利用模态迭加法进行动响应分析应注意的问题

采用MSC－MARC程序的模态迭加法，对具有指数规律冲击载荷作用下的简支矩形板进行了响应计算，指出并讨论了应用模态迭加法求解结构动响应时应注意的几个问题。     

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。     

非轴对称载荷作用下任意弹性边界圆板弹性动力响应

利用模态迭加法得出了任意弹性边界圆板在非轴对称横向集中阶跃载荷作用下弹性动力响应的精确解，作为算例，给出简支圆板在非轴对称载荷作用下板上典型点的挠度与时间的关系曲线。     

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。     

横向集中力作用下悬臂薄板形变分析

对悬臂矩形薄板上作用的横向集中力进行了处理，导出它在任意横向集中力作用下的挠度方程组。建立了悬臂薄板弯曲形变与尺寸、荷载、弹性模量和泊松比之间的关系。据此给出用悬臂薄板弯曲形变测定板材弹性模量和泊松比的实验方案。进行了钢、铝合金、有机玻璃和玻璃布酚醛复合板的弯曲实验和拉伸实验。二者数据一致。     

双模量矩形板的大挠度弯曲计算分析

双模量矩形板在外载荷作用下,会形成各向同性的拉伸区和压缩区,把双模量矩形板看成两种各向同性材料组成的层合板,采用弹性力学理论建立了双模量矩形板在外载荷作用下的静力平衡方程,利用静力平衡方程确定了双模量矩形板的中性面位置,推导出了双模量矩形板的大挠度弯曲变形微分方程。用加权残值法求得了双模量矩形板的大挠度弯曲变形时板中点挠度,把该方法计算结果与有限元计算结果进行了比较,说明了该计算方法是可靠的,并讨论分析了双模量对矩形板大挠度弯曲变形的影响。     

具有边梁的悬臂矩形板的弯曲问题

本文建议一个求解具有边梁悬臂矩形板弯曲问题的解析解法。该法将有边梁和无边梁悬臂矩形板弯曲问题的解融为一体，在有边梁悬臂矩形板的解中令边梁弯曲刚度为零即得到无国梁悬臂矩形板的解。     

在阻尼介质中简支矩形板的塑性动力响应

本文用矩量法求解简支矩形板的塑性动力响应,分析阻尼介质对简支矩形板塑性动力响应的影响,解出了矩形板的残余挠度和终止运动时间.     

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。     

Reissner厚板的一般解析解答及其应用

本文基于原始的 Reissner 板模型,根据文献中的控制方程,给出了 Reissner 厚板弯曲问题的一般解析解答形式。在此基础上,详细地讨论了均布荷载下四边固支矩形 Reissner 厚板的弯曲问题,并在 VAX-8200机上编制了相应的 FORTRAN 程序。本文提出的厚板解析方法,无论从力学意义上,还是数学运算上,都比习惯的迭加法简明的多。算例表明:结果可靠、方法可行。     

有自由边的各向异性平行四边形板的弯曲、振动与屈曲的傅里叶分析

得到了有自由边的各向异性平行四边形板在面内张力和剪力作用下自由振动、屈曲和弯曲问题的精确解析解。首先给出五个重傅里叶级数叠加解,然后通过叠加得到六种不同边界的解,包括悬臂板和四边自由的板等。对一些典型情况考查了其收敛性,结果令人满意。与其它精确解析解比较,其结果非常一致。     

弹性地基上正交各向异性自由矩形板的弯曲

本文运用文所建立的方法,研究Winkler弹性地基上正交各向异性自由矩形板弯曲问题的精确解。以受集中载荷作用的板为例,给出不同弹性系数地基上板的位移和弯矩的数字计算结果。     

Thermal effects on the bending response of fiber-reinforced viscoelastic composite plates using a sinusoidal shear deformation theory

Summary. The static thermo-viscoelastic responses of fiber-reinforced composite plates are investigated by the use of a refined shear deformation theory. In this theory, trigonometric terms are used for the displacements in addition to the initial terms of a power series through the thickness. The form of the assumed displacements of this theory is simplified by enforcing traction-free boundary conditions at the plate faces. No transverse shear correction factors are needed because a correct representation of the transverse shear strain is given. Using the method of effective moduli solves the equations governing the bending of simply supported fiber-reinforced viscoelastic composite plates. An exact closed-form solution is presented for plates subjected to nonuniform distributions of temperature. The validity of the present theory is demonstrated by comparison with solutions available in the literature. A wide variety of results are presented for the bending response of viscoelastic rectangular plates under thermal loads. The influences of plate aspect ratio, side-to-thickness ratio, thermal expansion coefficients ratio and constitutive and volume fraction parameters on the thermally induced response are studied.     

Discrete Fourier-series method in problems of bending of variable-thickness rectangular plates

The approach to the solution of the boundary-value problems of bending of elastic rectangular plates of variable thickness is presented. It is proposed to introduce into the resolving system of partial differential equations additional functions which enables the variables to be formally separated and the problem to be reduced to a unidimensional one by representing all the functions as a Fourier series in a single coordinate. In this case the problem can be solved by the stable numerical method of discrete orthogonalization. To calculate the additional functions, Fourier series of discretely assigned functions with allowance for variations in the plate thickness are used. The boundary-value problems for rectangular plates of variable thickness were solved assuming that their weight is unchanged.     

Determination of elastic constants from measured natural frequencies of specially orthotropic cantilever plates

Abstract

The present paper examines the possibility of evaluating the elastic constants of specially orthotropic rectangular thin plates from the measured natural frequencies of cantilever plates. An expression is developed for orthotropic rectangular thin cantilever plates to determine natural frequencies, and its validity is demonstrated through finite element analysis as well as using published test results.     

集中载荷下四边固支正交各向异性矩形板的线性弯曲问题

采用载荷叠加法将集中载荷下四边固支正交各向异性矩形板线性弯曲的挠度分为3个部分：集中载荷下四边简支板的挠度、上下边简支左右边受弯矩的板的挠度、左右边简支上下边受弯矩的板的挠度,3个挠度之和在满足固支边界条件的情况下即为所要求的挠度的解。采用MATLAB软件编写程序进行计算,并将相同长宽的板在4种不同的厚度和载荷情况下的挠度计算结果与有限元分析结果进行比较,验证了解析解的正确性。最后讨论了经典的Kirchhoff薄板假设对于集中载荷的适用性问题。     

三边固支一边自由混凝土矩形薄板的热弯曲

为了得到温度作用下三边固支一边自由混凝土矩形薄板的挠度和弯矩解析解。该文基于薄板的小挠度理论和叠加原理,考虑横向变温情况,将温度作用下的三边固支一边自由矩形薄板看作是面内温差作用下的三边简支一边自由的矩形薄板和相邻三边作用弯矩的三边简支一边自由矩形薄板的叠加。首先,通过在自由边界上试设具有待定参数的挠度函数,采用李维解法,推导出三边简支一边自由矩形薄板在自由边界挠度函数作用下的解析解;其次,推导出温度作用下三边简支一边自由矩形薄板的解析解;再之,利用相邻三边弯矩作用下四边简支矩形薄板的解答,推导出相邻三边弯矩作用下三边简支一边自由矩形薄板的解答;最后,采用叠加原理得出横向变温作用下三边固支一边自由矩形薄板的挠度和弯矩解析解,并利用MATLAB编制程序得到横向变温作用下三边固支一边自由矩形薄板的计算系数用表,从而为以后工程结构中三边固支一边自由混凝土矩形薄板在热环境下的设计计算提供了理论依据。     

弯曲矩形板的广义位移解及其边界值

本文应用功的互等定理,给出了弯曲矩形板的广义位移解及其边界值.从广义位移解可导出在各种载荷作用下具有各种边界条件矩形板的弯曲位移公式.本文导出的广义位移解的边界值是求解各种复杂边界条件矩形板弯曲的理论基础.     

Method of initial functions: stable algorithms in the analysis of thick laminated composite structures

Exact three-dimensional elasticity solutions for some static and dynamic problems of bending multi-layered anisotropic rectangular plates are presented. They are derived by the method of initial functions without employing any hypotheses about the character of the stress-strain state of the linearly elastic anisotropic structures. Two computationally stable algorithms of the method which extend the field of its application are developed. The results presented illustrate some possibilities of the designed stable algorithms. The analysis of multi-layered plates under concentrated static and harmonic dynamic loads are presented.