Optimization of linear segmented circular Mindlin plates for maximum fundamental frequency

This paper concerns the optimization of piecewise linear segmented circular Mindlin plates against vibration. For a given number of linear segments and plate volume, the thickness parameters and the segmental lengths are to be optimally chosen so as to maximize the fundamental frequency of free vibration. To solve this problem, an iterative optimization procedure together with the Ritz method for analysis has been used. The effects of the number of segments, transverse shear deformation and rotary inertia on the optimal design are investigated.     

Optimization of linear segmented circular Mindlin plates for maximum fundamental frequency

This paper concerns the optimization of piecewise linear segmented circular Mindlin plates against vibration. For a given number of linear segments and plate volume, the thickness parameters and the segmental lengths are to be optimally chosen so as to maximize the fundamental frequency of free vibration. To solve this problem, an iterative optimization procedure together with the Ritz method for analysis has been used. The effects of the number of segments, transverse shear deformation and rotary inertia on the optimal design are investigated.     

Optimal locations of point supports in plates for maximum fundamental frequency

This paper investigates the optimal locations of rigid point supports to maximize the fundamental frequency of free vibration of plates. The computational method uses the Rayleigh-Ritz method for the vibration analysis and the simplex method of Nelder and Mead for the optimization search of support locations. Optimal results have been obtained for various common shapes of plates with a few point supports. The results show that the frequency of the plate is sensitive to the locations of the point supports. Moreover, these new optimal results provide useful information to designers seeking to exploit the position of point supports in their plate designs. It has been found that multiple solutions are a common feature of this plate optimization problem.     

Optimum structure with homogeneous optimum cellular material for maximum fundamental frequency

Ultra-light cellular materials exhibit high stiffness/strength to weight ratios and bring opportunity for multifunctional performance. One of their potential applications is to build structure with optimum dynamic performance, which is extremely important for some structural parts in vehicle engineering and attracts a great attention. This paper presents a two-scale optimization method and aims at finding optimal configurations of macro structures and micro-structures of cellular material with maximum structural fundamental frequency. In this method macro and micro densities are introduced as independent design variables for macrostructure and microstructure. Optimizations at two scales are integrated into one system through homogenization theory and base material is distributed between the two scales automatically with optimization model. Microstructure of materials is assumed to be homogeneous at the macro scale to meet today’s manufacture practice and reduce manufacturing cost. Plane structure with homogeneous cellular material and perforated plate are studied. Numerical experiments validate the proposed method and computational model.     

Minimum-weight design of flexible arms for specified fundamental frequency

The problem of designing a minimum-weight one-link flexible arm for a specified fundamental frequency of vibration has been investigated. The optimum design problem is formulated as a nonlinear eigenvalue problem using the variational method. Two iteration schemes are developed to find the optimum solution in the normal and degenerated cases. Numerical results have indicated that a significant reduction in link weight can be achieved by the proposed method. For example, for a geometrically similar cross section and a specified fundamental frequency ranging from 1 Hz to 10 Hz, the weight of an optimum link is 400% to 600% lighter than that of an uniform link. © 1997 John Wiley & Sons, Inc.     

An ant colony optimization approach to multi-objective optimal design of symmetric hybrid laminates for maximum fundamental frequency and minimum cost

An ant colony optimization algorithm for optimum design of symmetric hybrid laminates is described. The objective is simultaneous maximization of fundamental frequency and minimization of cost. Number of surface and core layers made of high-stiffness and low-stiffness materials, respectively, and fiber orientations are the design variables. Optimal stacking sequences are given for hybrid graphite/epoxy-glass/epoxy laminated plates with different aspect ratios and number of plies. The results obtained by ant colony optimization are compared to results obtained by a genetic algorithm and simulated annealing. The effectiveness of the hybridization concept for reducing the weight and keeping the fundamental frequency at a reasonable level is demonstrated. Furthermore, it is shown that the proposed ant colony algorithm outperforms the two other heuristics.     

Topological indentation pattern design of plates for maximum frequency gap

The vibrational response of thin plates is improved by a new approach of indenting some portions along the normal direction so that the interval between two successive eigenfrequencies is enlarged while keeping their mass the same. Binary-coded genetic algorithm (GA) is used as the search algorithm. A stochastically-applied deterministic filter is developed like another genetic operator for GA to accelerate the convergence speed. The corresponding eigenfrequencies and their mode shapes are found by using finite element analysis. The results indicate significant improvement for the band-gap over no indentation designs and show the effectiveness of the new operator of GA.     

Optimal location of a cutout in rectangular Mindlin plates for maximum fundamental frequency of vibration

This brief note presents an effective numerical technique for determining the optimal location of a cutout in rectangular Mindlin plates for maximum fundamental frequency of vibration. Instead of adopting the widely-used finite element method for the vibration analysis, we propose that the Ritz method be employed as the latter method avoids the need to remesh and redefine connectivity for a perforated plate at every iteration step of the optimization procedure. The location of a cutout, of a given shape and size, is specified by the coordinates of the geometric centre of the cutout. The optimal values of these coordinates are determined using the Generalized Reduced Gradient (GRG) method. To demonstrate the method, optimal locations of circular and square cutouts in square plates are determined. The sensitivity of the fundamental frequency to the location of the cutout is also investigated.     

Optimality criterion for maximum fundamental frequency of free vibrations of frames including axial and bending effects

An optimality criterion for maximum multiple fundamental frequency of free vibrations for structures of prescribed weights is presented. The criterion includes both axial and bending effects and can be used for analysis of truss, beam and frame structures. The error norm based on the criterion is proposed and used to verify trial designs against the optimum. The accompanying iterative procedure reduces this error norm to zero and drives a trial design to the optimum. The modality of the design at the optimum and the corresponding set of Lagrange multipliers are determined automatically.     

平面线弹性问题的等几何形状优化方法

介绍具有等几何分析功能的GeoPDEs平台的数据结构和分析流程,针对二维平面形状优化问题,以控制顶点为设计变量,在推导出等几何分析的灵敏度计算公式后,提出基于GeoPDEs平台的灵敏度分析的高效实现方法,并采用移动渐近线法(Method of Moving Asymptotes,MMA)算法进行等几何形状优化.形状优化实例表明该方法收敛速度快,优化结果较理想.     

Discrete material selection and structural topology optimization of composite frames for maximum fundamental frequency with manufacturing constraints

Structural and Multidisciplinary Optimization - This paper proposes a methodology for simultaneous optimization of composite frame topology and its material design considering specific...     

Isogeometric analysis using polynomial splines over hierarchical T-meshes for two-dimensional elastic solids

Isogeometric analysis has become a powerful alternative to standard finite elements due to its flexibility in handling complex geometries. One of the major drawbacks of NURBS-based isogeometric finite elements is the inefficiency of local refinement. In this study, we present an alternative to NURBS-based isogeometric analysis that allows for local refinement. The idea is based on polynomial splines and exploits the flexibility of T-meshes for local refinement. The shape functions satisfy important properties such as non-negativity, local support and partition of unity. Several numerical examples are used to demonstrate the reliability of the present method.     

Design of variable-stiffness conical shells for maximum fundamental eigenfrequency

Fiber-reinforced composite conical shells with given geometry and material properties are optimized for maximum fundamental frequency. The shells are assumed to be built using an advanced tow-placement machine, which allows in-plane steering of the fibers, resulting in a variable-stiffness structure. In this paper, different path definitions for variable-stiffness shells are provided and used to optimize conical shells for maximum fundamental frequency, while manufacturing constraints that apply for tow placement are taken into account in the process. The influence of manufacturing constraints on the performance is shown; and improvements of variable-stiffness conical shells over conventional, constant-stiffness shells are demonstrated.     

计算延时线的最大工作频率

<正>1计算最大输入频率对于一个固定延迟的延时线电路,在计算所允许的最大输入信号频率时需要考虑的关键参数是输入信号的最小脉冲宽度。对于占空比为50%的周期性信号,脉冲宽度为周期的一半。但有些周期性的低频输入信号的占空比低于50%。这种情况下,输入信号瞬变之间的最     

面向等几何分析的几何计算

等几何分析方法是一种直接基于CAD模型的精确几何表示进行物理性能仿真分析的新方法.文中从几何计算的视角出发,对等几何分析方法的基本框架,以及面向等几何分析的几何设计与计算的相关工作进行了介绍,重点介绍适合分析的计算域参数化、适合分析的新型样条理论、等几何配点法、面向等几何分析的并行计算等4个方向的研究进展.最后对需要进一步深入研究的关键问题进行了探讨.     

Topological design of freely vibrating continuum structures for maximum values of simple and multiple eigenfrequencies and frequency gaps

A frequent goal of the design of vibrating structures is to avoid resonance of the structure in a given interval for external excitation frequencies. This can be achieved by, e.g., maximizing the fundamental eigenfrequency, an eigenfrequency of higher order, or the gap between two consecutive eigenfrequencies of given order. This problem is often complicated by the fact that the eigenfrequencies in question may be multiple, and this is particularly the case in topology optimization. In the present paper, different approaches are considered and discussed for topology optimization involving simple and multiple eigenfrequencies of linearly elastic structures without damping. The mathematical formulations of these topology optimization problems and several illustrative results are presented. An erratum to this article can be found at