脱层梁-板的后屈曲分析

研究了含任意位置脱层的梁-板的后屈曲问题,采用小参数摄动法,导出了系统的一阶和二阶控制方程,边界条件,连续条件,平衡条件及相容条件,在算例中给出了梁-板的后屈曲响应曲线,且与有关文献进行了比较。     

长持时爆炸冲击波荷载作用下梁板组合结构的动力响应

为研究钢筋混凝土梁板组合结构在长持时远爆冲击波荷载作用下的动力响应及毁伤形态,通过实验获得了梁板组合结构的破坏形态和背爆面中心点位移变化。利用有限元软件对钢筋混凝土梁板组合结构的动态响应过程进行数值模拟研究,模拟得到的结构破坏现象与实验吻合较好。在此基础上,分析了梁板组合结构在相同冲量、不同峰值爆炸荷载作用下组合结构的动态响应和破坏过程,并结合挠跨比与破坏形态划分破坏模式。研究结果表明,相同冲量作用下,随着爆炸荷载峰值强度增加,梁板组合构件的破坏程度逐渐增加,破坏模式从弯曲破坏向弯剪联合破坏转换,最后呈现冲切破坏模式;组合构件中板部分发生破坏的时间早于交叉梁部分、破坏程度大于交叉梁。     

杂交梁界面剪应力的理论分析和数值模拟

采用解析和数值方法研究FRP-混凝土杂交梁的界面应力问题。提出了杂交梁的新的力学模型和假设,克服了以往的分析模型中界面应力表达式非常复杂和界面应力的解析解与数值解相差较大的缺点,本文得到的FRP板加固梁的界面剪应力表达式与数值结果符合很好,并且具有简捷的表达式。利用有限元法研究了杂交梁各物理参数对界面剪应力的影响。研究表明,界面剪应力在FRP板的端部存在应力集中或应力奇性,这是造成杂交梁界面破坏的主要原因。这项研究对进行杂交结构的工程设计具有理论指导和参考价值。     

锅炉炉墙板梁结构随机响应的边界元方法

锅炉炉墙可简化成板，梁的组合结构，在燃烧脉动的激励下会形成随机性的振动。本文提出了一种借助于边界元方法进行随机激励作用下正交各向异性板，梁组合结构动力响应计算的一般方法。文中首先导出各向异性板，梁结构动力问题的边界积分方程，进而得到用于随机响应计算的板，梁结构的频率响应函数矩阵。在此基础上可以求出板，梁结构上任意点响应的均方值。这一方法的有效性在文中电站锅炉实际算例中得到了验证。     

梁板壳的几何大变形--从近似的非线性理论到有限变形理论

对梁板壳的线性理论、近似几何非线性理论与有限变形理论作了比较,介绍了有限转动理论,指出了应用有限变形理论求解梁板壳的大变形问题的高效率、高精度的巨大优越性。     

基于广义变分原理的梁板单元分析的数值流形方法

数值流形方法(NMM)是一种基于有限覆盖技术的新型数值方法.以该方法的覆盖位移模式为基础,利用广义变分原理中罚函数理论,详细推导了梁板流形单元的覆盖位移函数,刚度矩阵和应变矩阵,并建立了可应用于梁板单元分析的数值流形方法.最后通过算例分析表明,该方法在对梁板弯曲问题分析是有效的.     

强冲击载荷下单向加筋板拉伸撕裂的临界条件

针对固支单向加筋板在冲击载荷下的拉伸撕裂临界条件开展研究,首先将均布冲击载荷下的固支单向加筋板简化为带板梁模型,基于固支梁冲击变形理论解给出了加筋板最大永久变形理论解,之后基于复合运动场模型,修正了固支梁端点拉伸应变与最大永久变形关系式,并以等效应变达到失效应变作为拉伸撕裂条件,建立了加筋板在冲击载荷下的拉伸撕裂临界条件。经过数值模拟验证,该最大永久变形理论解和拉伸撕裂临界条件具有适用性,理论与数值误差小于15%。     

曲法线(面)假设下的板(梁)理论

本文分别从曲法面假设和曲法线假设出发,导出了与Timoshenko梁理论和Reissner板理论类似的平衡方程。考虑了切向载荷的作用,并且给出了相应的简化方案。本文理论所得到的梁、板内应力,在一定的条件下即为弹性理论平面问题或者空间问题的精确解答。在一般情况下,本文给出的修正的应力表达式,可以使精度大大提高。     

考虑尺寸效应板梁的磁弹性屈曲

研究表明,有限尺寸效应是影响板——梁磁弹性稳定性分析精度的主要原因。本文用边界元法分析了板边沿的磁感强度集中,然后用里兹法计算了软铁磁材料悬臂板——梁的临界屈曲磁场。通过和Moon-Pao的理论和实验结果以及Miga的有限元结果比较,表明本方法具有良好的精度,且计算方法简便。     

复杂外形薄浮板谐耦振问题的边界元—有限元混合解

1、引言由于浮板在海洋工程中的重要作用,近年来国内、外不少学者对它的动力分析进行了广泛的研究.1972年,Y. K. Wen和M. Shinozuka首先研究了矩形浮板和海水的相互作用问题,不过用的是简单的一维梁模型;1974年,Y. K. Wen又进一步用二维板理论研究了同一问题;1981年,Y. Tanaka用解析法计算了圆浮板的自由振动;最近作者针对局部变水深环境下浮板的谐耦振,又提出了一个变分解,虽然对板的外形没有多大限制,但解的精度在很大程度上依赖于振型形函数的选择。     

Some results of testing simple structures under constant and variable loading during creep

The design of two rigs for room-temperature creep testing is described. One is for testing beams in pure bending and the other for testing circular plates simply supported at the outer edge and loaded through a rigid central boss. A system for giving reproducible step-loading cycles is also described. Typical creep-deformation curves for commercially pure aluminum beams and plates under steady and variable loading are given. These test results are compared with predictions based on the tensile-creep behavior. The repeatability and accuracy of these results are also discussed.     

The large deflection problem of circular thin plate with variable thickness under uniformly distributed loads

In this paper, to begin with, the large deflection equation of variable thickness circular plates is given. By using small parameter method and revised iteration jointly a cubic approximate solution is obtained. A characteristic is also given for comparison with linear theory.     

THE LARGE DEFLECTION PROBLEM OP CIRCULAR THIN PLATE WITH VARIABLE THICKNESS UNDER UNIFORMLY DISTRIBUTED LOADS

In this paper,to begin with,the large deflection equation of variable thickness circular plates is given. By using small parameter method and revised iteration jointly a cubic approximate solution is obtained. A characteristic is also given for comparison with linear theory.     

Winkler地基上变厚度圆板的轴对称弯曲

本文提出了Winkler地基上变厚度圆板轴对称弯曲的传递矩阵算法。首先，根据贝塞尔函数理论获得了等厚度圆板和环板单元在任意荷载作用下轴对称弯曲的解析解，这些解均由通解和特解两部分组成。基于这些解析解，导出了等厚度圆板和环板单元的传递矩阵。然后沿径向将变厚度圆板划分成一个等厚度圆板单元和一系列等厚度环板单元，应用传递矩阵算法原理获得了变厚度圆板的整体传递矩阵。引入圆板的边界条件，给出了该板每条节线上的挠度、径向转角、径向弯矩和径向剪力。最后，讨论了受均布荷载作用的简支线性变厚度圆板的弯曲，将本文数值解与解析解进行比较，证实了本文方法的有效性，并简要地讨论了地基参数对板挠度和径向弯矩的影响。     

Semi-analytical buckling analysis of heterogeneous variable thickness viscoelastic circular plates on elastic foundations

Buckling analysis of the functionally graded viscoelastic circular plates has not been carried out so far. In the present paper, a series solution is developed for buckling analysis of radially graded FG viscoelastic circular plates with variable thickness resting on two-parameter elastic foundations, based on Mindlin's plate theory. The complex modulus approach in combination with the elastic-viscoelastic correspondence principle is employed to obtain the solution for various edge conditions. A comprehensive sensitivity analysis is carried out to evaluate effects of various parameters on the buckling load. Results reveal that the viscoelastic behavior of the materials may postpone the buckling occurrence and the stiffness reduction due to the section variations may be compensated by the graded material properties.     

Semi-analytical buckling analysis of heterogeneous variable thickness viscoelastic circular plates on elastic foundations

Buckling analysis of the functionally graded viscoelastic circular plates has not been carried out so far. In the present paper, a series solution is developed for buckling analysis of radially graded FG viscoelastic circular plates with variable thickness resting on two-parameter elastic foundations, based on Mindlin's plate theory. The complex modulus approach in combination with the elastic–viscoelastic correspondence principle is employed to obtain the solution for various edge conditions. A comprehensive sensitivity analysis is carried out to evaluate effects of various parameters on the buckling load. Results reveal that the viscoelastic behavior of the materials may postpone the buckling occurrence and the stiffness reduction due to the section variations may be compensated by the graded material properties.     

Finite expansion of a hole in an elastic-plastic thin plate of finite thickness

A finite deformation theory for axially symmetric thin elastic-plastic plates is obtained by a consistent approximation from the corresponding three-dimensional theory. This theory can be applied to plates of finite thickness, and is different from the usual plane stress theory. The problem of the expansion of a circular hole in an infinite plate is investigated and the effect of the transversely variable stress components is studied.     

Large deflection problem of circular plates with variable thickness under the action of combined loads

By using the modified iteration method of large deflection theory of plates with variable thickness^[1], we solve the problem of circular plates with variable thickness subjected to combined loads under the boundary conditions of the clamped edges and get comparatively more accurate second-order approximate analytical solution. If the results of this paper are degraded into the special cases, the results coinciding with those of papers [1, 2] can be obtained. In this paper, the characteristic curves are plotted and some comparisons are made. The results of this paper are satisfactory.     

Exact solutions for axisymmetric flexural free vibrations of inhomogeneous circular Mindlin plates with variable thickness

Circular plates with radially varying thickness, stiffness, and density are widely used for the structural optimization in engineering. The axisymmetric flexural free vibration of such plates, governed by coupled differential equations with variable coefficients by use of the Mindlin plate theory, is very difficult to be studied analytically.In this paper, a novel analytical method is proposed to reduce such governing equations for circular plates to a pair of uncoupled and easily solvable differential equations of the Sturm-Liouville type. There are two important parameters in the reduced equations.One describes the radial variations of the translational inertia and flexural rigidity with the consideration of the effect of Poisson's ratio. The other reflects the comprehensive effect of the rotatory inertia and shear deformation. The Heun-type equations, recently well-known in physics, are introduced here to solve the flexural free vibration of circular plates analytically, and two basic differential formulae for the local Heun-type functions are discovered for the first time, which will be of great value in enriching the theory of Heun-type differential equations.     

轴对称自由振动功能梯度材料微圆板中的热弹性阻尼

基于经典弹性薄板理论和单向耦合热传导理论,研究了材料性质沿厚度连续变化的功能梯度微圆板的热弹性阻尼特性．首先,考虑热力耦合效应,建立了功能梯度微圆板轴对称横向自由振动微分方程．然后,忽略温度梯度在面内的变化,建立了单向耦合变系数一维热传导方程．采用分层均匀化近似方法,将变系数热传导方程转化为一系列常系数的微分方程,利用上下表面的热边界条件和层间连续性条件获得了微圆板温度场解析解．将所得温度场代入微圆板的自由振动微分方程,得到了包含热弹性阻尼的复频率,从而获得了反映热弹性阻尼水平的逆品质因子．最后,针对材料性质沿板厚按幂函数变化的陶瓷-金属功能梯度微圆板,定量地分析材料梯度指数、几何尺寸、边界条件、温度环境等对微圆板热弹性阻尼的影响．