弹性半空间地基上预应力中厚矩形板的弯曲

基于Reissner-Mindlin一阶剪切变形理论,讨论在预加面内机械荷载或预加温度场作用下,弹性半空间地基上四边自由中厚矩形板的弯曲问题。把地基看作三维弹性半空间体,考虑地基变形的衰减。用一组数学上完备的二元多项式作为位形函数,采用pb-2 Rayleigh-Ritz法求得四边自由中厚矩形板的挠度和弯矩,并讨论了初应力对板的挠度和弯矩的影响。     

横观各向同性弹性半空间地基上四边自由各向异性矩形薄板弯曲解析解

选用更具广泛性的横观各向同性弹性半空间地基模型,来分析四边自由各向异性矩形地基板的弯曲解析解．将异性薄板的弯曲控制方程,与基于横观各向同性弹性半空间地基位移解建立的板与地基变形协调方程相结合,先按对称性分解,然后用三角级数法,得出横观各向同性弹性半空间地基上四边自由各向异性矩形薄板的弯曲解析解,包括地基反力、板的挠度及内力的解析表达式．该解析解克服了数值法的弊端,取消了对地基反力的假设,板的内力及地基反力求解更切实际．算例结果与文献结果吻合良好,证明本文方法的可行性．     

弹性半空间地基与四边自由异性矩形板相互作用的研究

选用弹性半空间地基模型分析四边自由各向异性矩形地基板的弯曲和稳态振动解析解。将异性薄板控制微分方程与基于弹性半空间地基位移解建立的板与地基变形协调方程相结合,先按对称性分解,然后采用三角级数法得出了弹性半空间地基上四边自由各向异性矩形薄板的弯曲和稳态振动解析解,包括地基反力(幅值)、板的挠度(幅值)、板的内力(幅值)的解析表达式。克服了数值法的弊端,取消了对地基反力的假设,得到了板的内力(幅值)及地基反力(幅值)更切实际的分布规律。算例结果不但与文献结果吻合良好,而且表明对于异形板,对称载荷能引起反对称的内力和变形。该方法使得半空间地基上各向异性矩形薄板这一复杂的接触问题的求解统一化、简单化、规律化。     

弹性半空间地基与四边自由异性矩形板相互作用的研究

选用弹性半空间地基模型分析四边自由各向异性矩形地基板的弯曲和稳态振动解析解。将异性薄板控制微分方程与基于弹性半空间地基位移解建立的板与地基变形协调方程相结合,先按对称性分解,然后采用三角级数法得出了弹性半空间地基上四边自由各向异性矩形薄板的弯曲和稳态振动解析解,包括地基反力(幅值)、板的挠度(幅值)、板的内力(幅值)的解析表达式。克服了数值法的弊端,取消了对地基反力的假设,得到了板的内力(幅值)及地基反力(幅值)更切实际的分布规律。算例结果不但与文献结果吻合良好,而且表明对于异形板,对称载荷能引起反对称的内力和变形。该方法使得半空间地基上各向异性矩形薄板这一复杂的接触问题的求解统一化、简单化、规律化。     

层状横观各向同性地基上异性矩形薄板的弯曲解析解

选用更具广泛性的层状横观各向同性弹性地基模型,来分析四边自由各向异性矩形地基板的弯曲解析解。先基于直角坐标下横观各向同性体的静力胡海昌通解,借助双重傅里叶变换及矩阵传递法,获得层状横观各向同性地基的静力位移场和应力场;然后将异性薄板的弯曲控制方程,与基于层状横观各向同性弹性地基的位移解建立的板与地基变形协调方程相结合,先按对称性分解,再用三角级数法,得出层状横观各向同性弹性地基上四边自由各向异性矩形薄板的弯曲解析解,包括地基反力、板的挠度及板的内力的解析表达式。克服了数值法的弊端,取消了对地基反力的假设,且避免了矩阵指数函数的计算;同时考虑了地基的层状性及板和地基的各向异性,从而得到板的内力及地基反力更切实际的分布规律。算例结果与文献的有限元结果吻合良好,证明本文方法是切实可行的。     

层状横观各向同性地基上异性矩形薄板的弯曲解析解

选用更具广泛性的层状横观各向同性弹性地基模型,来分析四边自由各向异性矩形地基板的弯曲解析解。先基于直角坐标下横观各向同性体的静力胡海昌通解,借助双重傅里叶变换及矩阵传递法,获得层状横观各向同性地基的静力位移场和应力场;然后将异性薄板的弯曲控制方程,与基于层状横观各向同性弹性地基的位移解建立的板与地基变形协调方程相结合,先按对称性分解,再用三角级数法,得出层状横观各向同性弹性地基上四边自由各向异性矩形薄板的弯曲解析解,包括地基反力、板的挠度及板的内力的解析表达式。克服了数值法的弊端,取消了对地基反力的假设,且避免了矩阵指数函数的计算;同时考虑了地基的层状性及板和地基的各向异性,从而得到板的内力及地基反力更切实际的分布规律。算例结果与文献的有限元结果吻合良好,证明本文方法是切实可行的。     

横观各向同性弹性半空间地基上正交异性矩形中厚板弯曲解析解

对横观各向同性体通解进行双重傅里叶变换,获得了直角坐标系下横观各向同性弹性半空间地基受任意竖向荷载作用下的位移积分变换解;在此基础上建立了板与地基的变形协调方程,并与三个广义位移变量描述的弹性地基上四边自由正交各向异性矩形中厚板的弯曲控制方程相结合,用三角级数法,得出横观各向同性弹性半空间地基上四边自由正交异性矩形中厚板受任意竖向荷载作用的弯曲解析解。相关算例分析表明,本文方法是有效的。     

板下地基位移分布规律及参数确定

将弹性半空间地基受任意竖向荷载作用下的静力位移积分变换解与弹性半空间地基上四边自由矩形板受任意竖向荷载作用下的弯曲解析解相结合,建立了求解板下地基位移的一般方法.对一些算例,进行大量数值计算分析,得出弹性半空间地基上四边自由矩形板下地基水平位移和竖向位移的分布规律,地基影响深度,并由此分布规律确定了其相应的简化模型-双参数地基模型的两个参数.     

位移模式对Cross—PLY矩形板热弹性响应的影响

本文建立了以Ｒｅｉｓｓｎｅｒ混合变分原理为基础的迭层板剪切变形理论来求解Ｃｒｏｓｓ－ＰＬＹ矩形板的热弯曲问题，用二种方式来模拟平面位移沿厚度的变化：将一阶剪切变形理论的平面位移叠加一项交错线性函数；设平面位移是分线性连续函数。为保证层间应力的连续性，将横向剪切应力处理成厚度坐标的二次函数，温度沿厚度线性变化。通过对称及反对称Ｃｒｏｓｓ－ＰＬＹ矩形板的热应力及挠度分析比较，指出了位移模式对热弹性响应     

用Laplace变换分析弹┐粘塑性梁的弯曲

在弹塑性梁弯曲变形理论基础上，本文用Ｌａｐｌａｃｅ变换进一步分析了弹－粘塑性梁的弯曲问题．并以矩形截面梁为例，说明弹－粘塑性梁弯曲时的弹性与粘塑性区的应力，梁的挠度及弹－粘塑性交线的计算     

基于无网格法的弹性地基加肋斜板频率数值解

为了给实际地基工程中的经济效益提供技术指标参考，应用无网格法计算加肋斜板在地基上的自由振动行为，应用移动最小二乘近似MLS和一阶剪切变形原理描述加肋斜板的位移场，分别建立斜板与肋条的势能泛函，使用Winkler弹性地基模型处理加肋板与地基之间的接触势能。通过斜板与肋条的位移协调关系寻找斜板和肋条节点参数转换公式，确立加肋斜板的自由振动控制方程。本文运用了无网格法的优势，即使肋条位置改变也不需重置网格。与有限元解的对比验证了本文方法的有效性和精确性。     

A non-classical Kirchhoff plate model incorporating microstructure,surface energy and foundation effects

A new non-classical Kirchhoff plate model is developed using a modified couple stress theory, a surface elasticity theory and a two-parameter elastic foundation model. A variational formulation based on Hamilton’s principle is employed, which leads to the simultaneous determination of the equations of motion and the complete boundary conditions and provides a unified treatment of the microstructure, surface energy and foundation effects. The new plate model contains a material length scale parameter to account for the microstructure effect, three surface elastic constants to describe the surface energy effect, and two foundation moduli to represent the foundation effect. The current non-classical plate model reduces to its classical elasticity-based counterpart when the microstructure, surface energy and foundation effects are all suppressed. In addition, the newly developed plate model includes the models considering the microstructure dependence or the surface energy effect or the foundation influence alone as special cases and recovers the Bernoulli–Euler beam model incorporating the microstructure, surface energy and foundation effects. To illustrate the new model, the static bending and free vibration problems of a simply supported rectangular plate are analytically solved by directly applying the general formulas derived. For the static bending problem, the numerical results reveal that the deflection of the simply supported plate with or without the elastic foundation predicted by the current model is smaller than that predicted by the classical model. Also, it is observed that the difference in the deflection predicted by the new and classical plate models is very large when the plate thickness is sufficiently small, but it is diminishing with the increase of the plate thickness. For the free vibration problem, it is found that the natural frequency predicted by the new plate model with or without the elastic foundation is higher than that predicted by the classical plate model, and the difference is significant for very thin plates. These predicted trends of the size effect at the micron scale agree with those observed experimentally. In addition, it is shown both analytically and numerically that the presence of the elastic foundation reduces the plate deflection and increases the plate natural frequency, as expected.     

基于遗传算法的弹性地基加肋板肋梁无网格优化分析

基于遗传算法及一阶剪切理论, 提出一种弹性地基上加肋板肋条位置优化的无网格方法. 首先, 通过一系列点来离散平板及肋条, 并用弹簧模拟弹性地基, 从而得到加肋板的无网格模型; 其次, 基于一阶剪切理论及移动最小二乘近似原理导出位移场, 求出弹性地基加肋板总势能; 再次, 根据哈密顿原理导出结构的弯曲控制方程, 并通过完全转换法处理边界条件; 最后, 引入遗传算法和改进遗传算法, 以肋条的位置为设计变量、弹性地基板的中心点挠度最小值为目标函数, 对肋条位置进行优化达到地基板控制点挠度最小的目的. 以不同参数、载荷布置形式的弹性地基加肋板为例, 与ABAQUS有限元结果及文献解进行比较. 研究表明, 采用所提出的无网格模型可有效求解弹性地基上加肋板弯曲问题, 结果易收敛, 同时基于遗传算法与改进混合遗传算法所提出的无网格优化方法均可有效优化弹性地基加肋板肋条位置, 后者计算效率相对较高, 只进行了三次迭代便可获得稳定的最优解, 此外在优化过程中肋条位置改变时只需要重新计算位移转换矩阵, 又避免了网格重构.      

弹性半空间地基上的矩形板

分析和计算了性半空间地基上四边自由矩形板的动力和静力问题，把地基看作三维性半空间体，考虑地基的衰减变形，假定地基与板之间完全粘着摩擦接解，用能量变分析理导出了一般方程，并作了数值算例，还分析了相刚度对动力和静力性能的影响。     

Bending of a fiber-reinforced viscoelastic composite plate resting on elastic foundations

Composite structures on an elastic foundation are being widely used in engineering applications. Bending response of inhomogeneous viscoelastic plate as a composite structure on a two-parameter (Pasternak’s type) elastic foundation is investigated. The formulations are based on sinusoidal shear deformation plate theory. Trigonometric terms are used in the present theory for the displacements in addition to the initial terms of a power series through the thickness. The transverse shear correction factors are not needed because a correct representation of the transverse shear strain is given. The interaction between the plate and the foundation is included in the formulation with a two-parameter Pasternak’s model. The effective moduli and Illyushin’s approximation methods are used to derive the viscoelastic solution. The effects played by foundation stiffness, plate aspect ratio, and other parameters are presented.     

A free rectangular plate on the two-parameter elastic foundation

This paper provides a rigorous solution of a free rectangular plate on the V.Z. Vlazov two-parameter elastic foundation by the method of superposition[1]. In this paper we derive basic solutions under the various boundary conditions. To superpose these basic solutions the most generally rigorous solution of a free rectangular plate on the two-parameter elastic foundation can be obtained. The solution strictly satisfies the differential equation of a plate on the two-parameter elastic model foundation, the boundary conditions of the free edges and the free corner conditions. Some numerical examples are presented The calculated results show that when the plane dimension of plate is given and the ratio between the laver depth and the plate thick is equal to 15, the two-parameter elastic model is near the Winkler’s. It shows that the Winkler model can be applied to the thinner layer.     

弹性地基上矩形薄板问题的Hamilton正则方程及解析解

利用辛算法求出弹性地基上矩形薄板问题的解析解,将弹性地基视为双参数弹性地基,直接从弹性矩形薄板的控制方程推导出了问题的Hamilton正则方程,为求出任意边界条件下问题的理论解奠定了基础,并且通过算例验证了文中所采用方法的正确性．     

Experimental and theoretical study of the buckling of narrow thin plates on an elastic foundation under compression

The paper describes the processes of elastic deformation of thin films under mechanical loading. The film is modeled longitudinally by a compressed plate arranged on an elastic foundation. A computer model of the buckling of the narrow thin plate with a delamination portion located on an elastic foundation is constructed. This paper also touches upon the supercritical behavior of the plate–substrate system. The experiments on the axial compression of a metal strip adhered to a rubber plate are performed, and 2 to 7 buckling modes are obtained therein. The critical loads and buckling modes obtained in the numerical calculations are compared with the experimental data. It is shown that there is the possibility of progressive delamination of the metal plate from the foundation if the critical load is exceeded. It is found that the use of the proposed approach, which, in contrast to other approaches, accounts for the elastic deformation of the substrate, causes the dependence between the critical bending stress and the stiffness of the foundation.     

Bending of orthotropic plates resting on Pasternak’s foundations using mixed shear deformation theory

The mixed first-order shear deformation plate theory(MFPT) is employed to study the bending response of simply-supported orthotropic plates.The present plate is subjected to a mechanical load and resting on Pasternak’s model or Winkler’s model of elastic foundation or without any elastic foundation.Several examples are presented to verify the accuracy of the present theory.Numerical results for deflection and stresses are presented.The proposed MFPT is shown simplely to implement and capable of giving satisfactory results for shear deformable plates under static loads and resting on two-parameter elastic foundation.The results presented here show that the characteristics of deflection and stresses are significantly influenced by the elastic foundation stiffness,plate aspect ratio and side-to-thickness ratio.