Nonlinear vibration of laminated plates on an elastic foundation

This paper studies the effects of initial stresses on the nonlinear vibrations of laminated plates on elastic foundations. The nonlinear partial differential equations based on Mindlin plate theory are derived for the nonlinear vibration of laminated plates in a general state of nonuniform initial stress. Both rotary inertia and transverse stress are considered. Using the derived governing equations, the nonlinear vibration behavior of an initially stressed cross-ply plate on a Pasternak or Winkler elastic foundation is studied. The Galerkin's approximate method is applied to the governing partial differential equations to yield ordinary differential equations. The ordinary differential equations are solved by Runge–Kutta method to obtain the ratio of nonlinear frequency to linear frequency. The initial stress is taken to be a combination of a pure bending stress and an extensional stress in the plane of the plate. It is found that the foundation stiffness and initial stresses may result in a drastic change of the nonlinear vibration behavior. The frequency responses of nonlinear vibration are sensitive to the initial stress, vibration amplitude, modulus ratio and foundation stiffness. The effects of various parameters on the nonlinear vibration are discussed.     

一种改进的Pasternak地基模型及层合地基板的解析解

从三维弹性力学基本方程出发,建立了正交异性材料层合板的状态方程,并提出一种改进的Pasternak弹性地基模型,给出了四边简支层合地基板的解析解。此解满足层合板的基本方程和层间连续条件,适合任意厚跨比,计及了所有材料常数,考虑了基底切向接触应力的影响。算例讨论了地基参数对几种地基模型的影响。计算结果表明,随着地基刚度的增大,剪应力的影响是不可忽略的。     

Hybrid numerical tool for nonlinear analysis of piled rafts

This paper presents a hybrid numerical tool for nonlinear piled rafts analysis. The nonlinear pile behavior is represented by a hyperbolic function, which intends to simulate the variation in pile stiffness during loading. As the nonlinear behavior of piles is restricted to a very thin zone next to the pile interface, only the linear elastic effects are considered in the interaction factors between foundation elements. The influence of using Kirchhoff or Mindlin plate finite elements to model the raft is discussed. The code was compared to other well tested numerical tools, three model tests on piled raft foundation carried out at the Nagoya Institute of Technology (NIT) and also a well-known case of piled raft foundation (Hyde Park Cavalry Barracks in London). The code showed a very good agreement, proving its consistency and potential for use in piled raft analysis and design.     

均质弹性半空间地基上圆形薄板的非线性弯曲

本文讨论了均质弹性半空间地基上,承受中心集中荷载或均布荷载,周边自由的弹性薄圆板的非线性弯曲问题.文中首先建立了问题的确定积分方程,然后用加权残数法求解非线性的积分方程组.并给出数值算例。     

Stochastic analysis of laminated composite plate considering stochastic homogenization problem

This paper discusses a multiscale stochastic analysis of a laminated composite plate consisting of unidirectional fiber reinforced composite laminae. In particular, influence of a microscopic random variation of the elastic properties of component materials on mechanical properties of the laminated plate is investigated. Laminated composites are widely used in civil engineering, and therefore multiscale stochastic analysis of laminated composites should be performed for reliability evaluation of a composite civil structure. This study deals with the stochastic response of a laminated composite plate against the microscopic random variation in addition to a random variation of fiber orientation in each lamina, and stochastic properties of the mechanical responses of the laminated plate is investigated. Halpin-Tsai formula and the homogenization theory-based finite element analysis are employed for estimation of effective elastic properties of lamina, and the classical laminate theory is employed for analysis of a laminated plate. The Monte-Carlo simulation and the first-order second moment method with sensitivity analysis are employed for the stochastic analysis. From the numerical results, importance of the multiscale stochastic analysis for reliability evaluation of a laminated composite structure and applicability of the sensitivity-based approach are discussed.     

Thermal postbuckling of laminated composite skew plates with temperature-dependent properties

Thermal postbuckling and consequently, the role of temperature dependence of material properties on the thermal postbuckling behavior of laminated composite skew plates have not been addressed in literature. Hence, this problem is investigated here. The plate governing equations are based on the first-order shear deformation theory (FSDT) and the geometrical nonlinearity is modeled using Green’s strain tensor in conjunction with the von Karman assumptions. Since the problem is geometrically and physically nonlinear, the differential quadrature method (DQM) as an accurate, simple and computationally efficient numerical tool is adopted to discretize the governing equations and the related boundary conditions. Then, a direct iterative method is employed to obtain the critical temperature (bifurcation point) and consequently the nonlinear equilibrium path (the postbuckling behavior) of symmetrically laminated skew plates. After validating the formulation and the method of solution, the effects of temperature dependence of the material properties on the postbuckling characteristic of laminated skew plates with different skew angle, boundary conditions, length-to-thickness ratio, number of layers and ply layout are investigated.     

全加劲两侧开缝钢板剪力墙弹性屈曲研究

采用有限元方法对全加劲两侧开缝钢板剪力墙在面内水平荷载作用下的弹性屈曲临界荷载、屈曲模态进行了研究。对影响其弹性屈曲性能的参数进行了分析,包括两侧和中部加劲肋与墙板的刚度比、两侧和中部加劲肋宽厚比以及墙板高厚比和边长比。给出了全加劲两侧开缝钢板剪力墙加劲肋的弹性屈曲设计参考公式,为开缝钢板剪力墙的应用提供依据。     

组合基础隔震系统地震反应分析

对组合基础隔震系统中叠层橡胶支座和滑板摩擦隔震支座的恢复力特点进行了研究 ,提出并分析了叠层橡胶支座的粘弹性模型和滑板摩擦隔震支座的粘刚塑性模型 ;即叠层橡胶支座采用弹性恢复力模型和粘滞阻尼恢复力模型 ;滑板摩擦隔震支座采用双线性库仑摩擦阻尼恢复力模型和粘滞阻尼恢复力模型。用提出的分析模型对振动台试验隔震房屋进行了三维非线性动力时程分析 ,并将分析结果和振动台试验结果进行了比较。结果表明所提出的分析模型不仅能有效预测上部结构的地震反应 ,而且分析和试验所得的隔震支座滞回曲线相似。     

Geometric nonlinear analysis of thin plates by a refined nonlinear non-conforming triangular plate element

Based on the refined non-conforming element method for geometric nonlinear analysis, a refined nonlinear non-conforming triangular plate element is constructed using the Total Lagrangian (T.L.) and the Updated Lagrangian (U.L.) approach. The refined nonlinear non-conforming triangular plate element is based on the Allman’s triangular plane element with drilling degrees of freedom [1] and the refined non-conforming triangular plate element RT9 [2]. The element is used to analyze the geometric nonlinear behavior of plates and the numerical examples show that the refined non-conforming triangular plate element by the T.L. and U.L. approach can give satisfactory results. The computed results obtained from the T.L. and U.L. approach for the same numerical examples are somewhat different and the reasons for the difference of the computed results are given in detail in this paper.     

弹性地基上中厚板分析的数值流形方法

针对中厚板弯曲分析问题,根据数值流形方法的特点及位移模式,对求解中厚板流形单元的覆盖位移函数、应变矩阵及刚度矩阵进行详细推导,并在Winkler弹性地基上建立Mindlin板流形单元的控制方程。最后通过计算表明,该法在弹性地基上中厚板的弯曲分析中是有效的。     

Postbuckling analysis of cross-ply laminated cylindrical shell panels under parabolic mechanical edge loading

Postbuckling equilibrium paths of simply supported cross-ply laminated cylindrical shell panels subjected to non-uniform (parabolic) inplane loads are traced in this paper. Love's shell theory with higher order shear deformation theory and von Kármán nonlinear strain–displacement relations are used in the mathematical formulation of the problem. In the first step, the plate membrane problem is solved to evaluate the stress distribution within the prebuckling range as the applied inplane edge load is non-uniform. The governing shell panel postbuckling equations are derived from the principle of minimum total potential energy using the above stress distributions. Adopting multi-term Galerkin's approximation, the governing equations are reduced into a set of non-linear algebraic equations. Newton–Raphson method in conjunction with Riks approach is employed to plot the postbuckling paths through limit points. Numerical results are presented for symmetric (0/90/0) crossply laminated cylindrical shell panels under parabolic inplane load, lateral distributed load and initial imperfections. Limit loads and snap-through behavior of shell panels are studied.     

Nonlinear stability of unsymmetrically laminated angle-ply shear-deformable plates in biaxial compression

The generalized Karman–Reissner equations governing large deflection of unsymmetrically laminated angle-ply shear-deformable rectangular plates are presented in this paper, based upon Karman and Reissner plate theories. Much effort has been concentrated on derivation of the Karman–Reissner equations for the laminates taking account of transverse shear effects so that only two unknown functions for nonlinear analysis need to be treated to gain a precise insight into the complexities; otherwise high-order refined plate theories must be applied. An asymptotic series solution is constructed according to the Karman-type refined theory for postbuckling behavior of the plates with the boundary condition of four edges simply supported. Typical numerical examples are presented for comparison with other nonlinear analytical and experimental results. The effects of shear deformation, lamination angle and geometrical imperfection on buckling and postbuckling behaviors of the laminates subjected to a combination of biaxial compressive loadings are examined for industrial application.     

弹性地基板的非线性分析

本文以路面工程为应用背景,针对弹性地基上承受横向载荷的板体进行了非线性有限元分析,采用考虑横向剪切变形的中厚板非协调单元模式,改进了数值性能,避免由于局部小面积受载时,剪切变形较大带来的误差,同时将地基刚度矩阵引入失衡力迭代格式中,保证解的收敛性.文中给出了载荷位于板中、板边、板角时的板体变形情况和破坏状况以及极限承载能力,并与塑性铰线理论、弹性薄板理论进行了比较和分析.     

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.     

面板堆石坝挤压式边墙的概化数值模型及应用

基于对挤压式边墙实际结构及工作性态分析,从合理性和简单性原则出发,建立了用于面板堆石坝应力位移有限元分析的挤压式边墙概化数值模型。该概化模型由等效板和等效接触面组成,分别采用了线弹性模型和清华接触面弹塑性损伤模型加以描述,其参数易于确定。采用该模型对某面板堆石坝应力变形进行了二三维有限元分析,并与原状模拟分析结果进行了对比。结果表明,概化数值模型能够合理地描述挤压式边墙的实际力学特性,且计算量较小,适用于面板堆石坝的应力变形有限元分析。     

A semi-analytical method for the elastic-plastic large deflection analysis of welded steel or aluminum plating under combined in-plane and lateral pressure loads

The aim of the present paper is to develop a semi-analytical method which can quickly and accurately compute the elastic–plastic large deflection response of welded steel or aluminum plating under a combination of biaxial compression/tension, biaxial in-plane bending, edge shear and lateral pressure loads, until the ultimate limit state is reached. The post-weld initial imperfections (i.e. initial deflection and residual stresses) are included in the method as parameters of influence. It is assumed that the plating is simply supported at all (four) edges which are kept straight. A unique feature of the developed method is that geometric nonlinearity associated with large deflection response of plating under combined loads is treated by analytically solving the nonlinear governing differential equations of the elastic large deflection plate theory, while material nonlinearity due to plasticity is dealt with implicitly by a numerical procedure. This approach reduces the magnitude of numerical computations, resulting in a saving of modeling effort and computing time. As another contribution, this paper investigates and discusses the ultimate strength characteristics of plating, by varying the plate properties and load combinations, based on elastic–plastic large deflection analysis using the developed method.     

移动荷载下正交各向异性地基无限大板的动力响应

以薄板理论和弹性动力学理论为前提,以位移分量为基本未知量,建立了直角坐标系下的移动谐振荷载作用下正交各向异性地基上覆无限大弹性板的力学模型和动力微分方程;然后用坐标变换和Fourier积分变换,且引入边界条件,推导了移动荷载作用下无限大板的挠度和薄板与地基之间的接触应力的积分形式解。基于推导的理论方法,编制了相应的计算程序,并对薄板表面作用线性谐振荷载问题进行了算例分析,验证了方法的正确性。最后,对移动谐振荷载作用下公路路面板的动力响应进行了参数分析,研究了土体参数、板参数、荷载速度、荷载频率对其影响规律。结果表明:土体的各向异性、板厚、板的弹性模量、荷载移动的速度和振动频率对板动力响应影响很大。     

各向同性和各向异性加劲板的局部屈曲和屈曲后的性能分析

研究了评估各向同性和各向异性加劲板的局部屈曲和屈曲后性能的方法。该方法考虑了2个加劲肋之间的加劲板块,用等效的各种不同刚度横向和转动弹簧代替其余的板块,作为所计算板块的弹性支座。在解决各向同性和具有任意边界条件的碾压对称组合板的局部屈曲问题时,采用二维里兹位移函数(pb-2Ritz)。通过板块的屈曲分析能准确地预测板的局部屈曲性能。最后,将此方法加以改进,用于预测表面已经局部屈曲的加劲板的屈曲后反应。选择适当的边界条件对所分析的构件在屈曲后性能的计算中是非常重要的。该方法计算的结果与相应的有限元结果符合较好。     

水平荷载桩桩土共同作用全过程分析

在桩基础的分析中 ,对水平荷载桩的计算长期限于弹性 ,而只考虑桩周土体的非线性。本文在考虑钢筋混凝土桩非线性损伤的情况下建立了一种空间耦合数值计算模型 ,并编制了相应的计算程序。通过算例分析证明了所设计的计算程序是合理的和可行的。本文方法可以模拟计算桩身混凝土损伤引起的刚度降低和桩周土体不同应变软化模式对桩身水平位移的影响 ,与传统的或规范意义下的分析方法相比具有机理分析清楚 ,物理意义更加明确的优点     

水平荷载桩桩土共同作用全过程分析

在桩基础的分析中,对水平荷载桩的计算长期限于弹性,而只考虑桩周土体的非线性。本文在考虑钢筋混凝土桩非线性损伤的情况下建立了一种空间耦合数值计算模型,并编制了相应的计算程序。通过算例分析证明了所设计的计算程序是合理的和可行的。本文方法可以模拟计算桩身混凝土损伤引起的刚度降低和桩周土体不同应变软化模式对桩身水平位移的影响,与传统的或规范意义下的分析方法相比具有机理分析清楚,物理意义更加明确的优点。