区间参数平面连续体结构频率非概率可靠性拓扑优化

研究了具有区间参数的平面连续体结构在固有频率非概率基频约束和频率禁区约束下的拓扑优化设计问题。考虑结构弹性模量、质量密度和频率约束限具有区间不确定性,根据SIMP材料插值方法和区间变量运算法则,构建了基于频率非概率可靠性约束的弯曲薄板和平面应力薄板结构的拓扑优化数学模型表达式,并给出了进化优化准则。算例及其结果表明文中模型和方法的有效性。     

利用导重法进行结构轻量化设计

结构轻量化设计的目的是以最少的设计资源设计出性能合格的产品结构,以降低产品生产成本,提高产品性价比和市场竞争力。结构轻量化的实质是材料重量在结构几何空间内及构件间的合理分配。导重法是可用于产品结构轻量化的结构优化有效方法,它可适用于包括各类单元的各种产品结构构件尺寸优化与结构几何形状优化以及结构拓扑优化;其目标与约束可以涉及各种结构静动力性态。首先给出结构优化导重法用于结构轻量化设计的具有广泛一般性的数学模型及其求解方法。接着给出一种新的包络函数-方根包络函数,使数目庞大的应力与位移约束凝聚为单值强度约束与单值精度约束;还给出适用于多数产品结构轻量化设计的单性态约束优化实用模型与解法;最后给出两个产品结构轻量化的应用实例,验证了导重法用于轻量化设计的有效性与广泛适用性。     

PREFORM DIE SHAPE DESIGN IN METAL FORMING USING AN OPTIMIZATION METHOD

An optimization algorithm for preform die shape design in metal-forming processes is developed in this paper. The preform die shapes are represented by cubic B-spline curves. The control points of the B-spline are used as the design variables. The optimization objective is to reduce the difference between the realized and desired final forging shapes. The sensitivities of the objective function with respect to the design variables are developed in detail. The numerical examples show that the optimization method and the sensitivity analysis developed in this paper are very useful and the design results are satisfactory. Importantly, the preform die shapes designed by this method are easily manufacturable and can be implemented in practical metal-forming operations. This optimization method and the sensitivity analysis can also be applied in the preform design of complex industrial metal-forming problems. © 1997 by John Wiley & Sons, Ltd.     

Optimal control of high harmonics for the generation of double attosecond pulses by using a chirped laser pulse

An efficient scheme for the optimization of ultrashort femtosecond pulse shapes interacting with an atom to control high harmonics spectrum and double attosecond pulse generation is presented. The time-dependent Schrödinger equation of one-dimensional hydrogen atom is solved numerically to obtain electric field emission. The genetic algorithm optimization method is used to control the phase and amplitude of ultrashort excitation laser pulses to generate the desired attosecond-shaped pulses. An appropriate cost function is introduced for genetic algorithm optimization of double attosecond pulse generation. It is shown that the relative intensity of two generated pulses, their delay time and duration can be controlled in this approach. Finally, the parameters of the optimized emitted attosecond pulse are compared with those of desired pulses, and the underlying physical mechanisms are discussed in detail.     

On the ‘interior Helmholtz integral equation formulation’ in sound radiation problems

This paper discusses the accuracy of the sound radiation (Helmholtz equation) BEM analysis when the source points are located inside the vibrating surface. It is shown that when these points are arranged in such a way that they compose a fictitious internal boundary, geometrically similar to the vibrating surface, then fictitious eigenfrequencies appear at larger values than those corresponding to the eigenfrequencies of the internal boundary. In this way, the direct-BEM analysis becomes capable of treating the non-uniqueness problem in a simple and efficient practical manner, which makes the method applicable for industrial purposes. Results are presented for the spherical monopole and dipole, while discussion is extended to a similarly vibrating cube.     

振动筛振动模态测试及分析

模态分析是研究结构动力学特性的一种近代方法,是系统辨识方法在工程振动领域中的应用[1]。本文对某一型号振动筛进行实验模态分析,得到固有频率、阻尼比和振型等模态参数,分析该振动筛结构设计中存在的问题,为后续的仿真计算模型的修正和结构优化设计提供参考。     

Simultaneous optimization of force and placement of friction dampers under seismic loading

It is known that the use of passive energy-dissipation devices, such as friction dampers, reduces considerably the dynamic response of a structure subjected to earthquake ground motions. Nevertheless, the parameters of each damper and the best placement of these devices remain difficult to determine. Some articles on optimum design of tuned mass dampers and viscous dampers have been published; however, there is a lack of studies on optimization of friction dampers. The main contribution of this article is to propose a methodology to simultaneously optimize the location of friction dampers and their friction forces in structures subjected to seismic loading, to achieve a desired level of reduction in the response. For this purpose, the recently developed backtracking search optimization algorithm (BSA) is employed, which can deal with optimization problems involving mixed discrete and continuous variables. For illustration purposes, two different structures are presented. The first is a six-storey shear building and the second is a transmission line tower. In both cases, the forces and positions of friction dampers are the design variables, while the objective functions are to minimize the interstorey drift for the first case and to minimize the maximum displacement at the top of the tower for the second example. The results show that the proposed method was able to reduce the interstorey drift of the shear building by more than 65% and the maximum displacement at the top of the tower by approximately 55%, with only three friction dampers. The proposed methodology is quite general and it could be recommended as an effective tool for optimum design of friction dampers for structural response control. Thus, this article shows that friction dampers can be designed in a safe and economic way.     

A sequential linear least square algorithm for tracking dynamic shapes of smart structures

This paper presents a sequential linear least square algorithm for tracking dynamic shapes of piezoelectric smart structures. The dynamic shape discussed in this paper is defined as a host structural shape varying with time, and the tracking technique is to find an electric voltage history for each piezoelectric device over a time period so that the desired structural movements can be achieved. In the theoretical formulation, dynamic equations of piezoelectric smart structures are introduced by finite element analysis, and then a solution procedure for a set of time‐dependent electric voltages is derived by combining the linear least square method and the Houbolt numerical integration scheme. The formulation indicates that this algorithm can be used to find the time‐dependent voltages for tracking structural movements of piezoelectric smart structures. The present novel formulation is then demonstrated through numerical examples for tracking dynamic shapes of piezoelectric smart beams and plates. The numerical results for the smart beam are compared with the experimental ones. It is shown that the present sequential linear least square algorithm is capable of efficiently simulating dynamic shape tracking for smart structures. Copyright © 2006 John Wiley & Sons, Ltd.     

Optimal Design of Alloy Steels Using Multiobjective Genetic Algorithms

Determining the optimal heat treatment regimen and the required weight percentages for the chemical composites to obtain the desired mechanical properties of steel is a challenging problem for the steel industry. To tackle what is in essence an optimization problem, several neural network-based models, which were developed in the early stage of this research work, are used to predict the mechanical properties of steel such as the tensile strength (TS), the reduction of area (ROA), and the elongation. Because these predictive models are generally data driven, such predictions should be treated carefully. In this research work, evolutionary multiobjective (EMO) optimization algorithms are exploited not only to obtain the targeted mechanical properties but also to consider the reliability of the predictions. To facilitate the implementation of a broad range of single-objective and multi-objective algorithms, a versatile Windows 2000®-based application is developed. The obtained results from the single-objective and the multiobjective optimization algorithms are presented and compared, and it is shown that the EMO techniques can be effectively used to deal with such optimization problems.     

基于虚载荷变量的无网格法形状优化的研究

将选择施加在"虚结构"控制点上的虚载荷作为形状优化的设计变量,并将它与无网格Galerkin法相结合来开展结构形状优化研究,采用罚函数法来施加边界条件,通过直接微分法建立了结构形状优化的离散型灵敏度分析算法,利用无网格法研究了节点坐标关于设计变量导数的计算。所提出的算法简单明了,它不仅解决了网格的畸变问题,而且简化了优化模型和迭代流程,并可使结构的受力特性得到进一步的改善。最后用2个工程实例验证了所建立的算法,并得到了形状优化结果。     

Comparative study of three methods for the simulation of two-dimensional photonic crystals

Three methods for the efficient simulation of two-dimensional photonic crystal structures are compared, namely, a semianalytical multiple-scattering technique; a vectorial eigenmode expansion technique; and a FDTD-ROM technique. The basic principles of each method are presented. For the semianalytical technique and for the vectorial eigenmode expansion technique, we show how reflections coming from abruptly terminated waveguides can be avoided. The main advantages and disadvantages of each method are discussed. Results from use of the three methods are compared for several photonic crystal structures.     

Shape optimization with topological changes and parametric control

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.     

Identification of a non-linear spring through the Fokker–Planck equation

Standard methods for the dynamic identification of civil engineering structures and mechanical systems generally rely on the determination of eigenfrequencies/eigenvectors and damping. A basic assumption for the use of these methods is the linear elastic behaviour of the tested structures. Nevertheless many structures exhibit a non-linear behaviour even at low levels of external excitation. For instance, reinforced concrete structures cracked by shrinkage or by the overcoming of the concrete tensile strength, exhibit different values of the flexural stiffness depending on the opening of the cracks. In the present paper a new methodology is presented to identify the characteristics of a non-linear mechanical system using the Fokker–Plank Equation (FPE) that allows evaluating the probability density function of the response of structural systems loaded with Gaussian white noise.     

The use of optimization procedures in tuning vibration dampers

This paper presents an algorithm for minimizing the resonance amplitudes of vibrating systems with dynamic vibration dampers. Damper parameters are optimised using an objective function which describes the maximum of the resonance curve for the first resonance. The algorithm described here is based on a spectral transfer function and can be applied to multi-degree-of-freedom systems. The research makes use of models of discrete as well as discrete-continuous systems. A method for formulating minimization problems is proposed which allows global optimization using gradient procedures. Sequential linear and quadratic programming methods are used. Examples of different mechanical systems with vibration dampers are also presented.     

Packaging optimization using the dynamic vector fields method

In this paper, a novel packaging optimization method for convex objects is presented. This method solves the packaging optimization problem through dynamic simulation of object positions and rotations over time. Object positions and orientations are determined by dynamic vector fields, which accelerate objects according to optimization objectives or physical effects between objects or their environment. Using these vector fields, any number of objectives or effects can be accounted for, and this scalability allows the method to potentially be employed to solve a wide variety of engineering packaging optimization problems. The current implementation, as presented in this paper, represents the foundation of the method that future improvements will build upon and is currently limited to the analysis of convex objects. Three basic vector fields are presented to solve packing density maximization problems: the first maximizes packing density, the second prevents collisions between objects, and the third optimally orients objects relative to each other. Collisions between objects are relaxed in this method, allowing objects to pass through each other, which provides the potential for reduced initial condition dependence and has shown promising results thus far. Several test problems are presented and solved, demonstrating the method and its ability to generate optimal solutions.     

Quantum-Inspired Evolutionary Algorithm for Topology Optimization of Modular Cabled-Trusses

This article proposes an alternative optimization framework applied to topology optimization of modular lightweight cabled-truss structures. These structures are described as a system of intrinsically positioned cables and triangular bar formations jointed at their ends by hinged connections to form a rigid framework. The optimized topologies are determined through a stochastic discrete optimization procedure that uses ground structure approach, nonlinear finite element analysis, and quantum-inspired evolutionary algorithms. The optimization searches for optimal mass reduction with minimal losses in stiffness, such relation, is expressed by the stiffness-to-mass ratio parameter. Nonlinear finite element analysis is used to evaluate the static structural response. In order to decrease computation time, kinematically instable and structurally invalid individuals are filtered before evaluation. Modular design approach is taken into consideration to reduce the number of design variables and increase the productibility of cabled-trusses. Symmetric structural response is desired since in several mechanical applications forces can assume different directions during the working cycle. A modular ground structure with 300 elements is optimized, and optimal truss and cabled-truss topologies are compared. Complementary analyses comprise the investigation of the structural performance under different number of modules and slenderness ratios. The results indicate that the proposed optimization framework leads to optimized structures. In addition, it was observed that cabled trusses presented significant improvements in structural performance when compared with trusses.     

对体积位移传感器的研讨

以不同边界条件的振动梁为例,提出通过分部积分方法设计特定形状的PVDF薄膜测量体积位移。这种分部积分方法得到的PVDF传感器形状不但与外激励力的性质（如激励力类型、位置以及频率等）无关,而且不需要振动梁的模态信息。研究表明,可以把振动梁的边界条件分为两类,即一端固定一端任意和两端位移为零,对于每一类边界条件可以用一种特定形状PVDF传感器测量其体积位移。     

Optimization of a passive structure for active vibration isolation: an interval-computation- and constraint-propagation-based approach

This article is concerned with the optimization of the mechanical structure of a one-degree-of-freedom vibration isolator. An efficient optimization algorithm based on an interval-computation method is used. The authors’ general objective is to include and develop an optimization step in the pre-design process of a smart structure. In this article, the idea of this pre-design is to obtain, very quickly and very simply, the global structural geometry of the passive isolation device. For this purpose, a simplified mathematical model is built, which describes the main natural mode shapes of the suspension device. The method is applicable to large-scale dynamic systems for a first optimization process step because it's clearly an effective time-saving optimization approach. The results obtained are quite sufficient for a first pre-design step. For a real case scenario, the optimized structure is applied to a numerical active vibration control process.     

Topology optimization of continuum structures for natural frequencies considering casting constraints

A method for the topology optimization on the natural frequency of continuum structures with casting constraints is proposed. The objective is to maximize the natural frequency of vibrating continuum structures subject to casting constraints. When the natural frequencies of the considered structures are maximized using the solid isotropic material with penalization (SIMP) model, artificial localized modes may occur in areas where elements are assigned with lower density values. In this article, the topology optimization is performed by the bi-directional evolutionary structural optimization (BESO) method. The effects of different locations of concentrated lump mass, different volume fractions and meshing sizes on the final topologies are compared. Both two and four parting directions are investigated. Several two- and three-dimensional numerical examples show that the proposed BESO method is effective in achieving convergent solid–void optimal solutions for a variety of frequency optimization problems of continuum structures.     

Robust optimization of structures subjected to stochastic earthquake with limited information on system parameter uncertainty

The optimization of structures subjected to stochastic earthquake and characterized by uncertain parameters is usually posed in the form of non-linear programming with stochastic performance measures where the uncertain parameters are modelled as random variables. Such an approach, however, cannot be adopted in many real life situations when the limited information about uncertainty can be only modelled as of the uncertain but bounded (UBB) type. A robust optimization strategy for stochastic dynamic systems characterized by UBB parameters is proposed in the present study in the framework of the response surface method (RSM). In evaluating the stochastic constraints, repeated computations of the dynamic responses are avoided by applying an adaptive RSM based on the moving least squares method. Numerical results are presented to highlight the effectiveness of the proposed procedure. The effect of parameter uncertainty is also studied by comparing the results obtained from the proposed optimization approach with the conventional stochastic optimization results.