四角点支承板的广义变分解

本文用广义变分法计算了四角点支承矩形板的弯曲及稳定。文中选用的位移函数满足了板的主要边界条件;从而能得到较好的近似解,且计算比较简便。     

夹层板弯曲问题的Hoff理论的解析解

本文根据Ｈｏｆ提出的夹层板理论和胡海昌、柳春图对该理论的简化理论，提出了矩形夹层板弯曲问题的解析解的一般格式，它可以用于求解各种边界条件下矩形夹层板弯曲问题的Ｈｏｆ理论的解析解。从而，使得考虑表层抗弯刚度的矩形夹层板弯曲问题求解格式化。     

四边弹性梁支承的矩形板非线性弯曲

本文给出四边弹性梁支承的矩形板在横向荷载作用下的非线性弯曲的重级数解。通过把板内的横向位移展成重傅里哀级数,在边界上的位移展成单傅里哀级数以及把应力函数展成广义傅里哀级数,使边界条件转化成了无穷线性代数方程,控制微分方程转化成了无穷非线性代数方程。文后给出了四边弹性梁支承和对边简支对边弹性梁支承的矩彤板非线性弯曲的计算结果。     

广义康托洛维奇法解任意四边形板的弯曲问题

本文从变分原理和双线性坐标变换出发,采用基于三次B样条函数的广义康托洛维奇法得到了带有各种边界条件任意四边形板弯曲的近似解答。样条函数广义康托洛维奇法是一种数值型的康托洛维奇法,因而它既能化二维问题为一维同题,同时又具有样条函数法收敛快、精度高、处理边界条件方便等优点。推导出的计算格式适用于各种边界条件,使梯形板、平行四边形板和矩形板的弯曲问题为本文的特殊情况。本文方法与通常有限元法相比,具有计算量小、精度高等显著特点,且通用性强,是一种很有前途的计算方法。     

双参数地基板的精度分析

为了板与地基相互作用理论的严密性和计算的可靠性,该文先纠正了双参数地基自由矩形板研究中长期存在的板外地基沉降衰减指数取值不当的问题;然后基于弹性半空间地基上四边自由矩形板的弯曲解析解,数值计算验证了实际地基反力与挠度不具有Vlazov双参数地基模型所导出的关系式;最后,通过对算例的数值计算及结果的对比分析,从板的弯曲变形角度,说明该文给出的衰减指数值才是适当的;同时,也分析给出了Vlazov双参数地基自由矩形板各种近似边界条件的计算精度。     

两角点支撑的矩形外伸板

在建筑工程中有一类边界条件较为复杂的矩形外伸板，它外伸部分的两角点被支撑，而其他的边为自由，本文用广义简支边的概念及迭加法，求解两角点支撑矩形外伸板的弯曲。     

一对边支承一对边自由的矩形板弯曲统一求解方法

根据边界条件的相近性，本文对一对边支承一对边自由的矩形板提出了一种统一的弯曲挠度表达式。该表达式切合板边界所能激发出的弯曲变形形态和角点位时所导致的非弯曲变形特点。它可以计算矩形板在任意荷载作用下和板边界发生任意支座位移时的弯曲。该方法求解思路清晰，收敛速度快，计算精度高。     

解Reissner板弯曲问题的一个新的边界元法

本文从虚功原理出发,以胡海昌导出的E、Reissner板弯曲理论归结为求解两个位移函数作为中间变量,推导出三个广义位移和三个广义力表示的边界积分方程。本文提出的方法适用于任意边界,任意载荷的薄板,中厚板弯曲。文未给出了固支。简支和自由三类边界的算例,均得到满意的结果。     

板柱结构矩形弹性板弯曲精确解法

板柱结构是工程中经常采用的受力体系,但至今尚无一种精确解法分析板中内力分布。将板柱结构矩形板的弯曲划分为广义静定和广义超静定二类。对于前者利用静力平衡条件确定柱支反力后撤去柱支座,柱支条件下板的弯曲即转换为四边自由矩形板在原荷载和柱支反力共同作用下的弯曲。挠度表达式采用了新的通解形式,其变形曲线符合四边自由边界所限定的变形特征,并采用组合特解,即特解同时满足平衡微分方程,自由边界上剪力分布条件及自由角点上作用力条件,从而可以利用四边边界条件和柱支座处的位移条件直接求解。对于广义超静定弯曲需要利用叠加法求解。这种解法可以分析板柱结构在任意柱支条件下和任意荷载作用下板的弯曲。通过逆向分析验证法真实地说明了本解法具有很高的计算精度。     

各向异性板平面应力问题的一般解析解

根据各向异性矩形板平面应力问题的基本方程精确地求得了位移函数的一般解。一般解包括三角函数和双曲线函数组成的解,还有代数多项式解。前者能满足四个边为任意边界条件问题;后者能满足四个角为任意边界条件等问题。这些边界条件用以决定一般解中的积分常数。因此一般解可用以求解任意边界条件下的平面应力问题。以四边为均匀分布和非均匀分布位移的对称角铺设复合材料板为例进行了计算和分析     

Bending-stretching analysis of thick functionally graded micro-plates using higher-order shear and normal deformable plate theory

In the present article, higher-order shear and normal deformable plate theory together with modified couple stress theory are developed to study the bending analysis of thick functionally graded rectangular micro-plates. One material length scale parameter is used for capturing the size effects. Utilizing the variational approach and also a principle of virtual displacement, a new form of equilibrium equations and the corresponding boundary conditions are derived. It is assumed that material properties vary through the thickness according to the power law function. Finally, an analytical solution for the bending problem of a simply supported FG rectangular micro-plate is presented.     

Nonlinear oscillation of unsymmetric angle-ply plate on elastic foundation having nonuniform edge supports

This paper is analytically concerned with nonlinear flexural oscillation of an unsymmetrically laminated angle-ply rectangular plate resting on a Pasternak-type elastic foundation. The plate edges are subjected to the varying rotational constraints. Based on dynamic von Kármán-type nonlinear plate theory a single-mode analysis is carried out. In the formulation of a solution the force function and bending moments along the four edges are expanded into generalized Fourier series. These moments are also replaced by an equivalent lateral pressure near these edges. Galerkin's procedure and the perturbation technique are applied to the equation of motion and the time equation respectively. Numerical results for the amplitude-frequency response of the plate are presented graphically for various high-modulus composite materials, geometries of lamination, aspect ratios, moduli of elastic foundation and boundary conditions. Present results are compared with the existing values.     

Bending vibration of a rectangular plate with arbitrarily located rectilinear crack

Harmonic flexural vibration of a rectangular plate with an arbitrarily located rectilinear crack is investigated. Double finite Fourier transformation of discontinuous functions is applied to a plate with arbitrary boundary conditions and subjected to transverse harmonic loading. Natural vibration of a simply supported plate is analyzed as a special case. The unknown amplitudes of discontinuities of the displacement and slope across the crack are determined by satisfying boundary conditions at the crack's edge. The square-root singularities of the bending moment at the crack's tips are built into the solution. The method of reduction is applied to the infinite characteristic determinant of the problem. Numerical values of three lowest frequencies of vibration of a square plate are obtained for a diagonally located crack of changing length.     

固支三维弹性矩形厚板的精确解

采用有限积分变换和状态空间理论相结合的方法推导出了固支三维弹性矩形厚板的精确解.在分析过程中摒弃以往薄板和中厚板理论中有关应力和位移函数的各种人为假定,完全从三维弹性力学基本方程出发,经过变量代换将关于应力和位移分量的六阶偏微分方程组化为2 个彼此独立的四阶、二阶矩阵微分方程,再利用有限积分变换的方法得到空间状态方程,并由Cayley-Hamilton定理求得应力和位移分量沿板厚度z 方向的传递矩阵,最后利用边界条件定解出待定常数,经过有限积分逆变换解得了固支三维厚板的精确解.通过计算实例验证了该文方法的正确性.     

Generalized hybrid quasi-3D shear deformation theory for the static analysis of advanced composite plates

This paper presents a generalized hybrid quasi-3D shear deformation theory for the bending analysis of advanced composite plates such as functionally graded plates (FGPs). Many 6DOF hybrid shear deformation theories with stretching effect included, can be derived from the present generalized formulation. All these theories account for an adequate distribution of transverse shear strains through the plate thickness and tangential stress-free boundary conditions on the plate boundary surfaces not requiring thus a shear correction factor. The generalized governing equations of a functionally graded (FG) plate and boundary conditions are derived by employing the principle of virtual work. Navier-type analytical solution is obtained for FGP subjected to transverse load for simply supported boundary conditions. Numerical examples of the new quasi-3D HSDTs (non-polynomial, polynomial and hybrid) derived by using the present generalized formulation are compared with 3D exact solutions and with other HSDTs. Results show that some of the new HSDTs are more accurate than, for example, the well-known trigonometric HSDT, having the same 6DOF.     

Boundary elements with equilibrium satisfaction: a consistent formulation for plate bending analysis considering Reissner’s theory

The present paper presents a self-equilibrated boundary element formulation for elastostatic analysis of Reissner’s plate bending problems. In this formulation, rigid body movements are introduced to the generalized displacement fundamental solution, resulting in modified boundary element matrices with inherent equilibrium satisfaction. The procedure is quite general and easy to implement into existing boundary element codes. In the end of the paper, numerical examples are presented, illustrating the benefits of the proposed formulation.