带转角自由度的三角形三棱柱单元

本文提出了一个带转角自由度平面三角形单元、两个带转角自由度空间三棱柱单元。对平面单元每个结点有两个线位移自由度、一个转角自由度；对空间单元每个结点有三个线位移自由度、三个转角自由度。这些单元列式简单，其中两个无多余零能模式，数值计算表明，它们的计算精度高。     

带转角自由度的四边形六面体单元

本文提出了三个带转角自由度单元，其中一个平面四边形单元，两个空间六面体单元。对平面单元每个结点有两个线位移自由度、一个转角自由度；对空间单元，每个结点有三个线位移自由度、三个转角自由度。这些单元列式简单，其中两个无多余零能模式，数值计算表明，它们的计算精度高。     

复合材料空间薄壁梁的有限元分析模型

在剪切梁理论的基础上, 采用9 节点平面单元模拟梁任意截面形状; 采用27 节点体单元, 模拟截面出平面外的二次翘曲位移, 从而建立了空间复合材料任意截面薄壁梁考虑二次翘曲的有限元分析模型。根据本文中导出的复合材料有限元模型编制了相应的分析计算程序。算例表明: 本文中建立的复合材料薄壁梁模型正确, 可以用于考虑多种耦合影响因素作用下复杂结构空间薄壁复合材料梁的有限元分析计算。      

杆梁组合结构的有限元分析

杆梁组合结构能够充分发挥建筑材料的物理性质,是工程中常用的一种结构形式,由于杆和梁单元的自由度不同,给这类组合结构的理论分析带来了困难。该研究针对杆梁组合结构内力分析过程中刚度矩阵的集成问题,基于不同类型结构构件间的连接关系建立了关联表,推导了基于关联表的结构整体刚度矩阵与单元刚度矩阵各元素之间的对应关系,建立了基于关联表的结构整体分析模型。算例分析的结果表明,该文所采用的关联表方法能够有效地处理杆梁组合结构的受力分析问题,此方法对于解决具有不同自由度数的单元的组合结构分析问题提供了简便可靠的思路。     

一种考虑剪滞效应的斜支承连续箱梁挠曲扭转分析方法

通过在支承坐标系下考虑约束条件,提出一种适用于斜支承连续箱梁挠曲扭转分析的薄壁箱梁单元。该单元具有10 个自由度,可方便地考虑斜支承连续箱梁的剪滞效应和扭翘变形。选取挠曲剪滞微分方程和约束扭转微分方程的齐次解作为单元位移函数,推导出单元刚度矩阵各元素的具体表达式。从剪滞翘曲应力的轴向平衡条件出发,建立双室箱形断面的剪滞翘曲位移函数,并给出了剪滞翘曲几何特性的一般计算公式。用所编制的电算程序SSCBA 对一个3 跨斜支承双室连续箱梁模型进行计算,计算值与实测值和ANSYS 壳单元结果均吻合较好,证实该箱梁单元是可靠的。计算表明:在跨中偏心荷载作用下,斜支承连续箱梁的剪滞翘曲变形和约束扭转翘曲变形对应力分布具有显著影响。     

薄壁结构弯扭耦合振动计算研究

本文建立了薄壁结构弯扭耦合振动的薄壁梁有限元模型,该模型考虑翘曲和剪切变形的影响,能精确描述薄壁梁的纯弯状态和百均匀扭转,并适用于任何形状的横剖面,本文重点讨论了翘曲位移协调问题,提出了新的不同剖面形式梁段间的翘曲位移协调方法,数值算例证实了本文的正确性。     

用高阶梁单元计算结构附带集中质量的灵敏度

采用高阶有限梁单元,研究梁或刚架结构附带集中质量的固有频率及其灵敏度计算问题。通过在节点上增加曲率和曲率的一阶导数两个独立的自由度,可以直接获得频率灵敏度计算所需的基本量。计算结果表明：用高阶梁单元,可以较精确地获得固有频率及其对集中质量位置的灵敏度值。此外,经过比较发现,在单元网格划分比较密集的情形下,采用通常的2节点4自由度梁单元,也能获得比较满意的频率灵敏度计算结果。     

复合材料薄壁梁的固有特性分析

本文采用复合材料薄壁梁的高次翘曲理论对复合材料薄壁梁的固有特性进行了分析,讨论了单闭室复合材料薄壁梁的高次翘曲,剖面分层对结构的固有特性的影响。数例表明,复合材料薄壁梁的高次翘曲函数和分层对结构的固有特性具有一定的影响。     

杆系结构分析中的直梁单元和曲梁单元

本文编制了杆系结构直梁单元的几何线性有限元程序。通过２个经典实例，对不同的直梁单元和曲梁单元进行了对比。结果表明：直梁单元与曲染单元的计算结果没有显示的不同。因而，在杆系结构的非线性分析中，可以采用直梁单元模拟曲梁，进行屈曲分析。     

一种基于纵横向有限条带的矩形薄板弯曲单元

本文基子单位宽纵横向有限条带的变位模式,构造了一个１２个自由度的矩形薄板弯曲单元,此单元满足了单元边界Ｃ１连续性,且自由度少,计算精度较高,可用于大型板系结构的计算分析。     

An improved theory and finite-element model for laminated composite and sandwich beams using first-order zig-zag sublaminate approximations

A new beam finite element based on a new discrete-layer laminated beam theory with sublaminate first-order zig-zag kinematic assumptions is presented and assessed for thick and thin laminated beams. The model allows a laminate to be represented as an assemblage of sublaminates in order to increase the model refinement through the thickness, when needed. Within each sublaminate, discrete-layer effects are accounted for via a modified form of DiSciuva's linear zig-zag laminate kinematics, in which continuity of interfacial transverse shear stresses is satisfied identically. In the computational model, each finite element represents one sublaminate. The finite element is developed with the topology of a fournoded rectangle, allowing the thickness of the beam to be discretized into several elements, or sublaminates, if necessary, to improve accuracy. Each node has three engineering degrees of freedom, two translations and one rotation. Thus, this element can be conveniently implemented into general purpose finite-element codes. The element stiffness coefficients are integrated exactly, yet the element exhibits no shear locking due to the use of a consistent interdependent interpolation scheme. Numerical performance of the current element is investigated for an arbitrarily layered beam, a symmetrically layered beam and a sandwich beam with low and high aspect ratios. The comparisons of numerical results with elasticity solutions show that the element is very accurate and robust.     

An accurate two-node finite element for shear deformable curved beams

An accurate two-node (three degrees of freedom per node) finite element is developed for curved shear deformable beams. The element formulation is based on shape functions that satisfy the homogeneous form of the partial differential equations of motion which renders it free of shear and membrane locking. The element is demonstrated to converge to the results obtained from a shear deformable straight beam when the beam becomes shallower. Numerical examples were performed to demonstrate the accuracy and efficiency with respect to previously published formulations. © 1998 John Wiley & Sons, Ltd.     

A four‐node,shear‐deformable shell element developed via explicit Kirchhoff constraints

An efficient, four‐node quadrilateral shell element is formulated using a linear, first‐order shear deformation theory. The bending part of the formulation is constructed from a cross‐diagonal assembly of four three‐node anisoparametric triangular plate elements, referred to as MIN3. Closed‐form constraint equations, which arise from the Kirchhoff constraints in the thin‐plate limit, are derived and used to eliminate the degrees‐of‐freedom associated with the ‘internal’ node of the cross‐diagonal assembly. The membrane displacement field employs an Allman‐type, drilling degrees‐of‐freedom formulation. The result is a displacement‐based, fully integrated, four‐node quadrilateral element, MIN4T, possessing six degrees‐of‐freedom at each node. Results for a set of validation plate problems demonstrate that the four‐node MIN4T has similar robustness and accuracy characteristics as the original cross‐diagonal assembly of MIN3 elements involving five nodes. The element performs well in both moderately thick and thin regimes, and it is free of shear locking. Shell validation results demonstrate superior performance of MIN4T over MIN3, possibly as a result of its higher‐order interpolation of the membrane displacements. It is also noted that the bending formulation of MIN4T is kinematically compatible with the existing anisoparametric elements of the same order of approximation, which include a two‐node Timoshenko beam element and a three‐node plate element, MIN3. Copyright © 2000 John Wiley & Sons, Ltd.     

弹性轴向约束平面钢梁火灾下非线性分析的弧线坐标法

以变形后构件的弧线长度和截面转角为基本未知量,提出了一种火灾升温下弹性轴向约束平面钢梁的非线性分析方法。以节点的内力和外力平衡为条件建立基本方程,可方便考虑几何非线性和材料的非线性。节点仅包含弧线长度和截面转角两个自由度,计算效率优于常规有限元法的梁单元。以承受均布荷载的梁为例,分析了荷载、轴向约束刚度、沿截面和纵向不均匀分布温度的影响,给出了梁跨中的挠度、轴力和弯矩随温度的变化关系,并分析了在不同温度下跨中截面应变和应力的分布。算例表明,该方法有足够的精度。     

An efficient finite element with layerwise mechanics for smart piezoelectric composite and sandwich shallow shells

In this work, we present a new efficient four-node finite element for shallow multilayered piezoelectric shells, considering layerwise mechanics and electromechanical coupling. The laminate mechanics is based on the zigzag theory that has only seven kinematic degrees of freedom per node. The normal deformation of the piezoelectric layers under the electric field is accounted for without introducing any additional deflection variables. A consistent quadratic variation of the electric potential across the piezoelectric layers with the provision of satisfying the equipotential condition of electroded surfaces is adopted. The performance of the new element is demonstrated for the static response under mechanical and electric potential loads, and for free vibration response of smart shells under different boundary conditions. The predictions are found to be very close to the three dimensional piezoelasticity solutions for hybrid shells made of not only single-material composite substrates, but also sandwich substrates with a soft core for which the equivalent single layer (ESL) theories perform very badly.     

一个适合于复合材料层合板分析的应力杂交单元

本文根据修正的余能变分原理构造了一个适合于复合材料层合板特点的三角形单元。此单元能够考虑横向剪切变形的影响和局部扭曲效应。三角形单元的三个顶点取为节点,每个节点具有5个自由度,三个位移自由度,二个转角自由度。文中用此单元计算了几种层合板的固有频率,并将结果与解析解进行了比较。计算表明,此单元计算精度较高,应用方便。     

Extended rotation‐free plate and beam elements with shear deformation effects

This paper describes a methodology for extending rotation‐free plate and beam elements to accounting for transverse shear deformation effects. The ingredients for the element formulation are a Hu–Washizu‐type mixed functional, a linear interpolation for the deflection and the shear angles over standard finite elements and a finite volume approach for computing the bending moments and the curvatures over a patch of elements. As a first application of the general procedure, we present an extension of the three‐noded rotation‐free basic plate triangle (BPT) originally developed for thin plate analysis to account for shear deformation effects of relevance for thick plates and composite‐laminated plates. The nodal deflection degrees of freedom (DOFs) of the original BPT element are enhanced with the two shear deformation angles. This allows to compute the bending and shear deformation energies leading to a simple triangular plate element with three DOFs per node (termed BPT+ element). For the thin plate case, the shear angles vanish and the element reproduces the good behaviour of the original thin BPT element. As a consequence the element is applicable to thick and thin plate situations without exhibiting shear locking effects. The numerical solution for the thick case can be found iteratively starting from the deflection values for the Kirchhoff theory using the original thin BPT element. A two‐noded rotation‐free beam element termed CCB+ applicable to slender and thick beams is derived as a particular case of the plate formulation. The examples presented show the robustness and accuracy of the BPT+ and the CCB+ elements for thick and thin plate and beam problems. Copyright © 2010 John Wiley & Sons, Ltd.     

A geodesic beam finite element for use in the-static analysis of reinforced circular cylindrical shells

The development of a geodesic beam finite element for use with a specific circular cylindrical shell finite element in the analysis of reinforced circular cylinders is described. The basic strain and curvature change equations are given and, from these, three versions of the geodesic beam element are developed. Two of the beams have nodal degress-of-freedom identical with the shell element. They differ in the treatment of the terms relating to rotation about the principal normal. The first version ignores this parameter but, under certain circumstances, the stiffness matrix contains terms which can contribute to the strain energy under arbitrary rigid body movement of the beam. This deficiency is removed by applying an aspect of Koiter's theory which is used to transform the curvature change equations. The introduction of additional rotational degress-of-freedom, at the end nodes of the beam element, produces a variation which is capable of accurately representing and transmitting in-surface bending effects to an adjoining beam element. Numerical evaluation successfully compares finite element solutions to basic problems for straight, circular and helical beams with theoretical strain energy solutions. Finally the beam is used in conjunction with a shell element to analyse an infinitely long circular cylinder, reinforced with equispaced rings, subjected to internal pressure.     

Composite plate analysis using a new discrete shear triangular finite element

This paper deals with the static and dynamic (free vibrations) analysis of plates built up with a symmetric series of orthotropic layers. The formulation of a new simple triangular finite element having three nodes and three degrees of freedom per node is presented. The element called DST (Discrete Shear Triangle) is free of shear locking and has a proper rank. It coincides with DKT (Discrete Kirchhoff Triangle) when the transverse shear effects are negligible. A large number of classical problems is considered to evaluate the performance of the element for the analysis of composite plates. Very satisfactory results are obtained for displacements, stresses and frequencies.     

A two‐noded locking–free shear flexible curved beam element

A new two‐noded shear flexible curved beam element which is impervious to membrane and shear locking is proposed herein. The element with three degrees of freedom at each node is based on curvilinear deep shell theory. Starting with a cubic polynomial representation for radial displacement (w), the displacement field for tangential displacement (u) and section rotation (θ) are determined by employing force‐moment and moment‐shear equilibrium equations. This results in polynomial displacement field whose coefficients are coupled by generalized degrees of freedom and material and geometric properties of the element. The procedure facilitates quartic polynomial representation for both u and θ for curved element configurations, which reduces to linear and quadratic polynomials for u and θ, respectively, for straight element configuration. These coupled polynomial coefficients do not give rise to any spurious constraints even in the extreme thin regimes, in which case, the present element exhibits excellent convergence to the classical thin beam solutions. This simple C⁰ element is validated for beam having straight/curved geometries over a wide range of slenderness ratios. The results indicates that performance of the element is much superior to other elements of the same class. Copyright © 1999 John Wiley & Sons, Ltd.