复变形式的各向异性板弯曲问题的基本解

提出了求解各向异性板弯曲问题基本解的新方法。得到的基本解简捷明了，相应的法向弯矩和相当剪力的表达式易求，故便于应用在一般边界条件的各向异性板弯曲问题的边界积分方程。     

Reissner板弯曲的复变函数分析方法

本文建立了Reissner板弯曲问题的复变函数分析方法,它可以有效地用于分析含一般孔洞板弯曲的应力集中问题。作为应用,文中还给出了一些计算实例。     

R-函数理论及准Green函数方法在正交各向异性板振动问题中的应用

首次将R-函数理论及准Green函数方法应用于求解固支正交各向异性薄板的自由振动问题。首先引入参数变换,将正交各向异性薄板的自由振动微分方程转化为双调和算子的边值问题,并应用R-函数理论,以解析函数形式描述复杂边界形状;利用问题的基本解和边界方程构造了一个准Green函数,该函数满足了问题的齐次边界条件;通过R-函数理论构造适当的边界方程,消除了积分方程核的奇异性;再采用Green公式将其化为第二类Fredholm积分方程。数值算例表明:该方法减少了理论计算量,精度较高。本文还证明了其优越性和正确性,是一种新型的数学方法。     

含孔扁薄球壳的复变函数解法

本文建立了含孔扁薄球壳的复变函数求解方法,从而为这一类问题的求解提供了一条有效而规范的途径.     

夹层板的复变边界元解法

本文用全纯函数表示微分方程△f(x,y)-λ(~2)f(x,y)=0的一般解,粮据全纯函数的Bekya积分表示法,建立了复数域内的边界积分方程并针对各种边界条件下Reissner型夹层板、Hoff型夹层板进行了数值求解。     

正交各向异性板的粘接接头应力分析

1.接头端部的荷载考虑一个正交各向异性板单肢搭接粘接接头(图1).取单位宽度并承受外力T的作用.可写出     

正交各向异性圆板大挠度问题的一种解法

本文基于Berger方法研究了正交各向异性圆板的大挠度问题。在所讨论问题的总势能泛函中引入中面应变不变量并应用欧拉变分方程,导得了非耦联的控制方程。最后由加权积分法给出均布载荷作用下周边固定和周边不动简支圆板的解析数值结果。     

弹性力学问题复变函数解法的应用与发展

对利用复变函数法求解弹性力学问题在过去100年中的发展进行了简要综述,介绍了自1909年Kolosov提出复应力函数法以来的弹性力学复变函数解法相关的几本具有影响的经典专著或教科书、复变函数方法在弹性问题壳体和空间问题的拓展,以及近些年来在解决更多力学问题上的新发展和新应用等.     

非均匀圆柱型正交各向异性圆板的弯曲

研究了非均匀圆柱型正交各向异性圆板在均布横向载荷作用下的弯曲问题，求得了折算刚度随半径按指数规律变化的非均匀圆柱型正交各向异性圆板弯曲问题的渐近解，给出了周边固支和简支条件下的渐近解．通过算例可以看出，这种非均匀性对圆板中心挠度的影响是显著的     

带有椭圆孔的各向异性无限板应力集中问题的简便解法

应用各向异性无限域椭圆孔问题的复应力函数基本解,给出了椭圆孔在任意外载作用下以积分形式表示的复应力函数解;并分别通过对椭圆孔周边均匀受载,无限远处均匀受载和承载螺栓孔这三个特例的分析结果,证实了本文解的正确性,一般性和实用性.     

各向异性平板开孔动应力集中问题的研究

采用各向异性平板弯曲波动理论及摄动方法，对正交各向异性平板开孔弯曲波的散射及动应力集中问题进行了分析研究，得到了此种平板稳态弯曲波动问题的渐近形式的分析解。同时采用保角映射技术，为求解正交各向异性平板开孔弹性波的散射及动应力集中问题提供了一种统一规范的方法。     

A Higher Order Asymptotic Analysis for Orthotropic Plates in Stress Edge Conditions

A higher order asymptotic analysis for orthotropic plates is presented with the leading order interior solution reduced to the well-known Kirchhoff plate theory. The boundary-layer solutions are decoupled into the plane strain and torsional deformations of a boundary-layer plane strip, which is analyzed by the Laplace transform method to formulate Saint-Venant’s principle in plate studies. The necessary and sufficient conditions for stress edge-data generating exponentially decaying solutions are established to derive the stress edge conditions for the higher order plate theory. Mathematics Subject Classifications (2000) 74K20, 74B05, 74G10, 74G50.     

Stress Concentration in an Orthotropic Plate with a Circular Hole under Dynamic Loading

The paper sets forth a photoelastic method for the determination of the dynamic stress concentration factor near a hole in an orthotropic plate. The stress distribution at the periphery of a circular hole is analyzed. The stress concentration factors for orthotropic and isotropic plates under dynamic and statical loading are compared     

On the Plane Orthotropic Stress Problem of Quasi-Static Thermoelasticity

The plane stress boundary value problem of quasi-static linear orthotropic thermoelasticity is discussed. The thermoelastic system on a bounded simply-connected domain is decoupled. The decoupled temperature equation is investigated by using accurate estimation and the contraction mapping principle. Representations of solutions of the field equation are obtained, and some solvability results are proved. The results are of both theoretical and numerical interest.     

二维小接触问题的焦散线分析

本文是以一组聚碳酸脂园盘试件,用焦散线法对小接触问题所进行的一系列实验分析,其中包括一个滚柱轴承的模拟分析,定量地得到了接触面宽度和面上的应力。对小接触奇异应力场给出可靠的定量结果,这是其他实验力学手段目前难以解决的。此外,本文的实验分析结果也与理论计算相当一致。     

Approximate Solution of an Axisymmetric Contact Problem with Allowance for Tangential Displacements on the Contact Surface

A structurally nonlinear contact problem of a punch shaped like a paraboloid of revolution is studied. An equation for the contactpressure density is derived with allowance for the radial tangential displacements of the boundary points of an elastic halfspace. A method for constructing a closedform approximate solution is proposed. The effect of the tangential displacements on the main contact parameters is discussed.     

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.     

薄板稳定问题的边界元法

本文基于小挠度薄板弯曲问题的基本解,建立了求解薄板稳定问题的边界积分方程,并计算了若干算例,结果表明用边界元法求解薄板的稳定问题是行之有效的.     

Contact Problem for a Rectangular Punch on the Porous Elastic Half-Space

The paper is concerned with a contact problem about rigid rectangular punch forced into a half-space made of a linear elastic isotropic material with voids. We use a Cowin–Nunziato model for the half-space, and reduce the problem to a double Fredholm integral equation of the first kind. Then we apply two different approaches, to solve this equation. The first one is based on a direct collocation numerical technique. The second method is asymptotic, and we use a small parameter that is the relative width of the punch. Finally, compliance of the punch is determined, and results of the two different methods are compared with each other, as well as with a Sivashinsky–Panek–Kalker solution. Mathematics Subject Classifications (2000) 74M15.     

无单元法求解任意边界条件下的中厚板弯曲问题

本文用无单元法进行不同边界条件下的中厚板弯曲问题的求解,提出了构造其近似位移函数的三种形式的权函数,从变分原理出发导出了Mindlin-Reissner中厚板弯曲问题的控制方程,并编制了相应的计算程序。数值算例表明,无单元法用于中厚板弯曲问题是合理可行的,其结果具有相当高的精度。