爆炸载荷作用下单向加筋方板的大挠度塑性动力响应分析

从分别列出加筋板面板以及加强筋的运动方程出发,详细分析了爆炸载荷作用下单向加筋固支方板的大挠度塑性动力响应.分析表明:取决于加强筋的相对刚度以及载荷峰值的大小,加筋板的运动将呈现三种不同的模式.限于讨论加筋板的总体变形模式.首先讨论了同时计及弯矩和面力(轴力)作用的解析解,在此基础上进一步讨论了忽略弯矩影响的薄膜解以及能量解.理论结果与已有的试验结果在多数情况下符合良好,表明提出的简化理论分析方法能对爆炸载荷下单向加筋固支方板的永久变形做出较为合理的预报.     

爆炸载荷作用下双向加筋方板的大挠度塑性动力响应

从分别列出加筋板面板以及加强筋的运动方程出发,分析了爆炸载荷作用下双向加筋固支方板的大挠度塑性动力响应。分析表明:取决于加强筋的相对刚度以及爆炸载荷峰值的大小,加筋板的运动将呈现3种不同的模式。该文限于讨论加筋板的总体变形模式,具体讨论了十字加筋以及双十字加筋固支方板在忽略弯矩影响下的薄膜解法。理论结果与已有的试验结果在多数情况下符合良好,表明该文提出的简化理论分析方法能对爆炸载荷下双向加筋方板的永久变形做出较为合理的预报。     

水面上弹性浮板在外载荷作用下的动力学特性研究

基于线性水波理论和Mindlin厚板动力学理论,采用Wiener-Hopf方法,研究了水面上浮动弹性平板局部受动载荷(周期分布载荷)作用下的动力学特性。首先将分析计算结果与采用其他方法得到的计算结果进行了对比和分析;其次,采用本文方法研究了三种周期载荷激励下浮板上挠度和动弯矩幅值的分布情况;最后,对浮板挠度幅值分布与不同周期载荷的中心位置及其分布宽度的关系进行了研究。     

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。     

冲击载荷下(纤维/聚合物)-金属层合板的大挠度动力响应

对冲击载荷下固支（纤维/聚合物）-金属层合方板和圆板的大挠度动力响应进行了理论研究。基于理想刚塑性假定和塑性极限屈服条件,建立了质量块体和爆炸冲击载荷下（纤维/聚合物）-金属层合板大挠度动力响应的理论模型,给出了固支（纤维/聚合物）-金属层合方板和圆板考虑弯曲和拉伸相互作用的大挠度响应解析解,进一步忽略弯曲的影响,得到了其动力响应的膜力解。研究结果表明,理论预测与已有实验结果吻合较好,该理论模型可以有效地预测质量块体和爆炸冲击载荷下（纤维/聚合物）-金属层合板的最大挠度。      

均匀热环境下四边固支矩形PCB薄板的自由振动

表面贴装形式中PCB板可简化为四边固支矩形薄板。基于刚性板的小挠度理论,推导了热载下四边固支矩形PCB薄板的自由振动微分方程。从微分方程中得出,热载下的PCB薄板等效于面内受均布张力的薄板,进而通过结构力学方法将热载下四边固支薄板振动问题转换为受面内均布张力固支薄板振动问题。利用虚位移理论,得出了温度沿厚度均匀线性变化的热载下四边固支矩形PCB薄板固有频率和自由振动的挠度值的计算方法。讨论了热载下温度、薄板的几何尺寸对矩形PCB薄板自由振动固有频率的影响。结论可为矩形PCB薄板在热载下的振动分析以及固有频率计算提供方法上的参考。     

矩形薄板弯曲问题的U变换-有限元法

该文扩展了U变换-有限元法分析弹性矩形薄板的范围。通过构造一个与简支、固支或二种边界条件组合的矩形板的等效系统,使刚度矩阵成为循环矩阵,采用U变换,成功解耦了有限元矩阵方程,使得有限元计算只须在一个单元上进行。给出了承受板中集中载荷和对边均布弯矩两种载荷形式下的板中挠度解析表达式。所得到的级数解不仅计算效率高,还能给出误差估计的显式表达式,能够直接掌控计算精度。算例中考察了几种不同边界条件下的计算结果,与已有理论结果的对比说明,该方法提高了计算的精度和效率。     

弹性浮板在周期集中载荷作用下的水弹性响应

基于线性水波理论和Mindlin厚板动力学理论,采用Wiener-Hopf方法,研究了水面上浮动弹性平板受周期集中载荷作用下的水弹性响应。流体被假设为不可压理想且等深,流动有势。首先分析求解了两种区域(自由水面下区域和浮板下区域)内等深流场的导波问题。而后将原来混合边值问题的求解归结为求解无穷线性代数方程组的问题。其次,采用该方法研究了三种周期集中载荷激励下浮板上挠度和动弯矩幅值的分布情况;最后,对浮板上挠度幅值分布与不同周期载荷的作用点的关系进行了研究。     

弯剪复合载荷作用下复合材料层合板屈曲的强度校核方法

基于复合材料各向异性板的大挠度方程，采用Ritz法和最小势能原理推导出了正交各向异性复合材料层合板在面内弯曲载荷作用下临界屈曲弯矩的解析解；给出了面内弯剪复合载荷作用下复合材料层合板屈曲的强度校核方法，并将本文方法所得结果与用有限元法（FEM）所得结果进行了比较。结果表明，本文方法与有限元方法相吻合，并且形式简洁，便于工程应用。     

分布载荷作用下简支功能梯度夹层板的弯曲分析

研究了四边简支具有功能梯度芯材的夹层板在分布载荷作用下的弯曲问题。基于Reissner假设, 根据功能梯度材料的本构方程得出了应力、位移及内力的表达式, 得到功能梯度夹层板的平衡方程; 针对四边简支的边界条件, 通过将挠度 w 与横向剪力 Q_x、Q_y 用双三角级数展开的方法, 求解平衡方程。采用本文方法分别求解了均布载荷作用下、芯材弹性模量线性变化的功能梯度夹层板与芯材为均质各向同性材料的夹层板的弯曲挠度, 并通过与经典解及有限元解进行比较, 证明了本文方法的正确性。     

Fourier solution to a thick cross-ply Levy type clamped plate problem

A hitherto unavailable Levy type analytical solution to the problem of deformation of a finite-dimensional general cross-ply thick rectangular plate, modeled using a higher order shear deformation theory (HSDT), is presented. A solution methodology, based on a boundary-discontinuous generalized double Fourier series approach is used to solve a system of five highly coupled linear partial differential equations, generated by the HSDT-based laminated plate analysis, with the C4-type clamped boundary condition prescribed on two opposite edges, while the remaining two edges are subjected to the SS3-type constraint. The numerical accuracy of the solution is ascertained by studying the convergence characteristics of deflections and moments of a square cross-ply plate. Hitherto unavailable important numerical results presented include sensitivity of the predicted response quantities of interest to lamination, lamina material property, and thickness-to-length ratio, as well as their interactions. Comparison with their SS2 counterparts demonstrates the effect of end clamping on the deflections and moments of thin to thick cross-ply plates.     

具有中间支承的矩形板自由振动分析

应用一般解析解来求解具有中间支承矩形板的自由振动问题。一般解析解能求解任意边界条件矩形板的振动问题,求解过程是将整块板看成是沿中间支承分开的两块板,沿支承边两块板的挠度均等于零,斜度和弯矩均相等,再由全部边界条件和连续性条件可以求解各阶频率和振型。对几种具有简支边,平夹边或自由边的混合边界矩形板进行了计算。     

A general solution for rectangular plate bending

A simple method is presented in which the displacement parameters related to the basic functions satisfying the boundary conditions along two opposite edges are substituted into the differential equation of plate bending. This results in an equation where the displacement parameters are all related. Based on a suitable transformation, an explicit expression for the determination of coefficients has been suggested which is a distinct departure from all the previous approaches where constants had to be evaluated from a set of simultaneous equations. A new treatment for catering the free edges of the plate where the characteristics beam function cannot be applied has been demonstrated. Examples have been presented for a variety of isotropic and orthotropic rectangular plates of different boundary conditions under various types of loadings for both coupled and uncoupled solutions. Though deflections obtained from both solutions indicated excellent accuracy, better agreement for moments were obtained for coupled solutions.     

An evaluation of the edge solution for a higher-order laminated plate theory

An analytical study was conducted to determine the edge effects upon a higher-order laminated plate theory due to Touratier (Int. J. Engng Sci., 29 (1991) 911-16). The problem considered is a sandwich plate simply supported along two opposite edges and clamped along its two others. The plate is loaded in statics by a pressure upon its top surface and the load is ‘sinusoidal-uniform’.

Results are presented for the transverse displacement and the stresses, using the theories of Kirchhoff-Love, Touratier and three-dimensional finite element computations. The results indicate clearly the importance of including transverse shear effects. Analytical calculations from the higher-order plate theory are in good agreement with three-dimensional finite element computations. Near to the clamped edges of the sandwich plate, a particular effect is shown upon the in-plane stresses, i.e. the Kirchhoff-Love theory.     

横向磁场中的功的互等定理

对于两个具有相同的材料、尺寸和形状,但可以具有不同的不变横向磁场作用,还可以具有不相同的静力边界条件和位移边界条件的金属模板进行了分析研究,并在这两个金属模板之间建立了功的互等定理。作为算例,应用该互等定理计算了在横向磁场中两对边简支和另两对边固定金属薄矩形板的固有频率。计算表明,该定理简便实用,适合于工程实际应用。     

Explicit local buckling analysis of rotationally-restrained orthotropic plates under uniform shear

The explicit closed-form local buckling solution of in-plane shear-loaded orthotropic plates with two opposite edges simply supported and other two opposite edges either both rotationally restrained or one rotationally restrained and the other free is presented. Based on the boundary condition of the other two opposite edges, two types of plates are considered: the RR (both the edges rotationally restrained) and RF (one edge restrained and the other free) plate elements. Different plate buckled shape functions are proposed, and the approximate explicit expressions for the buckling loads are derived using the Rayleigh–Ritz method for the plate with the generic rotationally-restrained (R) boundary conditions which can be reduced to two extreme cases, i.e., simply supported (S) and clamped (C). The accuracy of the derived explicit solutions is verified by comparing the predictions with the existing solutions and numerical finite element analysis, and excellent agreements are obtained. The effects of material and boundary restraining parameters on the local shear buckling behavior of the plate elements are discussed. The derived explicit formulas for the shear buckling loads are straightforward, efficient and reliable for preliminary engineering design and analysis of composite structures under primarily shear-dominant loading conditions.     

Experimental, numerical and analytical results for bending and buckling of rectangular orthotropic plates

Solid unstiffened, sandwich and hat-stiffened rectangular orthotropic fiber reinforced plastic (FRP) plates were tested for buckling by in-plane compression and for stresses and deflections under uniform out-of-plane pressure. The solid unstiffened and hat-stiffened plates were 154 × 77 cm (1 × w) (72 × 36 in), while the sandwich plates were 102 × 77 cm (1 × w) (48 × 36 in). Balsa core was used in the sandwich plates and in the hat-stiffeners. The two short edges of the unstiffened and sandwich plates were clamped, while the two long edges were simply supported. The two long edges of the hat-stiffened plates were free, while the short edges were clamped. The buckling load, as well as stresses and deflections from the tests, were then compared to those from finite element analysis (FEA) and analytic solutions. There was reasonably good agreement between FEA, analytic, and experimental buckling stresses for the unstiffened solid plates. There was reasonable agreement in buckling stresses between FEA and experimental results for the hat-stiffened plate. There was poor agreement between FEA, analytic, and experimental elastic buckling results for the sandwich plates because they failed in local buckling prior to global buckling. Under out-of-plane uniform pressure, FEA and analytic solutions of the stresses and deflections for the unstiffened solid plates agreed well with experimental results. There was poor agreement between FEA and experimental results for stresses and deflections of the hat-stiffened or sandwich plates. Experimental error could be traced, in part,to plate fabrication, the method of applying out-of-plane pressure, edge support, and instrumentation accuracy.     

Nonlinear oscillation of unsymmetric angle-ply plate on elastic foundation having nonuniform edge supports

This paper is analytically concerned with nonlinear flexural oscillation of an unsymmetrically laminated angle-ply rectangular plate resting on a Pasternak-type elastic foundation. The plate edges are subjected to the varying rotational constraints. Based on dynamic von Kármán-type nonlinear plate theory a single-mode analysis is carried out. In the formulation of a solution the force function and bending moments along the four edges are expanded into generalized Fourier series. These moments are also replaced by an equivalent lateral pressure near these edges. Galerkin's procedure and the perturbation technique are applied to the equation of motion and the time equation respectively. Numerical results for the amplitude-frequency response of the plate are presented graphically for various high-modulus composite materials, geometries of lamination, aspect ratios, moduli of elastic foundation and boundary conditions. Present results are compared with the existing values.     

均布载荷作用斜边自由的三角形板弯曲

本文应用功的互等定理研究了在均布载荷作用下斜边自由两边固定的三角形板弯曲问题，给出了该问题的精确切。