Stress-constrained topology optimization of continuum structures subjected to harmonic force excitation using sequential quadratic programming

Structural and Multidisciplinary Optimization - In this paper, we propose a method for stress-constrained topology optimization of continuum structure sustaining harmonic load excitation using the...     

基于无网格径向点插值方法的简谐激励下的连续体结构拓扑优化

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.     

Topology optimization of continuum structures subjected to pressure loading

This paper presents a generalization of topology optimization of linearly elastic continuum structures to problems involving loadings that depend on the design. Minimum compliance is chosen as the design objective, assuming the boundary conditions and the total volume within the admissible design domain to be given. The topology optimization is based on the usage of a SIMP material model. The type of loading considered in this paper occurs if free structural surface domains are subjected to static pressure, in which case both the direction and location of the loading change with the structural design. The presentation of the material is given in a 2D context, but an extension to 3D is straightforward. The robustness of the optimization method is illustrated by some numerical examples in the end of the paper. Received August 3, 1999     

索受外激励作用下索拱结构非线性动力学分析

研究索拱结构中索受外激励作用下索拱之间非线性动力学问题．利用已建立的索拱结构非线性动力学耦合面内运动微分方程,采用Galerkin方法把索拱结构的面内运动方程进行离散,然后利用多尺度法对离散的运动方程进行摄动得到索主共振情况下的平均方程,研究在索受到外激励作用下索振动对拱的振动产生的影响,同时对索拱结构内共振时的稳定、分叉及混沌情况进行了分析．结果表明：索某阶频率与拱某阶频率接近时可能出现内共振现象,能量在索拱之间相互传递,原本静止的拱也可能出现共振现象,共振频域区间内索拱振动将出现跳跃、分叉及混沌等复杂的非线性动力学行为．     

Topology optimization of continuum structures subjected to the variance constraint of reaction forces

In this paper, the attainment of uniform reaction forces at the specific fixed boundary is investigated for topology optimization of continuum structures. The variance of the reaction forces at the boundary between the elastic solid and its foundation is firstly introduced as the evaluation criterion of the uniformity of the reaction forces. Then, the standard formulation of optimal topology design is improved by introducing the variance constraint of the reaction forces. Sensitivity analysis of the latter is carried out based on the adjoint method. Numerical examples are dealt with to reveal the effect of the variance constraint in comparison with solutions of standard topology optimization.     

Analysis of engineering structures response to random wind excitation

In this paper, based on the present author's earlier study about the random process of wind, the elastic engineering structure response to wind load is analysed by means of the random vibration and finite element method. From the most general model the formulae for calculating the response power spectrum and mean square value of displacement and stress of structure are derived, with which both the static and dynamic response of structures can be obtained simultaneously. Finally, a large antenna structure in engineering is calculated as an illustration. Its response to Davenport's wind load spectrum is given.     

Design of an optimal damper to minimize the vibration of machine tool structures subject to random excitation

The vibration of machine tools during machining adversely affects machining accuracy and tool life, and therefore must be minimized. The cutting forces for stable turning are generally known to be random, and hence excite all the resonance modes. Of all these modes, those that generate relative motions between a cutting tool and a workpiece are of concern.This paper presents a new approach for designing an optimal damper to minimize the relative vibration between the cutting tool and workpiece during stable machining. An approximate normal mode method is employed to calculate the response of a machine tool system with nonproportional damping subject to random excitation. The major advantage of this method is that it reduces the amount of computation greatly for higher-order systems when responses have to be calculated repeatedly in the process of optimization. An optimal design procedure is presented based on a representative lumped parameter model that can be constructed by using existing experimental or analytical techniques. The two-step optimization procedure based on the modified pattern search and univariate search effectively leads the numerical solution to the global minimun irrespectively of initial values even under the existence of many local minima.     

On the optimal layout of structures subjected to probabilistic or multiply loading

The loading uncertainties can be expressed by the stochastic nature of any part of the load determination. If any information is probabilistic among the three independent data of the load determination (the magnitude, the line of action and/or the point of application) a more precise design requires to elaborate a probabilistic method. This goal can be obtained by the use of an appropriate approximation technique, in which the original stochastic mathematical programming problem is substituted by a deterministic one. A similar technique can be followed in case of a multiple loading. In addition to the numerical modelling a parametric study is given where the influence of the multiple loading is investigated to determine the optimal layout in function of the initial layout. The application is illustrated by numerical examples.     

Generalized incremental frequency method for topological designof continuum structures for minimum dynamic compliance subject to forced vibration at a prescribed low or high value of the excitation frequency

The application of multidisciplinary design optimisation is mostly confined to bi-disciplinary systems such as fluid-structure interaction problems. High fidelity models of three disciplines involving electromagnetic-thermal-structural designs are rare. Here, the multidisciplinary optimisation of such a design is presented. The device comprises a C-shaped iron core and a single coil. The problem is decomposed using a monolithic multidisciplinary feasible architecture. The multidisciplinary analyses involve a single three-dimensional finite element mesh for transient non-linear electromagnetic, non-linear-static thermal, and linear-static structural models. During each multidisciplinary iteration the mesh is linearly morphed. A gradient based optimisation algorithm in combination with a multi-start routine is applied to the constrained mass minimisation problem. Multidisciplinary feasibility is ensured by convergence of a single coupling parameter i.e. air-gap deformation. In conclusion, some multidisciplinary optimisation, analyses, and decomposition considerations are discussed.     

Discrete analysis method for random vibration of structures subjected to spatially correlated filtered white noises

Random vibration analysis of large-span space structures or high-rise structures which are subjected to spatially correlated filtered white noise excitations such as wind load and earthquake motion, has been a difficult problem in engineering computation. Based on the idea of the discrete analysis method of random vibration, this paper attempts to solve this problem. The formulae of calculating structural mean and mean square responses are given. As an example, the wind-induced vibration of a cable roof structure is analysed by using these formulae.     

Design of framed foundation subjected to vibration

The potential effects of repeated loads on the stiffness and the natural frequencies of framed foundations which support vibrating equipment such as compressors or turbine generators are described. The reason for the reduction of stiffness of concrete under repeated loads is explained. A two-dimensional element and a bar element are utilized to idealize reinforced concrete structures. Principal stresses are checked to determine the status of cracking of concrete. If the principal stress is greater than the tensile capacity of concrete, a stress crack is assumed to develop in the perpendicular direction to the corresponding stress. The element stiffness is modified to account for the crack. The modulus of elasticity of concrete is modified under repeated loads according to the stress state. The modulus of elasticity of concrete is assumed to be constant in compression, but varying in tension. Example beams are analyzed to study the effect of the reduction of modulus in tension zone. The reduction of modulus is found to give significant effect on the overall stiffness and the natural frequency of the structure.     

On an open problem related to the strict local minima ofmultilinear objective functions

This paper gives a combinatorial proof of a “yes” answer to an open question presented by Vidyasagar (ibid. vol.40, 1995), stated as follows: “Given a multilinear polynomial E(x): [0, 1] ⁿ→ℛ, is it true that E_b(x)=E(x)-b^t x has a strict local minimum over the discrete set {0, 1}ⁿ for almost all b of sufficiently small norm?” The given combinatorial proof is completed directly by providing a sufficient condition for a conjecture on the strict local minima of multilinear polynomials, also postulated in Vidyasagar, to hold. In addition, a simple counter-example is presented to demonstrate that the conjecture may be not true if the provided sufficient condition is not satisfied     

On human response to prolonged repeated whole-body vibration

The experiment was aimed at investigating human response to different doses of whole-body vibration (WBV), at checking adaptation to repeated exposures, at further evaluating the frequency weighting, and at examining the effect of a distinct interruption of prolonged exposure. Eight male seated subjects were exposed for 3 h to sinusoidal WBV in the z-axis with the frequencies 4 Hz and 8 Hz, at a constant acceleration level of 1·0ms^-2 rms,each frequency being repeated 4 times on consecutive days. Transmissibility, impedance, bioelectrical activity of trunk muscles, postural sway, performance in vigilance tasks, and the subjectively assessed psychological state, efforts, and stress experienced in performing the tasks were investigated. The transmissibility decreased during exposure time at 4 Hz and increased at 8 Hz when a controlled posture was maintained. The power-spectral density distribution and amplitude of postural sway were affected by WBV, depending on both duration and frequency. Performance data and rating data exhibited decrements and adverse effects, being greater beyond the ‘fatigue-decreased proficiency’ boundary (FDPB); adaptation and habituation were more pronounced at the FDPB dose. Generally, there were no cumulative effects. A pause for 20min did not essentially affect the reactions investigated.     

Neumann dynamic stochastic finite element method of vibration for structures with stochastic parameters to random excitation

This paper presents a method for the dynamic analysis of structures with stochastic parameters to random excitation. A procedure to derive the statistical characteristics of the dynamic response for structure is proposed by using dynamic Neumann stochastic finite element method presented herein. Random equation of motion for structure is transformed into a quasi-static equilibrium equation for the solution of displacement in time domain. Neumann expansion method is developed and applied to the equation for deriving the statistical solution of the dynamic response of such a random structure system, within the framework of Monte Carlo simulation. Then, the results from Neumann dynamic stochastic finite element method are compared with those from the first- and second-order perturbation stochastic finite element methods and the direct Monte Carlo simulation with respect to accuracy, convergence and computational efficiency. Numerical examples are examined to show that the approach proposed in this paper has a very high accuracy and efficiency in the analysis of compound random vibration.     

Frame response to a harmonic excitation,taking into account the effects of shear deformation and rotary inertia

The Timoshenko beam theory is used to compare experimental and analytical results in a steel frame subjected to a harmonic excitation. The very good agreement between the experimental and the theoretical results proves the usefulness of this ‘exact’ method over other methods as the finite elements.     

Subcritical excitation and dynamic response of structures in frequency domain

The main objective of this paper is to explore the idea of the critical, subcritical excitations for the assessment and prediction of the earthquake resistance of structures using frequency domain method. A technique for least-square fit of complex valued functions is also developed in this paper, to obtain the subcritical excitation. Results obtained in this study appear to be consistent with those obtained in the time domain method. However, the frequency domain method is more efficient in performing the analysis and needs less computing time.     

The applications of harmonic functions to robotics

Harmonic functions are solutions to Laplace's equation. Such functions can be used to advantage for potential-field path planning because they do not exhibit spurious local minima. Harmonic functions are shown here to have a number of properties that are essential to robotics applications. Paths derived from harmonic functions are generally smooth. Harmonic functions also offer a complete path-planning algorithm. We show how a harmonic function can be used as the basis for a reactive admittance control. Such schemes allow incremental updating of the environment model. Methods for computing harmonic functions respond well to sensed changes in the environment, and can be used for control while the environment model is being updated.     

On the prediction of material properties and topology for optimal continuum structures

A new formulation is presented for mathematical modelling to predict material properties for the optimal design of continuum structures. The method is based on an extended form of an already established characterization for continuum design, where the material properties tensor for an arbitrary structural continuum appears as the design variable. The extension is comprised of means to represent an independently specifiedunit relative cost factor, which appears simply as a weighting function in the argument of the isoperimetric (cost) constraint of the original model. A procedure is demonstrated where optimal black/white topology is predicted out of a sequence of solutions to material properties design problems having thisgeneralized cost formulation form. A systematic adjustment is made in the unit relative cost field for each subsequent solution step in the sequence, and at the stage identified with final topology, no more than a small fraction of a percent of the total element area in the system has material property density off the bounding black or white levels. This technique is effective for the prediction of optimal black/white topology design for design around obstacles of arbitrary shape, as well as the more unusual topology design problems. Results are presented for 2D examples of both types of problem. In addition to the treatment for (the usual) minimum compliance design, an alternate formulation of the design problem is presented as well, one that provides for the prediction of optimum topology with a generalized measure of compliance as the objective.