温度作用下四边固定矩形薄板解析解的商榷

本文基于薄板的小挠度理论,根据四边简支矩形薄板在横向变温作用下的解析解及四边固定矩形薄板的边界条件,通过应用虚功原理和叠加原理,推导了四边固定矩形薄板在横向变温作用下的挠度方程和内力解析解,从而为以后的工程计算提供理论依据。     

四边支承混凝土矩形薄板的热弯曲

混凝土矩形薄板不仅广泛应用于土木工程领域,而且广泛应用于诸如水利、石油化工、铁路、公路等诸多领域,本文根据近年来已获得的四边简支、四边固定、三边固定一边简支、一边固定三边简支、两邻边固定两邻边简支和两对边固定两对边简支矩形薄板在横向变温作用下的挠度和内力解析解,利用MATLAB软件编制程序得到了这类矩形薄板在横向变温作用下的挠度和内力计算系数用表,从而为以后工程结构中四边支承混凝土矩形薄板在热环境下的设计计算提供了理论依据。     

横向变温下四边简支矩形薄板的解析解

根据横向变温作用下各向同性材料弹性矩形薄板的平衡微分方程和边界条件,通过试取挠度函数,推导了四边简支情况下的挠度及内力计算公式,从而为该类板在温度作用下的结构计算提供了理论基础。     

受有边缘荷载的矩形板

弹性矩形薄板,在横向荷载作用下各种边界问题的小挠度解荅,在有关薄板理论的文献中均能找到。然而在边绿荷载作用下的计算,论述较少。这里,根据现有的弹性薄板小挠度基本方程式,导得了几种矩形板在边绿荷载作用下的内力及边绿位移计算公式。这些公式的推导原理简单,运算略繁,为省篇幅仅给出结果如下。     

混凝土简支矩形小挠度薄板的横向动力分析

通过建立混凝土简支矩形小挠度薄板受横向干扰时弹性力学的数理方程,解出方程的挠度函数,以此对其振动波形、波形衰减周期、最大振动反应及其时间等振动特征进行分析,并与静力分析的解比较,阐述了横向干扰混凝土简支矩形等厚薄板工程应用问题的若干基本观点。     

利用板的后屈曲理论对横向荷载作用下简支矩形板进行近似大挠度分析

介绍了一种近似分析方法,用于确定横向荷载作用下矩形简支薄板的大挠度性能。此法基于一个简单的测试函数,可描述板的初始形状、总变形和平面内均布压力下板最初的屈曲形状。因此,横向荷载下板的大挠度性能可以表示为板前屈曲和后屈曲的平面内刚度的比例函数,其中考虑了板的边界条件。由于目标函数的简单化,板的弯曲和膜作用是非耦合的。研究发现,该近似方法可以对大挠度性能进行比较好的分析。将近似方法的分析结果与有限元分析结果进行对比发现,在均布荷载下,两者计算的挠度值相差不超过10%。     

钢筋混凝土矩形薄板在弹性地基上的热屈曲

基于板的小挠度理论,考虑混凝土材料的非线性,推导了弹性地基上钢筋混凝土矩形薄板在热载作用下的平衡方程和稳定方程,给出了四边简支钢筋混凝土矩形薄板在均匀温度变化时临界屈曲温度变化的封闭解,讨论了板的材料常数、长宽比、相对厚度和基床系数等对临界屈曲温度变化的影响,从而为工程结构中弹性地基上钢筋混凝土矩形薄板的临界屈曲温度的计算提供了理论计算依据。     

局部荷载作用下简支板内力的传递规律研究

利用弹性力学四边简支矩形薄板的Navier解法,对工程中一些特殊局部荷载作用下的板建立整体模型、推导理论计算公式,并进行大量计算分析,进而研究其荷载和内力沿两个方向的传递规律。     

四边简支矩形薄板集中力作用中心弯矩影响面

根据弹性力学的相关理论,对四边简支矩形薄板的弯矩解答进行了分析,从影响面方面进行了论述,提出了在集中荷载作用下的四边简支矩形薄板的中心弯矩影响面的概念,并对其进行了研究,研究表明,四边简支矩形薄板的中心弯矩影响面在解决最不利荷载位置方面达到了很好的应用效果,最后进行了实例验证。     

考虑扭矩影响的矩形角板内力分析及配筋修正

混凝土角板两相邻边简支两相邻边固支,是最常见的楼板类型。工程上根据跨中弯矩和内支座负弯矩计算受力钢筋,简支边支座配置构造筋。基于弹性薄板小挠度理论,求解了板内弯矩和扭矩分布和两者数值关系。分析表明,在简支边角部部位,混凝土角板内力分布复杂,角部容易产生裂缝。依照现行做法,在带有简支边的角部配置构造配筋无法满足受力需要,必须配置受力钢筋。通过对比与四边固支、四边简支矩形板的内力分布差异,揭示了混凝土角板设计存在的问题,并对其合理设计提出了建议;其结论也可为边跨板设计提供参考。     

The effect of thermo-mechanical coupling for a simply supported orthotropic rectangular plate on non-linear dynamics

This paper is presented for the analysis of the large amplitude thermo-mechanically coupled vibration of the simply supported orthotropic rectangular thin plate. The governing partial differential equation of the large deflection orthotropic rectangular thin plate of thermo-mechanical coupling is derived and simplified to a set of three non-linear ordinary differential equations by the Galerkin method. The modeling result of numerical simulation indicated that the amplitude of the simply supported orthotropic rectangular thin plate decays under the various parameters of orthotropic materials. As these thermo-mechanical coupling factor, percentage of the Poisson ratio, percentage of the thermal conductance of the plate, percentage of the coefficient of thermal expansion, external in-plane force are decreased, the thermo mechanical damping of plate would be increased. The different thermal damping of the simply supported orthotropic plate can be controlled in the special range of the parameter.     

The stability of eccentrically compressed thin plates with a longitudinal free edge and with stress variation in the longitudinal direction

This paper presents results of the investigation of the stability of eccentrically compressed thin plates with one longitudinal free edge with the participation of loadings generating the variation of stresses in the direction of the length of a plate. A deflection function (5) is proposed to enable modelling of boundary conditions on the second longitudinal edge from a simply supported, through elastically restrained, to a built-in edge. Formulas are derived for work done by external force under loading generating the variation of stress according to a linear function and according to parabola 2°. Tables and plots of buckling coefficient (k) for variously supported and variously loaded plates with a free edge, which are not found in the literature, are determined. The effect of a longitudinal stress variation on the plate buckling modes is analyzed.     

Strength of biaxially loaded orthotropic plates

An approximate and simple method for rectangular orthotropic plates, loaded biaxially along two mutually perpendicular directions is presented. The theory is based on the energy method and it is free from difficult calculations such as those encountered when large deflection theory is used. Effects of initial imperfections are taken into account. The number and lengths of half-waves are assumed to be the same in the post-buckling stage as at incipient buckling. The finite buckled shape in the post-buckling stage is taken to be the same as that during incipient buckling. The Von Mises yield criterion is employed to determine the upper bound solution of the plate. Interaction curves for square plates subjected to longitudinal and transverse stresses, applicable to three different boundary conditions, four edges simply supported or four edges clamped or two opposite edges clamped with the other two edges simply supported, are presented in a non-dimensional form. Results for plates having different values of plate slenderness (b/t) and flexural rigidity ratios, D₂/D₁ are given.     

Laterally supported sandwich panels subjected to large deflections—Part 1: Test apparatus design and experimental results

This paper deals with the experimental characterization of the structural behavior of sandwich panels under distributed transverse loadings. A configuration typically used in aircraft interior applications is considered: a simply supported rectangular plate fixed by bolts on the two longitudinal edges or on all four edges. The panel and joint stiffness are experimentally evaluated and a test apparatus is designed and instrumented to measure the reaction shear loads at the panel attachment bolts and the transverse deflection of the plate. The results demonstrate the importance of a nonlinear analysis for the design of this type of structure. A companion paper, describes the FE analysis procedure utilized to simulate the nonlinear behavior of the tested panels. The numerical results are validated against the experimental results.     

Mechanical and thermal post-buckling analysis of FGM rectangular plates with various supported boundaries resting on nonlinear elastic foundations

Mechanical and thermal post-buckling analysis is presented for FGM rectangular plates resting on nonlinear elastic foundations using the concept of physical neutral surface and high-order shear deformation theory, and investigations on post-buckling behavior of FGM rectangular plates with two opposite simply supported edges and other two opposite clamped edges are also new. Approximate solutions of FGM rectangular plates are given out using multi-term Ritz method, and influences played by different supported boundaries, foundation stiffnesses, thermal environmental conditions and volume fraction index are discussed in detail. It is worth noting that the effect of nonlinear elastic foundation is small at the pre-buckling and initial post-buckling state and is significant with increasing deflection at the deep post-buckling state. Especially, comparisons of post-buckling for FGM rectangular plates resting on nonlinear elastic foundations with movable simply supported edge subjected to compression acting on the geometric middle surface and the physical neutral surface are innovative, and may be helpful to clarify typical mistakes in literature.     

弹性地基矩形薄板弯曲问题的新解析法

目前弹性地基矩形薄板弯曲问题的解析解法,一般采用相应齐次微分方程解加特解的方式选定位移函数,本文采用了新的方法选择位移函数,将其应用范围推广到了非均匀弹性地基矩形薄板弯曲问题.以四边固定正方形薄板为例进行了计算.其理论简单,计算容易,并适合于实际工程.