基于MSC Nastran的矿用电动轮自卸车货箱模态分析

针对矿用电动轮自卸车货箱的动态特性,提出基于模态分析结果的货箱结构改进方法.通过Patran建立货箱结构的有限元模型,应用MSC Nastran对其进行模态分析,得到货箱结构的动态参数.根据模态分析结果对货箱结构进行改进,货箱结构固有频率及振型得到较好的改善,为进一步研究矿用电动轮自卸车货箱的优化设计和预测疲劳寿命奠定基础.     

On the design optimization of built-up stiffened steel beams with buckling and frequency constraints

The literature on the structural design optimization of steel-plate girders indicates a need for more refined research studies to obtain optimal designs by formulating and solving the design problem that combines structural sizing and shape parameters in one unified, constrained problem. For this purpose, the structural optimization design problem of stiffened steel-plate girders is formulated with specified loading conditions and constraints on strength and serviceability considerations including limits on fundamental frequency and buckling modes. The finite-element method-based model is used to define the objective function and the structural/geometric response functions, while the geometric domain elements are used to systematically perturb the structural shape during the search for an optimal shape of the structure. The mathematical statement of the gradient-based-design problem is solved for an optimal structural size and shape with buckling and frequency constraints in addition to the traditional strength constraints. The numerical results obtained are compared with results obtained from a less formal ad hoc design procedure, and some conclusions are drawn to emphasize the design benefits obtained from solving the design problem for optimal structural size and shape.     

Optimum design of composite shells subject to natural frequency constraints

A technique for the optimum (minimum weight) design of a composite shell subject to constraints on its natural frequencies is presented. The optimization problem is posed as a general mathematical programming problem in which one or more of the inequality constraints involves the shell natural frequencies, which must be evaluated numerically during the optimization. For this reason, a method for numerically evaluating the natural frequencies of composite shells is also presented. The method is based upon the finite element method of structural analysis and Rayleigh's principle. Because the element used is applicable to anisotropic shells of arbitrary shape, the method is very general. By using Rayleigh's principle, the necessity of assembling overall mass and stiffness matrices for the shell is eliminated. The optimization is performed by nondimensionalizing the mathematical programming problem and using the penalty function method of Fiacco and McCormick to transform the problem to a sequence of unconstrained minimizations having solutions which converge to the solution of the original (constrained) problem. The unconstrained minimizations are performed using the variable metric method of Fletcher and Powell. Derivatives of the nondimensional frequency constraints are evaluated numerically using difference equations. The frequency calculation method is demonstrated by calculating the fundamental frequency for the transverse vibration mode of a multilayered cylindrical shell with fixed overall geometry and variable composite geometry. Results indicate that the frequency increases with increasing fiber orientation angle, fiber volume fraction, or lamina thickness. The optimization technique is demonstrated by minimizing the weight of the shell discussed above subject to a constraint on its fundamental transverse frequency. The design variables are the fiber orientation angle, the fiber volume fraction, and the lamina thickness. Results are presented and explained in terms of the physical aspects of the problem.     

大跨钢箱梁悬索桥地震响应有限元分析

根据某大跨钢箱梁悬索桥的设计图纸,采用ANSYS建立其有限元模型,采用壳单元对主梁进行模拟.通过不断调试找出最佳的主缆初始应力,完成悬索桥的初始找形分析.对悬索桥进行预应力模态分析,采用瑞利阻尼理论,通过悬索桥有限元模型的前2阶圆频率计算模型的质量阻尼和刚度阻尼.采用动力时程分析法对悬索桥进行地震响应有限元分析.结果表明:横桥向位移的最大峰值由横桥向地震波输入决定,纵桥向位移的最大峰值以及竖桥向位移的最大峰值主要由重力载荷工况决定,地震载荷工况对其贡献非常小.     

某SUV车架多目标拓扑优化设计

为得到同时满足刚度和动态要求的SUV车架,基于SIMP材料插值方法,分别以刚度最大和低阶模态固有频率最大作为优化目标建立拓扑优化模型,利用折中规划法建立多工况下刚度和低阶固有频率多目标优化模型,通过拓扑优化迭代得到新的SUV车架;对新车架进行仿真分析,得到其位移和应力分布及前4阶固有频率.其静态特性满足材料要求且有很大提高,第1阶固有频率提高到30.3 Hz,新车架质量减轻到193.3 kg.计算结果表明该方法能够很好地解决多目标下的结构优化问题。     

Nonlinear response of composite steel-concrete bridges

This paper is concerned with the overload behavior of a composite beam-slab type highway bridge consisting of steel stringers supporting a cast-in-place reinforced concrete slab. A nonlinear finite element analysis is used to determine the complete state of stress and deformation at any level of overload. A layered model together with an incremental iterative procedure is employed to determine the response of the bridge in the post-elastic range. The results of this analysis are compared with available experimental results for the case of a simply supported bridge. The bridge response under overloads is investigated, and the effects of some major design parameters are studied. Among these parameters are: beam size, torsional constant, slab thickness, Poisson's ratio, yield stress of steel girders and the ratio of transverse to longitudinal stiffness of the slab. The results obtained from this computer analysis compare favorably with experimental results in the elastic and the post-elastic range.     

Finite strip analysis of curved composite girders with incomplete interaction

This paper presents a finite strip analysis of curved composite girders with incomplete interaction. In the present analysis curved composite girder bridges are modelled by curved strip elements for the concrete slab and steel girder and spring elements for the shear connectors. The shear connectors are assumed as a two-dimensional spring element along the nodal line. The proposed method is applied to the analysis of curved box girders, curved plates and curved composite girder bridges with complete and incomplete interaction. Some analytical results obtained by this method are compared with the test results and theoretical values obtained by other methods, and they are in good agreement. Slip behavior of curved composite box girders is also discussed based on the results by the proposed method.     

Maximization of structural natural frequency with optimal support layout

The optimal layout of supports is one of the key factors that dominates static and dynamic performances of the structure. In this work, supports are considered as elastic springs. The purpose is to carry out layout optimization of supports by means of topology optimization method. The technique of pseudo-density variables that transforms a discrete-variable problem into a continuous one is used in order that the problem is easily formulated and solved numerically. In this formulation, a power law of the so-called solid isotropic material with penalty model is employed to approximate the relation between the element stiffness matrix and density variable. Such a relation makes it easy to establish the computing scheme and sensitivity analysis of natural frequency. Support layout design that corresponds to optimization of boundary conditions is studied to maximize the natural frequency of structures. Numerical results show that reasonable distributions of supports can be generated effectively.     

Optimization of the dynamic performance of a spaceframe structure

The objective of the study is to develop an optimization algorithm for the dynamic performance of a spaceframe structure. The algorithm uses many iterations of finite element modal analysis. After each analysis, the contribution factor of each element is evaluated, sorted, and ranked. The structure members are then modified based on the ranking of the contribution factors. Iterations continue until the preset criteria or the computational limitations are reached. As demonstrated in a reflector support structure, the algorithm works effectively to increase the natural frequency without increasing the weight.     

Influence surfaces by boundary element/least square methods coupling

This work presents a new application for calculating the influence surfaces of transverse displacements, directional derivatives and bending moments for generic bridge decks. A plate bending boundary element method formulation is coupled with the application of a continuous field surface derived by the least square procedure. This original BE formulation permits calculating influence surfaces of plates with polygonal, curved or circular geometry, and several transverse load conditions. The proposal allows future analysis of building floors and single and continuous bridge trusses connected to longitudinal and transversal girders. Numerical examples are presented to demonstrate the potential of the present formulation and the results are compared with analytical values and with usual vehicular loads.     

Optimal design of hybrid laminated composite plates with dynamic and static constraints

Optimization procedures are presented that consider the static and dynamic characteristic constraints for laminated composite plates and hybrid laminated composite plates subject to a concentrated load on the center of the plate. The design variables adopted are ply angle or ply thickness. Considered constraints are deflection, natural frequency and specific damping capacity. Using a recursive linear programming method, nonlinear optimization problems are solved, and by introducing the design scaling factor, the number of iterations is reduced significantly. Relating interactive optimization procedures with the finite element method analysis, various hybrid composite plates with arbitrary boundary conditions can be designed optimally. In the optimization procedure, verification of analysis and design of the laminated composite plates are compared with a previous paper. Various design results are presented on laminated composite plates and hybrid laminated composite plates.     

Multilevel optimization applied to hull girder design using three panel forms

A multilevel design scheme for ship's hull girders (longitudinal members between two adjacent transverse frames) is presented in this paper. This design scheme handles, very conveniently, the complexity of using an optimization algorithm for such complex design problems having a large number of design variables, nonlinear constraints dealing with different failure modes and interactions among substructures, and nonlinear design objectives. The conventional multilevel design technique is modified by introducing an approach called constraint coordination to increase the probability of achieving the overall optimum very efficiently.The scheme is demonstrated by application to the structural design of hull girders with simple structural modelling to represent inland waterway ships on which there was a special emphasis in the original research project (Rahman 1991). Three possible panel (consisting of one stiffener and its attached plating) forms; tee stiffened, flat-bar stiffened and corrugated, are optimized to synthesize the hull girder in order to achieve the most efficient structure. The effect of price-structure (labour rate to material price ratio) on the design is also investigated.     

A modified gradient method for finite element elastoplastic analysis by quadratic programming

The finite analysis problem with piecewise linear constitutive laws is formulated as a linear complementarity and a quadratic programming problem. The solution techniques using the well-known optimization methods of mathematical programming are discussed and a procedure, belonging to the class of gradient methods, is proposed which overcomes the computational difficulties that arise when there is a large number of variables.Through a physical interpretation of the gradient of the objective function, each mathematical step of the proposed optimization technique is translated into a corresponding physical operation on the structure and a mechanical solution procedure with a finite number of steps is derived.Finally, for the incremental analysis problem under non-holonomic constitutive laws the same procedure is adopted combined with the multistage loading technique. Illustrative examples for each of the preceding problems are given.     

变截面Z型折叠机翼振动特性的有限元与实验分析

Z型变截面折叠机翼作为一种可变体机翼结构,不同的折叠角对机翼稳定性有着重要的影响,因此研究不同折叠角度下的特性参数对机翼动态稳定性有着重要的意义.本文首先设计加工了Z型变截面可折叠机翼结构的实验模型,通过建立与实验模型相匹配的有限元模型,仿真得到不同折叠角度下机翼的前5阶固有频率和振型,针对不同折叠角度下机翼的固有特性,通过扫频实验得到机翼前5阶固有频率和模态振型,以及横向外激励作用下三段翼的频响曲线,对比分析有限元仿真与实验结果,验证结果的可靠性,这将对机翼结构设计以及特性参数的选取提供参考依据.     

Evolutionary natural frequency optimization of thin plate bending vibration problems

This paper extends the evolutionary structural optimization method to the solution for maximizing the natural frequencies of bending vibration thin plates. Two kinds of constraint conditions are considered in the evolutionary structural optimization method. If the weight of a target structure is set as a constraint condition during the natural frequency optimization, the optimal structural topology can be found by removing the most ineffectively used material gradually from the initial design domain of a structure until the weight requirement is met for the target structure. However, if the specific value of a particular natural frequency is set as a constraint condition for a target structure, the optimal structural topology can be found by using a design chart. This design chart describes the evolutionary process of the structure and can be generated by the information associated with removing the most inefficiently used material gradually from the initial design domain of a structure until the minimum weight is met for maintaining the integrity of a structure. The main advantage in using the evolutionary structural optimization method lies in the fact that it is simple in concept and easy to be included into existing finite element codes. Through applying the extended evolutionary structural optimization method to the solution for the natural frequency optimization of a thin plate bending vibration problem, it has been demonstrated that the extended evolutionary structural optimization method is very useful in dealing with structural topology optimization problems.     

Architecture of a coupled expert system for optimum design of plate girder bridges

A prototype knowledge-based expert system has been developed for optimum design of steel plate girders used in highway bridges. This expert system, called PG-BRIDGE1, is a coupled system in which AI-based symbolic processing is combined with the traditional numerical processing. Plate girders can be unstiffened or stiffened with single- or doublesided transverse stiffeners. They can be homogeneous or hybrid, made of high-strength flange plates and low-strength web plate. A mathematical optimization algorithm has been developed for minimum weight design of plate girders using the generalized geometric programming technique. The basis of design is the American Association of State Highway and Transportation Officials (AASHTO) specifications. The plate girders are subjected to the live (moving) loads of the AASHTO specifications. The knowledge base and symbolic processing has been developed using the Expert System Development Environment (ESDE). Numerical processing for structural analysis, optimization algorithm and graphics interface have been developed in FORTRAN 77.     

Structural optimization of the cross-beam of a gantry machine tool based on grey relational analysis

Crossbeam structural design of gantry machine tool is a multi-level, multi-index and multi-scheme decision-making problem. In order to solve the above problem, the optimum seeking model of crossbeam structure was built through using the grey relational analysis and Analytic Hierarchy Process. The finite element analysis of the static and dynamic performance parameters for four kinds of crossbeam structural schemes designed had been done, and the optimal design scheme was selected by using the optimum seeking model. After conducting sensitivity analysis for the optimal crossbeam selected, the reasonable design variables were obtained, and the dynamic optimization design model of crossbeam was established. Six groups of non-inferior solutions were obtained after solving the optimization design model. The optimal solution was selected from the non-inferior solution set through using the crossbeam structural optimization method based on grey relational analysis again, which makes the crossbeam’s dynamic performance improving greatly. The dynamic experiments on the crossbeams before and after optimization design were conducted, then the experimental results show that the first four order natural frequencies of the crossbeam increase 17.56 %, 19.36 %, 17.04 % and 19.58 % respectively, which proves that the structural optimization design method based on grey relational analysis proposed in this paper is reasonable and practicable.     

On optimal design of HDD suspension using topology optimization

 This paper explores the use of topological optimization to systematically design suspensions for hard disk drives (HDD). The design problem is posed as a material distribution problem, which varies spatial thickness of suspensions so as to enhance their dynamic performance. Due to the requirements for specific motion characteristics, suspensions are designed to have higher torsional and lateral frequencies while maintaining an adequate but not too high frequency for transverse bending. The torsional and lateral frequencies are generally higher in order than the transverse frequencies. Due to their non-convex nature, the optimizations of higher-order frequencies were proven to be more difficult than that of the fundamental frequency. To tackle the problem, present work adopted mode-tracking techniques, and attempted two different optimization algorithms to solve the design problem. With reference to the topological results obtained, it is found that the implementation based on sequential quadratic programming (SQP) performed better than that based on optimal criteria (OC). It was also found that the present design method could tremendously improve the dynamic performance of suspensions. Received: 31 December 2001/Accepted: 29 March 2002     

Structural topology optimization for frequency response problem using model reduction schemes

This study uses model reduction (MR) schemes such as the mode superposition (MS), Ritz vector (RV), and quasi-static Ritz vector (QSRV) methods, which reduce the size of the dynamic stiffness matrix of dynamic structures, to calculate dynamic responses and sensitivity values with adequate efficiency and accuracy for topology optimization in the frequency domain. The calculation of structural responses to dynamic excitation using the framework of the finite element (FE) procedure usually requires a significant amount of computation time; that is mainly attributable to repeated inversions of dynamic stiffness matrices depending on time or frequency intervals, which hastens the dissemination of the MR schemes in the analysis. However, using well-established MR schemes in topology optimization has not been prevalent. Therefore, this study conducted a comprehensive investigation to highlight the drawbacks and advantages of these MR schemes for topology optimization. In the results, the MS method, which generates reduction bases by considering some of the lowest eigenmodes, can lose the accuracy in both approximated structural responses and sensitivity values due to locally vibrating eigenmodes and higher mode truncation in the solid isotropic material with penalization (SIMP) approach. In addition, the RV and QSRV methods, which generate reduction bases by considering the external force, mass, and stiffness matrices of a structure, can be used as alterative model reduction schemes for stable optimization. Through several analysis and design examples, the efficiency and reliability of the model reduction schemes for topology optimization are compared and validated.