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...     

Nonlinear free bending vibrations of plates

A general solution for the Helmholtz differential equations is obtained in the complex domain and applied to the nonlinear, free, bending vibrations of plates. The analysis is based on the decoupled nonlinear von Karman field equations by Berger assumption for the large deformations of plates. The decoupled differential equation in terms of the deflection function is a fourth order Helmholtz differential equation. Its solution, called the dynamic deflection function, is obtained in the complex domain by means of newly defined first and second kind and modified Bessel functions. The dynamic deflection function can be applied to any plates having any shape and any boundary condition under any arbitrary dynamic loads. For plates with smooth boundary, the parameters of the dynamic deflection function are determined from the boundary conditions of the plates and the initial conditions of the vibrations. The analyses of plates with piece-wise smooth boundaries are obtained on the mapped planes. The nonlinear, free vibration of circular plates are investigated by the dynamic deflection function. The effect of stretching on the natural circular frequencies are illustrated.     

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.     

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.     

Static bending of perforated nanobeams including surface energy and microstructure effects

This article aims to present comprehensive model and analytical solution to investigate the static bending behavior of regularly squared cutout perforated thin/thick nanobeams incorporating the coupled effect of the microstructure and surface energy for the first time. The perforation influence is considered to be deriving equivalent geometrical and material characteristics. The modified couple stress theory is adopted to incorporate the microstructure effect while the modified Gurtin–Murdoch surface elasticity model is employed to incorporate the surface stress effect in perforated nanobeams. A variational formulation based on minimization of the total potential energy principle is employed to derive the equilibrium equations of perforated nanobeams based on both Euler–Bernoulli and Timoshenko beams theories are developed to investigate the associated effect of the shear deformation due to perforation process. Additionally, Poisson’s effect is also incorporated. Analytical closed-form for the non-classical bending profiles as well as the rotational displacement are developed for both beam theories considering the simultaneous effect of both couple stress and surface stress for both uniformly distributed and concentrated loading patterns. The verification of the developed model is verified and compared with previous works, and an excellent agreement is obtained. The applicability of the developed model is demonstrated and applied to study and analyze the nonclassical bending behavior of regularly squared perforated simply supported beams under different loading conditions. Additionally, effects of the perforation configuration parameters, beam size as well as beam aspect ratio on the bending behavior of perforated beams in the presence of microstructure and surface stress effects are also investigated and analyzed. The obtained results reveal that both couple stress and surface stress significantly affect the bending behavior of regularly squared cutout perforated beam structures. Results obtained are supportive for the design, analysis and manufacturing of perforated NEMS applications.

     

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.     

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.     

融合深度学习与最大间距准则的人脸识别方法

当前,人脸识别技术遇到的突出问题是光照、姿态、遮挡和表情等因素所引起的识别精度的下降,这些问题是人脸识别系统不完美的主要原因,深度学习是一种新的方法,可有效解决这些问题。首先通过引入深度学习算法进行多层次的学习,然后提取高层特征进行人脸描述,最后应用最大间距准则减小最小二乘估计产生的重建误差,实现有效的面部识别分类。该算法在ORL、CAS-PEAL和扩展Yale-B人脸数据库中进行了不同光照、姿态、遮挡、表情和容貌特征变化条件下的仿真实验。结果表明,所提出的算法比传统线性分类算法具有更高的效率和准确度。     

Optimization of cylindrically orthotropic circular plates including geometric non-linearity with a constraint on the fundamental frequency

Optimization of cylindrically orthotropic circular plates is studied with a constraint on the fundamental frequency when the effect of geometric nonlinearity is included. Details of finite element formulation for inclusion of geometric nonlinearity, derivation of optimality criterion and recurrence relations are presented. Results for various values of orthotropy parameter are given in tables.     

A finite element analysis of beams on elastic foundation including shear and axial effects

A displacement finite element method for analyzing a beam on continuous elastic foundation is presented. A three-dimensional model which accounts for the effects of both the Filonenko-Borodich and Pasternak foundation models in a consistent and complete way is used. A variational principle is introduced with the slope field due to bending only and the displacement field approximated by independent quantities subjected to variation. Numerical examples illustrate the accuracy of the element, the importance of shear, axial and shear-axial interaction effects associated with continuous elastic foundation, and finally the application of the element to a rotor supported by two hydrodynamic journal bearings.     

Geometrically non-linear free vibrations of clamped simply supported rectangular plates. Part I: the effects of large vibration amplitudes on the fundamental mode shape

The geometrically non-linear free vibrations of thin isotropic and laminated rectangular composite plates with fully clamped edges have been successfully investigated in previous series of works using a theoretical model based on Hamilton’s principle and spectral analysis. The objective of this work is the extension of the above model to the case of clamped clamped simply supported simply supported rectangular plates, denoted by CCSSSSRP, in order to determine their fundamental non-linear mode shape, and associated amplitude-dependent resonant frequencies, and flexural stress distribution. Numerical data are given for both linear and non-linear analysis, for various plate aspect ratios and vibration amplitudes. Good agreement was found with previous published results.     

Modeling the effects of emphasis and question on fundamental frequency contours of Cantonese utterances

Emphasis and question are two factors that have significant effects on F/sub 0/ contours for various languages, among which tone languages require more careful study because their F/sub 0/ contours show complex interaction between lexical tones and sentence intonation. This paper employs the command-response model for the process of F/sub 0/ contour generation to investigate the effects of these two factors for Cantonese, a typical tone language with nine tones. Analysis shows that the major effect of emphasis is on phrase commands, whereas the polarity and the amplitude of the tone commands in the emphasized part are hardly affected so that the inherent tone command patterns are maintained. In the intonation question, the inherent tone command in the later part of the sentence-final syllable is always substituted by a positive tone command. The particle question, on the other hand, maintains the inherent tone command for the question particle. In both types of questions, a sentence-final phrase command is added or enhanced, and a particular ending tone command is attached, the amplitude of which can indicate the degree of inquisitive intention. By comparison, the effect of emphasis starts from the target part for emphasis but is not confined to it, whereas the effect of question is localized in the sentence-final part and especially concentrated within the ending syllable. Nevertheless, both of them can be represented in the framework of the command-response model, by which F/sub 0/ contours for expressive speech can be generated efficiently.     

Modeling and control of coupled bending and torsional vibrations offlexible beams

An evolution equation which governs coupled bending and torsional vibrations of flexible beams with a tip body is derived based on Lagrangian dynamics. A feedback control scheme is shown for suppressing the vibrations     

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.     

Feedback control of decoupled bending and torsional vibrations of flexible beams

In this article, we consider a flexible beam with a rigid body, of which the bending vibration and the torsional vibration are decoupled. Therefore we need two control motors to suppress the vibrations. Each set of dynamic equations is treated in the form of an appropriate Hilbert space. A stabilizing feedback control law of each rotation motor will be established on the basis of modal analysis. A set of experiments has been carried out, and the results demonstrate the effectiveness of the dynamic model and the proposed control law. © 1994 John Wiley & Sons, Inc.