献
6.
H. Fredricson 《Structural and Multidisciplinary Optimization》2005,30(3):193-200
This paper deals with joint penalization and material selection in frame topology optimization. The models used in this study are frame structures with flexible joints. The problem considered is to find the frame design which fulfills a stiffness requirement at the lowest structural weight. To support topological change of joints, each joint is modelled as a set of subelements. A set of design variables are applied to each beam and joint subelement. Two kinds of design variables are used. One of these variables is an area-type design variable used to control the global element size and support a topology change. The other variables are length ratio variables controlling the cross section of beams and internal stiffness properties of the joints. This paper presents two extensions to classical frame topology optimization. Firstly, penalization of structural joints is presented. This introduces the possibility of finding a topology with less complexity in terms of the number of beam connections. Secondly, a material interpolation scheme is introduced to support mixed material design. 相似文献
7.
A. Gersborg-Hansen M. P. Bendsøe O. Sigmund 《Structural and Multidisciplinary Optimization》2006,31(4):251-259
This note addresses the use of the finite volume method (FVM) for topology optimization of a heat conduction problem. Issues
pertaining to the proper choice of cost functions, sensitivity analysis, and example test problems are used to illustrate
the effect of applying the FVM as an analysis tool for design optimization. This involves an application of the FVM to problems
with nonhomogeneous material distributions, and the arithmetic and harmonic averages have here been used to provide a unique
value for the conductivity at element boundaries. It is observed that when using the harmonic average, checkerboards do not
form during the topology optimization process.
Preliminary results of the work reported here were presented at the WCSMO 6 in Rio de Janeiro 2005, see Gersborg-Hansen et
al. (2005b). 相似文献
8.
This paper will propose a topology optimization approach for the design of large displacement compliant mechanisms with geometrical non-linearity by using the element-free Galerkin (EFG) method. In this method, the Shepard function is applied to construct a physically meaningful density approximant, to account for its non-negative and range-bounded property. Firstly, in terms of the original nodal density field, the Shepard function method functionally similar to a density filter is used to generate a non-local nodal density field with enriched smoothness over the design domain. The density of any node can be evaluated according to the nodal density variables located inside the influence domain of the interested node. Secondly, in the numerical implementation the Shepard function method is again employed to construct a point-wise density interpolant. Gauss quadrature is used to calculate the integration of background cells numerically, and the artificial densities over all Gauss points can be determined by the surrounding nodal densities within the influence domain of the concerned computational point. Finally, the moving least squares (MLS) method is applied to construct the shape functions using the weight functions with compact support for assembling the meshless approximations of state equations. Since MLS shape functions are lack of the Kronecker delta function property, the penalty method is applied to enforce the essential boundary conditions. A typical large-deformation compliant mechanism is used as the numerical example to demonstrate the effectiveness of the proposed method. 相似文献
9.
A new topology optimization using adaptive inner-front level set method is presented. In the conventional level set-based
topology optimization, the optimum topology strongly depends on the initial level set due to the incapability of inner-front
creation during the optimization process. In the present work, in this regard, an algorithm for inner-front creation is proposed
in which the sizes, the positions, and the number of new inner-fronts during the optimization process can be globally and
consistently identified. In the algorithm, the criterion of inner-front creation for compliance minimization problems of linear
elastic structures is chosen as the strain energy density along with volumetric constraint. To facilitate the inner-front
creation process, the inner-front creation map is constructed and used to define new level set function. In the implementation
of inner-front creation algorithm, to suppress the numerical oscillation of solutions due to the sharp edges in the level
set function, domain regularization is carried out by solving the edge smoothing partial differential equation (smoothing
PDE). To update the level set function during the optimization process, the least-squares finite element method (LSFEM) is
adopted. Through the LSFEM, a symmetric positive definite system matrix is constructed, and non-diffused and non-oscillatory
solution for the hyperbolic PDE such as level set equation can be obtained. As applications, three-dimensional topology optimization
of shell structures is treated. From the numerical examples, it is shown that the present method brings in much needed flexibility
in topologies during the level set-based topology optimization process. 相似文献
10.
为开展多工况下曲面结构的拓扑优化,采用两向正交类桁架连续体材料模型和有限元分析方法,以杆件在结点位置的密度和方向为优化设计变量进行结构优化。根据有限元分析结果,采用满应力准则法优化各单一工况下的材料分布。按照多工况与各单工况下材料的方向刚度最大值的差值最小为原则,优化多工况下的杆件方向和密度分布。将杆件竖直位置的质心连线作为拓扑优化的平面Prager结构,以3个算例表明该方法的有效性。 相似文献
11.
12.
To accommodate the dual objectives of many engineering applications, one objective to minimize the mean compliance for the stiffest structure under normal service conditions and the other objective to maximize the strain energy for energy absorption during excessive loadings, topology optimization with a multimaterial model is applied to the design of an energy-absorbing structure in this paper. The effective properties of the three-phase material are derived using a spherical microinclusion model. The dual objectives are combined in a ratio formation. Numerical examples from the proposed method are presented and discussed. 相似文献
13.
为实现更加先进的拓扑优化算法,研究采用反应扩散方程的水平集结构拓扑优化方法,通过理论推导给出算法中的参数选择建议.该方法允许在拓扑优化过程中生成新的孔洞,初始结构无须包含孔洞,不需要重新初始化步骤,从而可提高算法的收敛性.针对传统拓扑优化中主要采用体积约束、以柔度最小为目标和体积保留率设定存在一定主观性的问题,探究不同体积保留率下的结构应力水平的变化规律,结果显示可以依据结构最大应力水平与体积保留率的变化规律确定最优体积保留率. 相似文献
14.
In this paper a simple and robust approach is presented for spectral matching of ground motions utilizing the wavelet transform and an improved metaheuristic optimization technique. For this purpose, wavelet transform is used to decompose the original ground motions to several levels, where each level covers a special range of frequency, and then each level is multiplied by a variable. Subsequently, the enhanced colliding bodies optimization technique is employed to calculate the variables such that the error between the response and target spectra is minimized. The application of the proposed method is illustrated through modifying 12 sets of ground motions. The results achieved by this method demonstrate its capability in solving the problem. The outcomes of the enhanced colliding bodies optimization (ECBO) are compared to those of the standard colliding bodies optimization (CBO) to illustrate the importance of the enhancement of the algorithm. 相似文献
15.
The optimal design of a casting feeding system is considered. The problem is formulated as the volume constrained topology
optimization and is solved with the finite element analysis, explicit design sensitivity, and numerical optimization. In contrast
to the traditional topology optimization where the objective function is defined on the design space, in the presented method,
the design space is a subset of the complement of the objective function space. To accelerate optimization procedure, the
nonlinear unsteady heat transfer equation is approximated with a Poisson-like equation. The feasibility of the presented method
is supported with illustrative examples. 相似文献
16.
17.
针对用有限元法进行连续体结构拓扑优化时需不断重构网格来处理网格畸变和网格移动,且存在数值计算不稳定等问题,基于无网格径向点插值方法(Radial Point Interpolation Method,RPIM)对简谐激励下的连续体结构进行拓扑优化.选取节点的相对密度作为设计变量,以结构动柔度最小化为目标函数,基于带惩罚的各向同性固体微结构(Solid Isotropic Microstructure with Penalization,SIMP)模型建立简谐激励下的优化模型;采用伴随法求解得到目标函数的敏度分析公式;利用优化准则法求解优化模型.经典的二维连续体结构拓扑优化算例证明该方法的可行性和有效性. 相似文献