横观各向同性热弹性梁的精化理论

本文从横观各向同性梁的二维问题出发,研究了横观各向同性热弹性梁的精化理论。首先,在不作任何预先假设的条件下,利用横观各向同性热弹性理论和Lur’e算子函数,获得了由梁中线上的物理量表示的位移场和应力场。对热弹性梁上下表面承受非齐次边界条件的情况,推导出梁的近似控制微分方程。再舍去温度项,则横观各向同性热弹性梁的精化理论退化为横观各向同性梁的精化理论。     

Nonlinear Dynamic Bending Analysis of Plates Using a Higher-Order Shear Deformation Theory

The transient dynamic elastoplastic bending analysis of plates is investigated. Higher-order shear deformation theory is employed for the purpose, so as to have more realistic transverse shear representation. The formulation requires C⁰ continuity for nodal variables. Isoparametric parabolic finite element discretization is adopted. The yield criteria incorporated are von Mises and Tresca along with associated flow rules. The isotropic hardening is also included. Equations of motion are satisfied at discrete time intervals using direct integration method and central difference scheme. A special mass lumping scheme is adopted. As critical time step is very important in explicit integration scheme, precaution has been taken so as to have the time step smaller than the critical one. Numerical examples are solved and compared with solutions from literature. The formulation is shown to be superior in comparison to previous formulations, being more generic in all respects.     

基于高阶变形理论的夹层板的弯曲与振动

考虑面板和夹芯的面内刚度和横向剪切刚度以及抗弯刚度,考虑了高阶剪切变形,根据横向剪应变分布情况给出横向剪切转角的位移函数,基于哈密尔顿原理,推导了基于高阶变形理论、适用于软、硬夹芯情况夹层板的基本方程.作为算例,以四边简支条件下的夹层板的弯曲与振动,在不同的面板与芯层的弹性模量比和厚度比下进行了计算,并与Reissner理论、Hoff理论以及邓宗白基于Reissner理论的修正模型的计算结果进行了对比.与前述理论与方法相比,论文方法考虑因素更为全面,对夹层板的适用范围更为广泛,计算结果更为精确.针对Nastran软件计算夹层板的振动问题,对其适用范围作了简要分析.     

Bending of Nonthin Transversally Isotropic Plates with Curvilinear Openings

The problem on the spatial stress–strain state of a nonthin transversally isotropic plate with a curvilinear nearly circular opening is considered. The plate is assumed to be subject to bending moments on the opening contour and at infinity. To solve the problem, it is proposed to make mutual use of two well-know methods — expansion of the displacement and stress components into Fourier series in Legendre polynomials of the thickness coordinate and boundary-shape perturbation. The equations and recurrent relations necessary for solution of the problem in an arbitrary approximation are presented     

带剪切型压电激励器的板的高阶剪切变形理论

利用压电材料固有的正，逆压电效应可以对结构变形和振动进行控制。与外加电场与极化方向平行于板厚度的压电材料的拉伸作动机制相比，外加电场与极化方向垂直的压电材料的剪切作动机制可以在作动器内产生较小的应力，从而降低作动器边界产生分层破坏的危险。本文对于压电材料的剪切作动机制进行研究，应用三阶剪切变形理论建立带剪切型压电激励器的智能层合板模型。采用哈密顿原理导出带剪切型压电激励器的层合板的控制方程。采用空间法得到了各种边界条件组合条件下板的解析解。数值算例对一三层板采用高阶和一阶剪切变形理论进行计算，结果表明两种理论所得的变形曲线很相似。但对于厚度剪切型激励器而言，由于激励器是引起板的剪切变形，而高阶剪切变形理论比一阶剪切变形理论能更好地反映结构的剪切应变能，因此高阶剪切变形理论可以提供板变形的更为精确的解。因此，对于厚度剪切型激励器，剪切变形理论的选取对于板变形结果的好坏有重要的作用。     

用高阶剪切变形理论研究双模量梁的弯曲

利用高阶剪切变形理论研究了双模量梁的弯曲变形问题,推导出了双模量梁的挠曲线方程及弯曲正应力公式．讨论分析了翘曲函数的指数n对挠度、正应力的影响．研究结果表明：拉压弹性模量的差异对梁的弯曲应力有较大影响．把高阶剪切变形理论的计算结果与弹性理论计算结果进行比较,可知该方法计算精度非常高．     

Theory of Deformation of Isotropic Hyperelastic Bodies

Deformation of isotropic hyperelastic bodies is considered. The solution of the problem of gravitational compression of a sphere is given as an example of application of the theory.     

A Refined Model of Viscoelastic-Plastic Deformation of Flexible Plates with Spatial Reinforcement Structures

Journal of Applied Mechanics and Technical Physics - A refined model of viscoelastic-plastic deformation of flexible plates with spatial reinforcement structures has been developed. Strains of the...     

考虑剪切变形的各向同性,正交各向异性矩形板的屈曲和后屈曲

本文讨论考虑横向剪切变形的各向同性、正交各向异性矩形板的屈曲和后屈曲性态。应用Reissner理论,采用文[1]提供的摄动方法,给出了完善和非完善各向同性、正交各向异性矩形板的后屈曲平衡路径,并与薄板理论结果作了比较。     

Determination of Interlaminar Stresses in Bending Problems for a Stack of Transversely Isotropic Plates

A mechanical and mathematical bending model for a stack of transversely isotropic plates is developed. The resolving equations for deflections and tangential displacements are supplemented with a system of differential equations for normal and tangential contact stresses. It is demonstrated that for stacks consisting of an arbitrary number of identical plates with no friction between them, the initial system of equations for contact stresses can be reduced to Helmholtz equations. This transition allows obtaining the complete eigenvalue spectrum for the Laplasian of the problem and, in special cases, eigenfunctions. They are Krylov functions when bending is cylindrical and Bessel functions when bending is axisymmetric     

On the Bending, Vibration and Stability of Laminated Rectangular Plates with Transversely Isotropic Layers

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剪切变形对FGM圆板轴对称屈曲的影响

基于一阶剪切变形板理论，推导了功能梯度材料圆形板在边界面内均布压力作用下的轴对称屈曲方程。在推导过程中，忽略了前屈曲耦合变形。利用一阶板理论与经典板理论屈曲方程之间在数学形式上的相似性，得到了一阶板理论下功能梯度材料圆板与经典板理论下均匀圆板临界屈曲载荷之间的解析关系。利用这个解析关系，可以直接从已有的较为简单的经典理论的结果，获得一阶板理论下功能梯度材料板的临界屈曲载荷。     

压电复合材料层板柱面弯曲的精化理论

本研究旨在建立精确的压电复合材料层板理论。位移场和电势场采用近似表达，其沿板厚的分布通过构造高精度的位移分布函数和电势分布函数来描述。这两个函数由三雏弹性平衡方程和静电平衡方程的特解来导出，从而满足复杂的力电耦合关系和各类连续条件，保证了本文理论的高精度。本文理论仅涉及4个位移和电势变量，且不随层数的增加而增多，较之变量随层数而增多的分层理论简单得多，平衡方程形式简单；也便于发展成有限元等数值模型。通过与三维精确解比较，算例显示了本文理论的高精度和有效性。     

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．     

Elastoplastic Bending of Plates Resting on Elastic Subgrade under Rotational Symmetry Conditions*

An analysis of rotationally symmetric plates resting on an elastic subgrade is presented. The plates are made of an elastic, perfectly plastic material that obeys Johansen's yield condition and associated flow rule. The analysis is simplified by assuming that any plate element is either entirely elastic or entirely plastic. This assumption is practically fulfilled for a sandwich plate. Differential equations that describe the behavior of plastic zones during the deformation process are derived and solved in closed form. Examples of solutions for uniformly loaded circular plates are given.     

高阶剪切变形理论下三边夹紧一边铰支复合材料层板的几何非线性分析

首先用虚位移原理推导出以位移形式表达的Reddy型高阶剪变形理论复合材料层板的非线性控制方程及相应的边界条件。选定的五个位移函数均满足三边夹紧一边铰支边界条件，用Galerkin方法把无量纲化之后的控制方程转化为一组非线性代数方程组，用线性化的方法和可调节参数的修正迭代法求解这组方程。最后求出了不同复合材料的挠度和弯矩值。     

反对称斜交叠层板双向弯曲问题的横向基理论解

研究反对称斜交叠层板的双向弯曲问题。根据横向基理论，在厚度方向，给出了三个方向位移沿厚度的分布规律；在面内方向，采用升阶谱位移函数；然后，应用最小势能原理导出叠层板的静力控制方程。通过对多种层数和铺层角的层板力学响应计算分析表明：在典型位置的应力分布，本文解与三维弹性解符合很好，并有较好的收敛性。     

Deformation of Piecewise-Homogeneous Plates

Forced planar vibrations of a rectangular plate consisting of two rectangular subdomains are studied. The mechanical properties of the subdomains are essentially different. The boundary conditions for the subdomains may also be different. It is shown that the more the difference between the properties of the subdomains, the closer to a certain limit is the first resonance frequency of the plate. It is established that under certain boundary conditions, the displacements in each of the subdomains may have their own specific features     

Integration of an Equilibrium System in an Enhanced Theory of Bending of Elastic Plates

The complete integral of the system of partial differential equations governing the equilibrium bending of elastic plates with transverse shear deformation and transverse normal strain is constructed by means of complex variable methods. The process helps to elucidate the physical meaning of certain analytic constraints imposed on the asymptotic behavior of the solutions and shows that in the case of an infinite plate, any analytic solution has finite energy if and only if the bending and twisting moments, the transverse shear force, the displacements in vertical planes, and two other characteristic quantities vanish at infinity. An example is discussed to illustrate the theory.