中厚板弯曲问题的拟薄板边界元分析

本文从简化的Reissner理论出发,利用叠加原理和功的互等定理导出了中厚板弯曲问题的一组基本解,然后,导出了类似于求解薄板经典理论的边界积分方程组。本文提出的方法适用于任意边界、任意荷载的薄板、中厚板的弯曲问题,使求解中厚板弯曲问题的工作量减小到与求解薄板的工作量相同。文中计算了若干例题,结果是令人满意的。     

弹性半空间地基上正交异性矩形板弯曲通解

本文先对受任意边界约束的正交各向异性矩形薄板,在各种形式荷载作用下的弯曲问题,构造了四次逐项可导的带有补充项的双重正弦傅里叶级数新通解.该解析解既不需要叠加,对不同的物性参数又不需要分类,而且待定系数少又具有明确的物理含义,这使得正交各向异性矩形薄板的弯曲问题求解统一化、简单化、规律化.然后将新通解与弹性半空间受任意竖向荷载作用下的静力位移积分变换解相结合,得出弹性半空间地基上受任意边界约束的正交各向异性矩形板,在任意竖向荷载作用下的弯曲解析解.本文还给出了算例分析,其结果与文献吻合良好,证明本文的方法是切实可行的.     

四边任意支承条件下弹性矩形薄板弯曲问题的解析解

利用辛几何法推导出了四边为任意支承条件下矩形薄板弯曲的解析解。在分析过程中首先把矩形薄板弯曲问题表示成Hamilton正则方程，然后利用辛几何方法对全状态相变量进行分离变量，求出其本征值后，再按本征函数展开的方法求出四边为任意支承条件下矩形薄板弯曲的解析解。由于在求解过程中并不需要人为的事先选取挠度函数，而是从弹性矩形薄板弯曲的基本方程出发，直接利用数学的方法求出问题的解析解，使得这类问题的求解更加理论化和合理化。文中的最后还给出了计算实例来验证本文方法的正确性。     

关于由环板解到圆板解过渡问题的一点注记

考虑均布荷载作用下圆薄板弯曲问题的一个简单例子(图1)容易得到图1(a)圆板的初参数解     

简支可动矩形薄板大挠度弯曲问题的变率配点解

本文采用变率配点法，分析了均布荷载作用下矩形薄板的大挠度弯曲问题．算例表明了此方法的有效性     

轴对称圆薄板大挠度微分方程的数值分析方法

根据轴对称问题的特点,利用级数展开和求极限法则,证明了轴对称大挠度圆薄板在圆心处应满足的边界条件,并以圆薄板轴对称大挠度弯曲变形微分方程为基础,建立了圆心处非奇异的轴对称大挠度圆板弯曲微分方程,从而可以方便地利用现有的常微分方程数值求解方法(如变步长龙格-库塔法)对实心圆板的轴对称问题进行数值求解,又不必像摄动法那样推导复杂的公式。在数值求解轴对称圆板大挠度弯曲变形微分方程时,将非线性微分方程的求解主要归结为迭代求解圆心处三个未知边界条件的问题,即圆心处的径向膜力、圆心处的挠度、圆心处挠度的二阶导数,并提出了相应的求解方法。实例中,对于圆薄板受均布横向荷载的问题,分析了周边固支边界条件下的非线性弯曲问题,给出了中心挠度参数大范围变化时的荷载和部分边界值变化曲线,并与经典摄动解进行了对比。对比结果可见,本文方法和摄动法的解非常接近,在量纲归一化中心挠度不超过4.0时,两种方法解的相对误差均小于5.0%。另外,本文还分析了与挠度有关的液体压力作用下和集中荷载作用下周边固支圆板的非线性弯曲问题。通过算例可见:本文方法可以灵活处理不同的荷载问题;对于不同的问题,计算过程相似,不必推导复杂的计算公式,计算精度容易控制。     

Reissner矩形板的弯曲问题

本文根据Rcissncr平板理论,提出了矩形中厚板弯曲问题的解答,应用本文中的(5)、(9)式,可求解通常边界条件下,承受横向均布力q_0以及承受横向均布力和板边法向弯矩等组合荷载共同作用下的矩形中厚板的弯曲问题,而且使这类问题的解答规律化。     

用广义阶梯函数简化计算简支圆板在复杂荷载作用下的极…

本文将广义阶梯函数应用于薄板的塑性极限分析问题，用以简化计算简支圆板在复杂荷载作用下的极限荷载。文中针对简支圆板在任意局部均布荷载和线性分布荷载共同作用下的塑性极限分析问题，并考虑荷载的五种不同的分布形式，给出相应的极限荷载的计算公式。     

用广义阶梯函数简化计算简支圆板在复杂荷载作用下的极限荷载

本文将广义阶梯函数应用于薄板的塑性极限分析问题，用以简化计算简支圆板在复杂荷载作用下的极限荷载。文中针对简支圆板在任意局部均布荷载和线性分布荷载共同作用下的塑性极限分析问题，并考虑荷载的五种不同的分布形式，给出相应的极限荷载的计算公式。     

关于由环板解到圆板解过渡问题的一点注记

<正> 考虑均布荷载作用下圆薄板弯曲问题的一个简单例子(图1)容易得到图1(a)圆板的初参数解     

用“膜力因子法”分析简支刚塑性圆板的大挠度动力响应

在板的变形过程中,当其挠度与厚度同量级时,膜力的作用与弯矩的作用同样重要;当其挠度超过厚度甚至接近板的面内尺寸的量级时,相对于弯矩的作用,膜力的作用是更主要的。本文发展了一种基于能量平衡的简便的“膜力因子法”,有效地解决了当板的挠度达到厚度量级时弯矩和膜力联合作用问题;用这种方法并结合塑性膜阶段的分析成功地求解了简支刚塑性圆板在冲击载荷作用下的大挠度塑性响应问题。所得结果与Florence实验结果符合良好,比已有理论近似结果有所改进。     

Use of a curved grating in shadow moiré

The shadow-moiré method has been extended to study the large displacements of a uniformly loaded hyperbolic-paraboloid shell. The new technique employs a curved grating which is everywhere equidistant from the initial position of the surface, as in the application of a plane grating in the study of plates. The theory of the curved grating is developed. Experimental verification is reported and a significant increase in accuracy over the equivalent plane grating is observed. The proposed improvement can be applied to the study of any ruled surface.     

The perturbation parameter in the problem of large deflection of clamped circular plates

In the problems of large deflection of clamped circular plates under uniformly distributed loads, various perturbation parameters relating to load, deflection, slope of deflection, membrane force, etc, are studied. For a general perturbation parameter, the variational principle is used for the solution of such a problem. The applicable range of these perturbation parameters are studied in detail. In the case of uniformly loaded plate, perturbation parameter relating to central deflection seems to be the best among all others. The method of determination of perturbation solution by means of variational principle can be used to treat a variety of problems, including the large deflection problems under combine loads. This paper is completed under the guidance of Prof. Chien Wei-zang.     

Analysis of cantilever plates by the line-solution technique

Summary The application of the line-solution technique to the analysis of uniformly loaded cantilever plates is described in this paper. In this method, the two-dimensional partial differential equation of plate theory is reduced to a set of ordinary linear differential equations by replacing the derivatives in one direction by their finite-difference equivalents. The resulting equations are solved numerically by the matrix-progression technique.Three different approaches are suggested for the elimination of the corner forces which arise as a result of using Kirchhoff's boundary conditions. Numerical results are presented and compared with those of previous theoretical and experimental investigations.     

Moiré patterns of slope contours in flexed plates

A simple method is described for the measurement of partial slopes in flexed plates. The interference of the resultant distorted reflection of a referenceline grating, projected by means of a collimated monochromatic light on the polished surface of a flexed plate, with an identical grating yields a moiré pattern of the partial-slope contours of the plate. The method can be applied to determine the moment and strain distribution of any type and shape of plate loaded to any loading mode. As an illustration, the method has been applied to determine the partial-slope distribution in laterally loaded square plates either supported at their corners or simply supported. Comparison of the results with existing numerical solutions shows the accuracy of the method.     

SPH粒子初始化均布方法及其均布质量评价

光滑粒子流体动力学(SPH)是一种拉格朗日型无网格粒子法，粒子均布程度是影响SPH分析精度和稳定 性的重要因素．本文基于射线法提出了一种在异形多边形区域内均布SPH粒子的方法，先在多边形的最小外包 矩形范围内均布粒子，再通过射线法和辅助筛选条件保留区域内的粒子；通过生成粒子的Voronoi多边形计算 其变异系数值(Cv)，作为SPH粒子均布质量的评价标准，其值越小，粒子均布质量越高．为验证该方法提高分 析精度的有效性，基于爆轰侵彻的经典实验，建立由经典三角形和四边形均布粒子法构建的模型甲、模型乙和 本文模型丙，用 LS-DYNA 中的 SPH 模块进行仿真分析．研究表明，模型丙的 Cv 分别比模型甲和模型乙低 4.88 %和5.22 %；模型甲、乙和丙射流头部速度分别为5 960、5 900和6 060 m/s，较经典实验的6 100 m/s分别 相差2.3 %、3.3 %和0.7 %，相对于模型甲和模型乙，模型丙计算精度提高了1.6 %和2.6 %．因此，本文方法可 快速有效地均匀布置SPH粒子，提高分析精度     

Bending of uniformly cantilever rectangular plates

An exact solution is given for the bending of uniformly loaded rectangular cantilever plates by using the idea of generalized simply supported edge together with the method of superposition. As illustrative examples, a square plate and a rectangular plate with the ratio of the clamped edge to the neighbouring free edge equal to two are solved numerically. The results are compared with those obtained from approximate methods to confirm the validity of the method presented.     

De-wrinkling of pre-tensioned membranes

Thin membranes are used in the spacecraft industry as extremely lightweight structural components. They need to be stiffened, usually by applying discrete forces, and this increases their susceptibility to wrinkling in regions where high tensile stresses develop. We consider a regular polygonal membrane uniformly loaded at its corners by equal forces and we prevent wrinkle formation by trimming the edges of the polygon into very gentle curves. We confirm this performance through simple physical experiments using Kapton, a typical membrane material and, using computational analysis, we show how the distribution of compressive stresses, responsible for causing wrinkles, dissipates following trimming. Finally, we accurately predict the required level of trimming for any number of sides of polygon using a simple, linear model, which invokes a plate-bending analogy.     

General analytic solution for elastic bending of reissner plates

I.GeneralAnalyticSolutionforThickRectangularPlates1.1BasicequationsandboundaryconditionsTheoryofthewidelyusedReissuerplatesisquiteaccurateforengineeringcomputationand,asisshowninFig.l,ithasthefollowingassumDtionsfa)AthickrectangularplatewithmaterialpropertiesofelasticmodulusE,Poisson'sratiop,shearmodulusGanddimensionsofainlength,binw.idth.hinheightisconsiderd.anditsstrainsandstressescanbedescribledinthedeflectionofthemid-planeWandrotationsaroundx-axisandJ.-axisAandac,respectively.b)Thepl…     

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.