应用多刚体离散化方法对梁的动力屈曲和后屈曲分析

基于梁的多刚体离散化模型（有限段模型）,建立了梁的链式多刚体-铰链-弹簧系统模型,利用坐标变换方法建立了相应的非线性多自由度系统的参数振动方程,并利用约束参数法对所得到的多度系统的Mathieu-Hill方程进行了梁的动力屈曲分析,得到系统的参数共振域．因为所用的离散化模型与动力方程对梁的变形并无限制,所以可以用所得到的数学模型在其失稳域对梁的动力后屈曲进行数值仿真分析．通过实例的数值仿真,证明了这种梁的参数振动模型与分析方法的正确性．     

用截面变形耦合有限元法分析复合材料梁

复合材料板和梁具有优良的特性, 从而获得了广泛的应用．然而由于材料的各向异性, 使得对这类材料构件作变形和应力分析时,即使应用如有限元法的数值分析手段仍是非常复杂费时的．为此提出了一个可应用常规有限单元法,分析等截面复合材料梁承受均匀拉弯扭载荷的一个简单精确分析的实施方法．由于巧妙地利用了变形的对称特性,使得分析只需建立在梁的一个切片构造的几何模型上,用常规三维实体有限单元进行结构离散．推导了精确的变形场模式,并借助结构平移自由度的耦合关系使得数值分析易于实施．并通过数值算例来阐明方法的实施过程．     

Assessing the Effects of Porosity on the Bending,Buckling, and Vibrations of Functionally Graded Beams Resting on an Elastic Foundation by Using a New Refined Quasi-3D Theory

Mechanics of Composite Materials - A new refined quasi-3D shear deformation theory for bending, buckling, and free vibration analyses of a functionally graded porous beam resting on an elastic...     

Topology Optimization of Flexible Multibody Systems Using Equivalent Static Loads and Displacement Fields

Topology optimization techniques are applied in most cases for static applications. However, recently topology optimization procedures for structures under dynamic loads have been the focus of several studies. In this work, a topology optimization scheme for flexible multibody systems using equivalent static loads and displacement fields is investigated. The optimization problem is formulated using a homogenization method, more precisely, the solid isotropic material with penalization (SIMP) approach. The objective function in the optimization problem is the compliance and the method of moving asymptotes is used as optimizer. The objective function and the sensitivities are computed directly from the displacement field computed in the dynamic simulation. The examples of a 2-arm manipulator and a slider-crank mechanism are presented and the results are discussed to verify the improved dynamical behavior through this optimization method. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Secondary Buckling Analysis of Thin Rectangular Plates Based on the Wavelet Galerkin Method北大核心CSCD

Application of the wavelet Galerkin method (WGM) to numerical solution of nonlinear buckling problems was studied with classical elastic thin rectangular plates. First, the discretized scheme of the von Kármán equation were introduced, then a simple calculation approach to the Jacobian and Hessian matrices based on the WGM was proposed, and the wavelet discretized scheme-based eigenvalue equation method, the extended equation method and the pseudo arc-length method for nonlinear buckling analysis were discussed. Second, the secondary post-buckling equilibrium paths of elastic thin rectangular plates and the effects of aspect ratios, boundary conditions and bi-directional compression on the mode jumping behaviors, were discussed in detail. Numerical results show that, the WGM possesses good convergence for solving buckling loads on rectangular plates, and the obtained equilibrium paths are in good agreement with those from the stability experiments, the 2-step perturbation method and the nonlinear finite element method. Given the feasibility of combination with different bifurcation computation methods, the WGM makes an efficient spatial discretization method for complex nonlinear stability problems of typical plates and shells. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

Free Vibration Analysis of Laminated Composite Plates Resting on Elastic Foundations by Using a Refined Hyperbolic Shear Deformation Theory

The free vibration of laminated composite plates on elastic foundations is examined by using a refined hyperbolic shear deformation theory. This theory is based on the assumption that the transverse displacements consist of bending and shear components where the bending components do not contribute to shear forces, and likewise, the shear components do not contribute to bending moments. The most interesting feature of this theory is that it allows for parabolic distributions of transverse shear stresses across the plate thickness and satisfies the conditions of zero shear stresses at the top and bottom surfaces of the plate without using shear correction factors. The number of independent unknowns in the present theory is four, as against five in other shear deformation theories. In the analysis, the foundation is modeled as a two-parameter Pasternak-type foundation, or as a Winkler-type one if the second foundation parameter is zero. The equation of motion for simply supported thick laminated rectangular plates resting on an elastic foundation is obtained through the use of Hamilton’s principle. The numerical results found in the present analysis for free the vibration of cross-ply laminated plates on elastic foundations are presented and compared with those available in the literature. The theory proposed is not only accurate, but also efficient in predicting the natural frequencies of laminated composite plates.     

板梁组合结构可靠性分析的随机边界元法

本文用随机边界元法分析了随机荷载作用下具有随机边界条件的正交各向异性板、梁组合结构的可靠性.文中首先给出正交各向异性板、梁组合结构的边界积分方程,进而基于随机边界元法建立了随机结构可靠性分析方法和得到用于计算正交各向异性板、梁组合结构可靠性指标的公式.算例表明了本文方法的有效性.     

Analysis of Mechanical Properties and a Design Method of Reinforced Timber-Concrete Composite Beams

Mechanics of Composite Materials - Based on the loading features of reinforced timber-concrete composite (TCC) beams, a calculation model of their ultimate flexural capacity is established. To...     

非线性自然弯扭闭口薄壁复合梁的广义变分原理

对复合材料自然弯扭闭口薄壁细长梁在小应变、大位移和大转动的情况作了研究,建立了两端边界均为完全约束的该梁大变形弹性理论的非完全广义变分原理的泛函。由泛函驻值条件可以导出所给问题的平衡方程及全部边界条件。上述方法可方便地推广到其它各种不完全约束边界的情况。此外,利用上述结果还可以得到该梁在小位移理论中的基本方程和有关公式。     

中厚度复合材料夹芯层板变分渐近精细模型

为准确预测对中厚度复合材料夹芯层板分层开裂至关重要的沿厚向应力/应变分布,利用板固有小参数将原三维板分析严格拆分为沿厚向的一维分析和二维板非线性分析,并将原三维能量渐近扩展为系列二维近似能量泛函;通过对近似能量泛函中主导变分项(含翘曲项)的渐近修正,得到与原三维模型尽可能接近的近似能量,从而构建无需任何场变量假设的精细模型,并转换为工程常用的Reissner模型形式．通过4层复合材料夹芯板柱形弯曲算例表明:基于所构建模型重构的三维场精度较一阶剪切变形理论和经典层合理论更好,与精确解基本一致;由于所构建的变分渐近模型为等效单层板模型,在保证足够精度的前提下,相比三维有限元计算可减少2~3阶计算量,在精确性和有效性间取得较好的折衷．     

A Uniqueness Theorem in the Inverse Spectral Theory of a Certain Higher-Order Ordinary Differential Equation Using Paley-Wiener Methods

The paper examines a higher-order ordinary differential equationof the form where D = i(d/dx),and where the coefficients a_jk, j,k [0,m], with a_mm = 1, satisfycertain regularity conditions and are chosen so that the matrix(a_jk) is hermitean. It is also assumed that m > 1. More precisely,it is proved, using Paley–Wiener methods, that the correspondingspectral measure determines the equation up to conjugation bya function of modulus 1. The paper also discusses under whichadditional conditions the spectral measure uniquely determinesthe coefficients a_jk, j,k [0,m], j + k 2m, as well as b andthe boundary conditions at 0 and at b (if any).     

On Changes of Variable Preserving the Convergence and Absolute Convergence of Fourier Series in the Haar Wavelet System

Mathematical Notes - It is established that, among all continuously differentiable homeomorphic changes of variable, the absolute convergence of Fourier series in the Haar wavelet system is...