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1.
This paper deals with topology optimization of load carrying structures defined on a discretized design domain where binary
design variables are used to indicate material or void in the various finite elements. The main contribution is the development
of two iterative methods which are guaranteed to find a local optimum with respect to a 1-neighbourhood. Each new iteration
point is obtained as the optimal solution to an integer linear programming problem which is an approximation of the original
problem at the previous iteration point. The proposed methods are quite general and can be applied to a variety of topology
optimization problems defined by 0-1 design variables. Most of the presented numerical examples are devoted to problems involving
stresses which can be handled in a natural way since the design variables are kept binary in the subproblems. 相似文献
2.
Free material design deals with the question of finding the lightest structure subject to one or more given loads when both
the distribution of material and the material itself can be freely varied. We additionally consider constraints on local stresses
in the optimal structure. We discuss the choice of formulation of the problem and the stress constraints. The chosen formulation
leads to a mathematical program with matrix inequality constraints, so-called nonlinear semidefinite program. We present an
algorithm that can solve these problems. The algorithm is based on a generalized augmented Lagrangian method. A number of
numerical examples demonstrate the effect of stress constraints in free material optimization.
Dedicated to Pauli Pedersen on the occasion of his 70th birthday. 相似文献
3.
A new method called the growing ground structure method is proposed for truss topology optimization, which effectively expands
or reduces the ground structure by iteratively adding or removing bars and nodes. The method uses five growth strategies,
which are based on mechanical properties, to determine the bars and nodes to be added or removed. Hence, the method can optimize
the initial ground structures such that the modified, or grown, ground structures can generate the optimal solution for the
given set of nodes. The structural data of trusses are manipulated using C++ standard template library and the Boost Graph
Library, which help alleviate the programming efforts for implementing the method. Three kinds of topology optimization problems
are considered. The first problem is a compliance minimization problem with cross-sectional areas as variables. The second
problem is a minimum compliance problem with the nodal coordinates also as variables. The third problem is a minimum volume
problem with stress constraints under multiple load cases. Six numerical examples corresponding to these three problems are
solved to demonstrate the performance of the proposed method. 相似文献
4.
O. da Silva Smith 《Structural and Multidisciplinary Optimization》1997,13(2-3):155-166
In truss topology optimization against buckling constraints, the extension from considering a single load case to include multiple loading conditions remains an unsolved problem in the ground structure approach. The present paper suggests a heuristic method attempting to take the multiple load situation into account. A method by Pedersen (1993, 1994) considering only single loading conditions is generalized to include multiple load cases. Based on the ground structure approach the algorithm allows for variable ground structures allowing for, for instance, geometrical restrictions such as concave or even disconnected design domains (Smith 1995b). 相似文献
5.
On an alternative approach to stress constraints relaxation in topology optimization 总被引:5,自引:4,他引:1
Matteo Bruggi 《Structural and Multidisciplinary Optimization》2008,36(2):125-141
The paper deals with the imposition of local stress constraints in topology optimization. The aim of the work is to analyze
the performances of an alternative methodology to the ε-relaxation introduced in Cheng and Guo (Struct Optim 13:258–266, 1997), which handles the well-known stress singularity problem. The proposed methodology consists in introducing, in the SIMP
law used to apply stress constraints, suitable penalty exponents that are different from those that interpolate stiffness
parameters. The approach is similar to the classical one because its main effect is to produce a relaxation of the stress
constraints, but it is different in terms of convergence features. The technique is compared with the classical one in the
context of stress-constrained minimum-weight topology optimization. Firstly, the problem is studied in a modified truss design
framework, where the arising of the singularity phenomenon can be easily shown analytically. Afterwards, the analysis is extended
to its natural context of topology bidimensional problems. 相似文献
6.
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
7.
This paper considers the problem of optimal truss topology design subject to multiple loading conditions. We minimize a weighted
average of the compliances subject to a volume constraint. Based on the ground structure approach, the cross-sectional areas
are chosen as the design variables. While this problem is well-studied for continuous bar areas, we consider in this study
the case of discrete areas. This problem is of major practical relevance if the truss must be built from pre-produced bars
with given areas. As a special case, we consider the design problem for a single available bar area, i.e., a 0/1 problem.
In contrast to the heuristic methods considered in many other approaches, our goal is to compute guaranteed globally optimal
structures. This is done by a branch-and-bound method for which convergence can be proven. In this branch-and-bound framework,
lower bounds of the optimal objective function values are calculated by treating a sequence of continuous but non-convex relaxations
of the original mixed-integer problem. The main effect of using this approach lies in the fact that these relaxed problems
can be equivalently reformulated as convex problems and, thus, can be solved to global optimality. In addition, these convex
problems can be further relaxed to quadratic programs for which very efficient numerical solution procedures exist. By exploiting
this special problem structure, much larger problem instances can be solved to global optimality compared to similar mixed-integer
problems. The main intention of this paper is to provide optimal solutions for single and multiple load benchmark examples,
which can be used for testing and validating other methods or heuristics for the treatment of this discrete topology design
problem. 相似文献
8.
Because model switching system is a typical form of Takagi-Sugeno(T-S) model which is an univer sal approximator of continuous nonlinear systems,we describe the model switching system as mixed logical dynamical (MLD) system and use it in model predictive control (MPC) in this paper.Considering t hat each local model is only valid in each l ocal region,we add local constraints to local models.The stability of proposed multi-model predictiv e control (MMPC) algorithm is analyzed, and the p erformance of MMPC is also demonstrated on an in ulti-multi-output(MIMO) simulated pH neutralization process. 相似文献
9.
Because model switching system is a typical form of Takagi-Sugeno(T-S) model which is an universal approximator of continuous nonlinear systems, we describe the model switching system as mixed logical dynamical (MLD) system and use it in model predictive control (MPC) in this paper. Considering that each local model is only valid in each local region,we add local constraints to local models. The stability of proposed multi-model predictive control (MMPC) algorithm is analyzed, and the performance of MMPC is also demonstrated on an inulti-multi-output(MIMO) simulated pH neutralization process. 相似文献
10.
Topology optimization of continuum structures with local and global stress constraints 总被引:3,自引:3,他引:0
J. París F. Navarrina I. Colominas M. Casteleiro 《Structural and Multidisciplinary Optimization》2009,39(4):419-437
Topology structural optimization problems have been usually stated in terms of a maximum stiffness (minimum compliance) approach.
The objective of this type of approach is to distribute a given amount of material in a certain domain, so that the stiffness
of the resulting structure is maximized (that is, the compliance, or energy of deformation, is minimized) for a given load
case. Thus, the material mass is restricted to a predefined percentage of the maximum possible mass, while no stress or displacement
constraints are taken into account. This paper presents a different strategy to deal with topology optimization: a minimum
weight with stress constraints Finite Element formulation for the topology optimization of continuum structures. We propose
two different approaches in order to take into account stress constraints in the optimization formulation. The local approach
of the stress constraints imposes stress constraints at predefined points of the domain (i.e. at the central point of each element). On the contrary, the global approach only imposes one global constraint that gathers
the effect of all the local constraints by means of a certain so-called aggregation function. Finally, some application examples
are solved with both formulations in order to compare the obtained solutions. 相似文献
11.
In this paper we develop a variable neighborhood search (VNS) heuristic for solving mixed-integer programs (MIPs). It uses CPLEX, the general-purpose MIP solver, as a black-box. Neighborhoods around the incumbent solution are defined by adding constraints to the original problem, as suggested in the recent local branching (LB) method of Fischetti and Lodi (Mathematical Programming Series B 2003;98:23–47). Both LB and VNS use the same tools: CPLEX and the same definition of the neighborhoods around the incumbent. However, our VNS is simpler and more systematic in neighborhood exploration. Consequently, within the same time limit, we were able to improve 14 times the best known solution from the set of 29 hard problem instances used to test LB. 相似文献
12.
Topology optimization of large scale stokes flow problems 总被引:2,自引:2,他引:0
This note considers topology optimization of large scale 2D and 3D Stokes flow problems using parallel computations. We solve
problems with up to 1,125,000 elements in 2D and 128,000 elements in 3D on a shared memory computer consisting of Sun UltraSparc
IV CPUs. 相似文献
13.
Hong Guan Yin-Jung ChenYew-Chaye Loo Yi-Min XieGrant P Steven 《Computers & Structures》2003,81(3):131-145
The principal stress based evolutionary structural optimisation method is presented herein for topology optimisation of arch, tied arch, cable-stayed and suspension bridges with both stress and displacement constraints. Two performance index formulas are developed to determine the efficiency of the topology design. A refined mesh scheme is proposed to improve the details of the final topology without resorting to the complete analysis of a finer mesh. Furthermore, cable-supported bridges are optimised with frequency constraint incorporating the “nibbling” technique. The applicability, simplicity and effectiveness of the method are demonstrated through the topology optimisation of the four types of bridges. 相似文献
14.
In this paper, we consider storage loading problems under uncertainty where the storage area is organized in fixed stacks with a limited height. Such problems appear in several practical applications, e.g., when loading container terminals, container ships or warehouses. Incoming items arriving at a partly filled storage area have to be assigned to stacks under the restriction that not every item may be stacked on top of every other item and taking into account that some items with uncertain data will arrive later. Following the robust optimization paradigm, we propose different MIP formulations for the strictly and adjustable robust counterparts of the uncertain problem. Furthermore, we show that in the case of interval uncertainties the computational effort to find adjustable robust solutions can be reduced. Computational results are presented for randomly generated instances with up to 480 items. The results show that instances of this size can be solved in reasonable time and that including robustness improves solutions where uncertainty is not taken into account. 相似文献
15.
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
16.
A. Gersborg-Hansen O. Sigmund R.B. Haber 《Structural and Multidisciplinary Optimization》2005,30(3):181-192
This paper describes a topology design method for simple two-dimensional flow problems. We consider steady, incompressible laminar viscous flows at low-to-moderate Reynolds numbers. This makes the flow problem nonlinear and hence a nontrivial extension of the work of Borrvall and Petersson (2003).Further, the inclusion of inertia effects significantly alters the physics, enabling solutions of new classes of optimization problems, such as velocity-driven switches, that are not addressed by the earlier method. Specifically, we determine optimal layouts of channel flows that extremize a cost function which measures either some local aspect of the velocity field or a global quantity, such as the rate of energy dissipation. We use the finite element method to model the flow, and we solve the optimization problem with a gradient-based math-programming algorithm that is driven by analytical sensitivities. Our target application is optimal layout design of channels in fluid network systems. Using concepts borrowed from topology optimization of compliant mechanisms in solid mechanics, we introduce a method for the synthesis of fluidic components, such as switches, diodes, etc. 相似文献
17.
研究在服务组合预先优化阶段及在运行时容错处理阶段对重构的服务组合进行基于QoS的在线全局优化方法,提出并实现了一种结合修正单纯形法和启发式枚举法解决多目标全局组合最优化问题,加快了解空间搜索的收敛速度以及提高了目标函数的优化水平。 相似文献
18.
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
19.
In this work, we explore simultaneous geometry design and material selection for statically determinate trusses by posing
it as a continuous optimization problem. The underlying principles of our approach are structural optimization and Ashby’s
procedure for material selection from a database. For simplicity and ease of initial implementation, only static loads are
considered in this work with the intent of maximum stiffness, minimum weight/cost, and safety against failure. Safety of tensile
and compression members in the truss is treated differently to prevent yield and buckling failures, respectively. Geometry
variables such as lengths and orientations of members are taken to be the design variables in an assumed layout. Areas of
cross-section of the members are determined to satisfy the failure constraints in each member. Along the lines of Ashby’s
material indices, a new design index is derived for trusses. The design index helps in choosing the most suitable material
for any geometry of the truss. Using the design index, both the design space and the material database are searched simultaneously
using gradient-based optimization algorithms. The important feature of our approach is that the formulated optimization problem
is continuous, although the material selection from a database is an inherently discrete problem. A few illustrative examples
are included. It is observed that the method is capable of determining the optimal topology in addition to optimal geometry
when the assumed layout contains more links than are necessary for optimality. 相似文献
20.
The problem of optimally designing the topology of plane trusses has, in most cases, been dealt with as a size problem in which members are eliminated when their size tends to zero. This article presents a novel growth method for the optimal design in a sequential manner of size, geometry, and topology of plane trusses without the need of a ground structure. The method has been applied to single load case problems with stress and size constraints. It works sequentially by adding new joints and members optimally, requiring five basic steps: (1) domain specification, (2) topology and size optimization, (3) geometry optimization, (4) optimality verification, and (5) topology growth. To demonstrate the proposed growth method, three examples were carried out: Michell cantilever, Messerschmidt–Bölkow–Blohm beam, and Michell cantilever with fixed circular boundary. The results obtained with the proposed growth method agree perfectly with the analytical solutions. A Windows XP program, which demonstrates the method, can be downloaded from http://www.upct.es/~deyc/software/tto/. 相似文献