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。     

土-桩-筏共同作用的混合分析法

提出了一种土-桩-筏共同作用的混合分析法.将桩和桩间土简化为弹簧作用于筏板下,桩土相互作用系数基于Mindlin解和Boussinesq解,为避免桩端应力集中,在桩端面上进行应力积分,并引入修正参数来考虑桩挤开土的实际情况.筏板采用无剪切闭锁的四边形厚薄板通用单元进行有限元分析.根据桩土柔度系数得到桩土柔度矩阵,求逆后与筏板刚度矩阵耦合,形成土-桩-筏体系的刚度矩阵.桩的沉降计算和土层参数的确定与规范法一致,适用于成层地基上变桩长、变桩径情况,板单元适用于平面形状不规则的薄板及中厚板.通过计算Poulos提出的经典桩筏基础模型并与其它几种典型方法对比,表明该法合理、实用.     

结构分析中厚、薄板通用的ACM单元刚度矩阵

常规的ACM单元只能用于薄板结构分析。本文给出一个可以通用于薄板和厚板结构分析且不会出现剪切自锁的ACM单元刚度矩阵。     

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。     

高阶四边形单元的流形方法

在原有的三角形单元的流形方法的基础上，提出了高阶四边形单元的流形方法。该法简化了数学和物理网格，减少了小块物理覆盖的生成数量，采用解析解的单纯形积分，提高了应力和应变的计算精度。首先推导了四边形单元的权函数，并给出四边形单元的高阶位移方程的一般表达式。进一步推导了应变和应力以及单元的刚度矩阵等，最后通过具体实例验证了高阶四边形流形单元的计算应力和应变的准确性。     

竖向荷载下桩筏基础通用分析方法

根据已有的竖向荷载下刚性板桩筏基础分析结果提出了一种竖向荷载下桩筏基础的通用分析方法。桩筏基础分析中考虑了4种相互作用,分别为桩–土–桩、桩–土–板、板–土–桩和板–土–板相互作用。筏板分析采用有限单元方法,以厚薄板通用四边形等参单元进行分析。该方法可以分析由任意桩长、桩半径和刚度特性的桩群以及任意厚度和几何外形的筏板组成的竖向受荷桩筏基础。应用该方法不需要划分桩土体单元,其分析复杂程度基本等同于弹性地基板基础,且分析过程简洁。通过与各种方法的比较证明该方法是合理可行的,精度上也满足要求。     

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。     

一种求解弹性地基上矩形薄板弯曲问题的高精度单元

从Winkler弹性地基模型出发,以单位宽纵横向有限条带为位移模式,建立矩形薄板单元总势能泛函,由最小势能原理导出刚度方程。此单元有12个自由度,满足单元边界导数的连续性,并可直接得到单元显式刚度矩阵。数值结果表明,本文方法自由度少,计算精度高,可用于Winkler弹性地基板的计算分析。     

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.     

加劲板有限元屈曲分析

本文提出了加劲板屈曲分析的等参加劲板弯曲单元。在西文的方法中，加劲松件可放在平板单元内部任意位置，而不必放在节线上，由于等参二次单元能较容易地适应曲线边界，层状板材和横向剪切变形。公式暨能应用于薄板又能适用于厚板。并给出了各种正交含可变斜交角的斜交加劲板之临界荷载和加劲参数，其结果表明与某些文章发表过结果完全一致。     

Effect of transverse shear strains on plates resting on elastic foundation using modified Vlasov model

A four-noded quadrilateral (PBQ4) and an eight-noded quadrilateral (PBQ8) plate bending element based on Mindlin plate theory are adopted for the analysis of thin and thick plates resting on elastic foundation using modified Vlasov model. The terms of vertical deflection stiffness matrix and shear deformation stiffness matrix of the subsoil are evaluated using finite element method, and presented in explicit forms. Selective reduced integration technique is used in addition to full integration technique for both the types of the elements to avoid shear-locking problem that occurs under the thin plate limit. It has been demonstrated that the performance of the eight-noded quadrilateral element is excellent for thin and thick plates on elastic foundation when selective-reduced integration technique is used. General conclusion can be drawn from the results that the effect of the shear strain on the behavior of the plate resting on subsoil is always quite small for free plates compare to the supported ones.     

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。     

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。     

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.