基于改进Vlasov模型的弹性地基上平板横向剪应变分析

运用Vlasov模型对弹性基础上的薄板和厚板进行分析,采用了基于Mindlin板理论的4结点四边形和8结点四边形弯曲单元。运用有限元法对底层土的竖向挠度刚度矩阵和剪切变形刚度矩阵进行推算。针对2种类型的板单元,采用完全积分方法和选择性简化积分方法进行分析,以避免极限状态下薄板的剪切闭锁问题。研究发现：在选择性简化积分方法中,8结点四边形板单元非常适用于分析弹性基础上的薄板和厚板。结果表明：相比有支撑的平板,剪应变对底层土上无支撑平板的影响非常小。     

无剪切闭锁的厚薄通用板单元

基于广义协调理论构建了一个具有12个自由度的四边形厚薄板通用单元,利用虚位移原理,将Winkler弹性地基的转动支承作用引入单元刚度矩阵,得到考虑地基转动支撑作用的板单元。算例表明,由于考虑了转动支承作用,所构建的板单元精度高,收敛性好,无剪切闭锁,具有厚薄板通用性。     

弹性支承厚板在局部载荷下的弯曲

在建筑结构设计中弹性支承板的计算一般采用有限元法和图表法。在理论上没有一般性的解析表达式,无论是薄板还是厚板,本文由边界积分法给出了一般封闭解析解的表达式。作为算例,求解了局部均布荷载作用的弹性支承四边简支厚板的弯曲问题,并相应地以图表的形式给出了计算结果,并与有限元结果进行了对照,证明本文给出的一般性的封闭解析解的表达式是正确的。     

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。     

Stability of variable thickness shear deformable plates—first order and high order analyses

This work presents analysis of the buckling loads for thick elastic rectangular plates with variable thickness and various combinations of boundary conditions. Both the first order and high order shear deformation plate theories have been applied to the plate's analysis. The effects of higher order non-linear strain terms (curvature terms) are considered as well. The governing equations and the boundary conditions are derived using the principle of minimum of potential energy. The solution is obtained by the extended Kantorovich method. This approach is combined with the exact element method for the stability analysis of compressed members with variable cross-section, which provides for the derivation of the exact stiffness matrix of tapered strips including the effect of in-plane forces. The results from the two shear deformation theories are compared with those obtained by the classical thin plate's theory and with published results.     

一种考虑剪切变形影响的厚薄板通用单元

依据深梁理沦,推导了厚板在平面应变状态下考虑剪切影响的剪切因子λ,并构造了厚薄板通用单元。在薄板极限情况下,这种厚薄板通用单元自动退化为原来的薄板单元,消除了剪切闭锁现象。算例结果表明,文中构造的厚薄板单元的计算精度较高,有一定的实用性。     

双参数地基横向受荷桩的传递矩阵法解

为研究地基土体剪切刚度沿深度变化对横向受荷桩工作性状的影响,基于Newmark法和Pasternak双参数地基模型,假设土体剪切刚度为幂函数分布,由单元的挠曲微分方程求得了各结点的横向抗力。忽略了土体压缩变形和剪切变形的耦合作用后,对各结点的横向抗力做了简化,进而导出了单元的场传递矩阵及桩的总体传递矩阵;根据桩底边界条件,求得了桩的初始状态向量,确定了各结点的状态向量。算例分析表明:土体的剪切作用对减小顶位移和桩身最大弯矩有一定的贡献,且对中长桩的影响较长桩明显;土体剪切刚度沿深度变化对桩顶位移影响很小,地面处土体剪切刚度对其影响较大,双参数地基模型能够更好的模拟桩土的实际工况。     

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.     

Bilinear Load–Displacement Curve of Semi-supported Steel Shear Walls

Elastic stiffness and ultimate shear capacity are two main parameters of a structural system to obtain its ideal bilinear load–displacement. In the previous studies, the ultimate shear capacity of semi-supported steel shear walls (SSSW) which are a new lateral resisting system, has been determined. In this system, wall plates do not have any direct connection to the main columns of structure and they are connected to secondary columns which do not carry the gravity loads. The used thin plate in the SSSW elastically buckles at low levels of lateral loads and the wall plate stays on a fairly vast region with elastic post-buckling behavior (elastic stiffness). In this study, the Von-Karman plate equations are solved by the Galerkin method to find displacement field of the wall plate in the elastic post-buckling region as well as the maximum shear load after which the plasticity expand in the wall plate. Thus, the elastic stiffness of system is calculated. As the analytical procedure is complicated, the method is applied on 144 examples with different material and geometrical properties. Using linear regression technique, a concise formula is proposed to predict the elastic stiffness of system. The dimensions of wall plate are only the effective parameters in the suggested formula and the elastic stiffness is independent of the overturning moment, section of secondary columns and yield stress of material. Using the ultimate shear capacity and elastic stiffness, an ideal bilinear curve is obtained for the lateral load versus the horizontal displacement. The shear capacity at the end of elastic post-buckling region and out of plane displacement are acceptably validated with those of FE analysis for some examples.     

Quadrilateral shear panel

Various models of structures and structural elements use an assembly of stringers and shear panels. The normal forces in the stringers can vary linearly and the membrane panels have constant shear. Often, these shear panels can be just rectangular but sometimes shear panels with a non-rectangular shape need to be used. In this paper a mathematical formulation is presented for a linear–elastic shear panel with a quadrilateral shape. The panel stiffness matrix is derived by the discrete element method, which yields a simple and efficient computational formulation. Comparison with finite element computations shows that the stiffness matrix is sufficiently accurate for engineering design.     

The transition from thin plates to moderately thick plates by using finite element analysis and the shear locking problem

Two simple plate bending elements, based on Mindlin theory for analysis of both moderately thick and thin plates, are presented in this paper. These elements have either four nodes or eight nodes with 12 and 24 DOF, respectively. To illustrate the accuracy of these finite elements named as TURE12 and TURE24, several numerical examples of displacements and stresses for both thin and moderately thick plate bending problems are presented and discussed with a range of finite element meshes and thickness-to-plate length ratios. In addition, the bending and shearing behaviours of a Mindlin plate are analyzed with respect to shear locking. In order to test the shear locking, the results obtained from the Mindlin plate analysis using 4- or 8-noded elements with full, reduced, and selective reduced integration are compared with the exact classical thin plate solution.     

Bending analysis of folded plates by the FSDT meshless method

In this paper, a meshfree Galerkin method that is based on the first-order shear deformation theory (FSDT) will be introduced to analyse the elastic bending problem of stiffened and un-stiffened folded plates under different loadings and boundary conditions. Folded plates are regarded as assemblies of plates that lie in different planes. The stiffness matrices of the plates are given by the meshfree method. Employing the element concept, which is borrowed from the finite element method, and treating every plate as a big element, the global stiffness matrix of the whole folded plate is obtained by superposing the stiffness matrices of the plates. This is about the same for the analysis of stiffened folded plates. They are considered as assemblies of stiffened plates. The stiffness matrices of the stiffened plates are also given by the meshfree method. Superior to the finite element methods, no mesh is required in determining the stiffness matrices for the plates and the stiffened plates in this paper, which means time-consuming and accuracy-suffering remeshing is entirely avoided for problems such as large deformation or crack propagation in folded plates or stiffener position changes of stiffened folded plates. To demonstrate the accuracy and convergence of the method, several numerical examples are calculated by it and the finite element commercial software ANSYS. Good agreement is observed between the two sets of results.     

桩筏结构复合地基中筏板受力分析的理论计算模型与试验研究

由于缺乏刚性桩复合地基之上筏板受力的合理计算公式,目前中国高速铁路桩筏结构复合地基中筏板的设计计算仍采用简化算法,其计算结果的准确合理性尚不满足要求,为此拟对桩筏基础之上的筏板进行理论求解。选取桩筏结构中单桩作用的筏板区域作为求解单元,将该单元结构视为位于单桩和Winkler弹性地基共同支撑的四边滑支Reissner矩形中厚板,将Reissner矩形中厚板的基本方程导入Hamilton体系,利用辛几何中的分离变量及本征函数展开等方法,求出矩形中厚板弯曲问题的解析解,进而可求得复合地基上筏板的内力、挠度、桩顶反力和桩间土压力等设计值。最后将现场试验实测值与理论模型解析解的计算结果进行对比,结果采用文中理论模型计算得到的筏板弯矩、桩顶轴力及桩间土压应力等与现场实测结果吻合较好,表明在桩筏结构复合地基的筏板设计中,提出的理论模型是一种准确可靠的计算方法。     

Nonlinear analysis of imperfect laminated thin plates under transverse and in-plane loads and resting on an elastic foundation by a semi-analytical approach

The large deflection and postbuckling behavior of imperfect composite laminated plates exposed to a combined action of transverse loads and in-plane edge compressions and resting on an elastic foundation are investigated in this paper by a semi-analytical approach. The formulations are based on the classical laminated plate theory (CLPT), and include the plate–foundation interaction effects via a two-parameter model (Pasternak-type) from which Winkler elastic foundation can be recovered as a limiting case. The present approach employs a perturbation technique, one-dimensional differential quadrature approximation and the Galerkin procedure to model the nonlinear performance of the plate with arbitrary combination of simply supported, clamped or elastic rotational edge constraints. Studies concerning its accuracy and convergence characteristics are carried out through some numerical illustrations. Effects of foundation stiffness, plate aspect ratio, total number of plies, fiber orientation, initial geometrical imperfection, the character of boundary conditions, and load patterns on the nonlinear behavior of the plate are studied. Typical numerical results are given in dimensionless graphical forms.     

加劲钢板剪力墙抗剪性能分析

利用ANSYS有限元软件对交叉加劲钢板剪力墙的抗剪性能进行了研究,重点分析了肋板刚度比和加劲肋宽厚比对剪力墙荷载—位移曲线的影响。研究表明,设置交叉加劲肋能够显著提高钢板剪力墙的承载能力;肋板刚度比对于厚板和薄板抗剪性能的影响不同,对薄板的影响大于厚板;然而无论是厚板还是薄板,加劲肋宽厚比对于墙板荷载—位移曲线的影响都很小。     

弹性地基上厚板的计算分析

以弹性地基上Reissner板为研究对象,地基采用双参数模型,把地基效应归并到厚板的弯曲微分方程中。利用导出的双参数地基上厚板弯曲问题的基本解,从虚功原理出发,依据胡海昌的中厚板弯曲理论,推导出三个广义位移表示的边界积分方程。适用于任意边界条件、任意形状及任意荷载的薄板及中厚板的弯曲问题。文中给出了算例,并对各种参数变化进行了分析,获得了满意的结果。     

On the hysteretic behavior of trapezoidally corrugated steel shear walls

At present, corrugated plates have numerous applications such as web of plate girders and aerospace applications. Higher out‐of‐plane stiffness and initial elastic strength of the corrugated plates compared with flat plates are reasons for consideration. This study investigates the behavior of trapezoidally corrugated steel plate shear walls (TCSPSWs) under monotonic and cyclic loadings. Finite element analyses that include both material and geometric nonlinearities are employed for the examination. The results from finite element analysis are verified through tested specimen findings. Moreover, the behavior of the steel shear walls with the flat infill panels and the corrugated plate infill panels is compared. The results show that explicit dynamic analysis is the most suitable analysis for the TCSPSWs under quasi‐static loading. Furthermore, although strength of the TCSPSWs obtained from the finite element analysis and the test are fully coincident in elastic region, nonetheless, they are fairly coincident in elastic–plastic and plastic region. Copyright © 2012 John Wiley & Sons, Ltd.     

利用Maple计算弹性基础上任意四边形筏板的振动

本文研究弹性基础上任意四边形中厚板的横向振动问题。利用计算软件Maple ,采用pb 2Ritz法求得板的自振频率。并通过算例考察了基础刚度参数、边界条件、横向剪切变形等对板振动特性的影响。     

Free vibration analysis of variable thickness thin and moderately thick plates with elastically restrained edges by DQM

A differential quadrature (DQ) procedure is developed for free vibration analysis of variable thickness moderately thick plates with edges elastically restrained against translation and rotation. The governing equations are based on the first order shear deformation theory and the rotary inertia effects are considered. Comparisons with known thin plate and uniform thickness Mindlin plate solutions are carried out to verify the applicability and accuracy of the analysis. Plates with linear or nonlinear varying thickness in one or two directions can be considered. It is demonstrated that using this DQ procedure, classical boundary conditions such as simply supported, clamped and free edges for variable thickness, thin as well as moderately thick plates can be simulated without any numerical difficulties. The effects of different combinations of constraints at edges, aspect ratio, thickness-to-length ratio, and stiffness parameter values on accuracy and convergence behaviors of the plates are presented. Some new results are presented for bi-linearly variable thickness plates with elastically restrained edges.     

双参数弹性地基厚板分析的边界元法

以弹性地基上Ｒｅｉｓｓｎｅｒ板为研究对象，地基采用双参数模型，把地基效应归并到厚板的弯曲微分方程中。利用「４」导出的双参数地基上弯曲问题的基本解，从虚功原理出发，依据在胡海昌的中厚板弯曲理论，推导出三个广义位移表示的边界积分方程。适用于任意边界条件，任意形状及任意荷载的薄板及中厚板的弯曲问题。