冷弯薄壁型钢住宅结构整体扭转效应分析

为了研究冷弯薄壁型钢住宅结构平面质量中心、楼层形心与刚度中心偏差较大时,结构整体扭转效应的不利影响,将楼层平面内水平荷载(风、地震)作用下结构位移分解为平动和转动2种状态,得到相应状态下各组合墙体所承担的剪力,然后将其效应进行叠加,推导出了结构的线弹性层间扭转角及组合墙体剪力和侧移变形计算公式.对某冷弯薄壁型钢多层住宅结构在水平荷载作用下的层间扭转效应进行了简化计算,并运用ANSYS进行了数值模拟分析.结果表明:水平扭转效应对该类结构影响显著,简化计算公式和有限元程序数值模拟所得结果具有较好的一致性,简化计算公式可供实际工程中对该类结构整体扭转效应的计算分析时参考.     

Torsion analysis of thin-walled beams including shear deformation effects

The first part of the paper develops a theory for the torsional analysis for open thin-walled beams of general cross-sections which accounts for shear deformation effects. Statically admissible stress fields are postulated in agreement with those resulting from the Vlasov thin-walled beam theory. The principle of stationary complementary energy is then adopted to formulate the governing field compatibility condition under the stress fields postulated. The naturally arising boundary terms are found to relate the warping deformations to the internal force fields. A torsion beam example is solved using the new theory in order to illustrate its applicability to practical problems. The second part of the paper implements the solution numerically in a force-based finite element context. Two finite elements are developed by assuming linear and hyperbolic bimoment fields. The FEA solutions are shown to provide lower bound representations of the stiffness when compared to those based on conventional beam theories founded on postulated kinematic assumptions.     

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.     

考虑剪力滞后影响的框筒结构动力时程分析

框筒结构采用薄壁杆件模型.先从结构总势能出发,求得哈密顿对偶体系,由两端边值问题精细积分法中的区段混合能矩阵推导出结构的层单元刚度矩阵,利用有限元刚度集成法形成结构的总体刚度矩阵.采用多质点体系质量矩阵,阻尼矩阵采用瑞雷阻尼,再利用动力时程分析的精细积分法对结构进行动力时程分析,编制相应的Matlab程序.最后通过具体算例分析,将结果与文献结果进行对比,从而验证了本文方法分析动力问题的可行性.     

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。     

Load–deflection behaviour of thin-walled plates with a single bolt in shearing

This paper presents an experimental, numerical and analytical study of the behaviour of thin-walled plates connected by a single bolt under shear. Eighteen tests were carried out to provide detailed data of load–deflection and load–strain curves for validation of the finite element simulation model. The validated finite element model was then used to perform a comprehensive set of parametric studies to investigate the effects of different design parameters on the connected plate behaviour, including initial stiffness, ultimate resistance and maximum deformation at the ultimate resistance. It was found that the stiffness and ultimate resistance could be predicted accurately by using existing methods. The analytical study therefore focused on developing a method to calculate the maximum plate deformation (hole elongation) at the ultimate resistance. Based on the parametric study results, methods of calculating the ultimate deformation were proposed, based on different failure modes of the connection.     

考虑圣维南翘曲变形的初始扭转薄壁梁单元刚度矩阵

基于传统薄壁直梁力学模型,对初始扭转薄壁梁有限元数值模型进行系统的分析与研究。首先基于初始扭转梁的几何变形微分关系,导出初始扭转薄壁梁圣维南翘曲应变。根据传统薄壁直梁有限元力学模型,考虑初始扭转梁圣维南翘曲变形,建立其有限元单元刚度矩阵。最后,通过椭圆截面初始扭转梁算例,并与ANSYS三维实体有限元分析结果进行对比分析,表明建立的考虑圣维南翘曲变形的初始扭转薄壁梁单元刚度矩阵具有良好的精度。     

Exact solutions for thin-walled open-section composite beams with arbitrary lamination subjected to torsional moment

The exact solutions for torsional analysis of thin-walled open-section composite beams with arbitrary lamination subjected to torsional moment are presented for the first time. For this, a general thin-walled composite beam theory with arbitrary lamination is developed by introducing Vlasov's assumption and the equilibrium equations and the force–deformation relations are derived from the energy principle. Applying the displacement state vector consisting of 14 displacement parameters and the nodal displacements at both ends of the beam, the displacement functions are derived exactly. Then, the exact stiffness matrix for torsional analysis is determined using the force–deformation relations. As a special case, the closed-form solutions for symmetrically laminated composite beams with various boundary conditions are derived. Finally, the finite element procedure based on Hermitian interpolation polynomial is developed. To demonstrate the validity and the accuracy of this study, the numerical solutions are presented and compared with the closed-form solutions and the finite element results using the Hermitian beam elements and ABAQUS's shell elements.     

薄壁梁的单元刚度矩阵及其应用

按文[1]述截面正投影绕定轴转动的概念,直接导出薄壁梁的单元刚度矩阵,并利用直接刚度法求解弯心不共线的连续梁。算例表明,它和用柔度矩阵按力法求解的结果是相同的,但计算过程更简单。     

Nonlinear free vibration analysis of asymmetric thin-walled circularly curved beams with open cross section

A finite element formulation is present for the nonlinear free vibration of thin-walled curved beams with non-symmetric open across section. The kinetic and potential energies are derived by the virtual principle. The energy functional includes the effect of flexural–torsional coupling, the torsion warping and the shear center location. For finite element analysis, cubic polynomials are utilized as the shape functions of the two nodal thin-walled curved elements. Each node possesses seven degrees freedom including the warping degree of freedom. The nonlinear eigenvalue problem has been solved by the direct iteration technique. The results are compared with those for straight beams as available in the literature. The results for nonlinear free vibration analysis of curved beams for various radii and subtended angle are presented.     

基于能量变分剪切效应空间梁单元刚度矩阵及荷载列阵推导

为了系统研究空间梁单元考虑剪切变形影响时的刚度矩阵及荷载列阵,将能量变分原理应用于空间梁的单元分析。建立了考虑剪切效应的空间梁单元位移函数,利用最小势能原理导出了这种空间梁单元的刚度矩阵和荷载列阵的表达式,显式积分得到单元刚度矩阵,同时计算了平面内部分非节点荷载作用下的等效节点荷载,修正了相关文献中的部分错误。计算结果表明:该方法所得到的单元刚度矩阵与相关文献中其他方法的计算结果完全一致,为编制空间巨型结构的有限元程序奠定基础,对推算其他类型单元刚度矩阵及其荷载列阵也具有理论意义和应用价值。     

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.     

单向碳/环氧和玻纤/环氧复合材料扭转疲劳性能

提出碳/环氧复合材料作为柔性梁材料的可行性。对相同树脂基体的单向碳纤维复合材料和玻璃纤维/环氧复合材料的扭转疲劳性能进行研究。碳纤维复合材料的初始扭转刚度几乎与玻璃纤维复合材料相同。采用有限元计算的扭转刚度与试验结果吻合:扭转刚度主要受控于材料的剪切刚度。通过控制正弦波扭转的角度,进行了恒定受拉轴向荷载下的扭转疲劳试验。尽管根据循环次数降低了扭矩和扭转刚度振幅,无论是碳纤维还是玻璃纤维复合材料都没出现严重的破坏现象。X-射线CT的检查结果以及有限元计算的结果显示:主要是沿着纤维方向裂缝扩展引起扭转刚度的退化,碳纤维扭转疲劳寿命高于玻璃纤维复合材料。因此,根据扭转刚度和张拉-扭转疲劳性能,证实碳纤维具有很好的性能,可作为柔性梁的抗扭材料。     

横观各向同性层状地基平面应变问题的解析层元解

从横观各向同性平面应变弹性体的基本控制方程出发,通过Fourier积分变换和Cayley-Hamilton定理推导出单层横观各向同性地基的传递矩阵,然后再通过矩阵变换求得单层地基的精确刚度矩阵,即解析层元解;根据有限层法原理组合得到总刚度矩阵,通过求解总刚度矩阵得到横观各向同性层状地基平面应变问题在积分变换域内的解答,应用Fourier逆变换得到物理域内的精确解。编制相应的计算程序,计算结果与有限元软件模拟结果吻合。算例分析表明土的分层特性和横观各向同性性质对土体变形有明显影响。     

Buckling analysis of thin-walled open members—A finite element formulation

In a companion paper, a variational principle based on the principle of stationary complementary energy was developed for the buckling analysis of thin-walled members with open cross-sections. In this paper, the variational principle is adopted to formulate a finite element buckling solution. The formulation successfully incorporates shear deformation effects, a feature that is neglected in most available buckling solutions. By adopting a non-orthogonal coordinate system, the solution successfully captures the transverse load position effect relative to the shear center. A series of examples demonstrate the validity of the finite elements formulated and their applicability to a wide variety of buckling problems. Examples include column flexural and torsional buckling, lateral torsional buckling of beams with a variety of end conditions and subjected to a variety of moment gradients. The formulation is shown to be applicable to beams with mono-symmetric sections. In all cases, the validity of the new solution is assessed and established through comparisons to well-established closed-form and/or numerical solutions.     

梁和框架结构的大变形非线性分析

描述了有限元方法分析梁和框架结构的几何非线性问题,考虑大转动的影响,在有限转动公式的级数展开式中,取二阶近似,从而形成线性刚度矩阵和几何刚度矩阵,推导了大变形情况下梁的本构方程,算例表明：对于较复杂的几何非线性问题,本文提出的方法是有效的。     

薄壁曲线箱梁空间分析的梁段单元

广义符拉索夫薄壁梁理论耦合有限元技术 ,推导出一种能模拟拉压、弯曲、扭转、扭翘、剪切和剪力滞效应的薄壁曲线箱梁梁段单元。单元为两节点九自由度 ,除了常规梁单元的六个自由度外 ,还有三个分别考虑扭翘、剪切和剪力滞效应的自由度。利用变分原理在曲线坐标系下推导了单元刚度矩阵的显式及其等效结点荷载列阵。并在推导中考虑了曲线箱梁横截面剪心与形心不重合的影响。算例表明了本单元的有效性和准确性。     

Shear lag analysis by the adaptive finite element method: 1. Analysis of simple plated structures

Due to the presence of sharp stress gradients, traditional finite element analysis using uniform meshes for the solution of shear lag problems for thin-walled structures is inefficient and will result in inaccurate values of effective breadth ratio. By using the adaptive finite element analysis, it is possible to obtain results with predetermined accuracy with a minimum amount of computational cost. An adaptive finite element analysis procedure is used to deal with the problem of shear lag effects of plated structures with arbitrary dimensions and geometry. This study consists of two parts. In Part 1 of the study, shear lag effects in simple plated structures, such as straight rectangular, single-cell box girders are studied. In Part 2 of the study, the adaptive refinement procedure will be extended to the shear lag analysis of complex plated structures such as core walls with openings, multi-cell box girders and box girders with curve flanges.     

Quadruply coupled linear free vibrations of thin-walled beams with a generic open section

The coupled vibration of thin-walled beams with a generic open section induced by the boundary conditions is investigated using the finite element method. If the axial displacement of the pin end is restrained at another point rather than the centroid of the asymmetric cross section, the axial vibration, two bending vibrations, and torsional vibration may be all coupled. The element developed here has two nodes with seven degrees of freedom per node. The shear center axis is chosen to be the reference axis and the element nodes are chosen to be located at the shear centers of the end cross sections of the beam element. Different sets of element nodal degrees of freedom corresponding to different pin ends are considered here. The relation between element matrices referred to different sets of element nodal degrees of freedom is derived.

Numerical examples are presented to demonstrate the accuracy of the proposed method and to investigate the effects of different pin ends on the coupled vibrations of the thin-wall beam.     

Experimental and analytical studies on a streamlined steel box girder

A new type of streamlined girder (lenticular cross-section) bridge with a thin-walled steel box girder is proposed. In order to deal with the problem of increasing traffic congestion, this bridge is designed with a large width-to-span ratio, which results in significant shear lag effects and causes non-uniform stress distribution in the three-cell thin-walled box girder, especially along the flanges of the girder. The aim of this study is to investigate the effect of shear lag in thin-walled box girder bridges with large width-to-span ratios through both experimental and numerical studies. A large-scale Plexiglas model is tested under different loading cases. The material parameters are obtained from physical characteristics tests and tensile tests. In addition, a computational model is presented for a comprehensive simulation of a girder bridge including the orthotropic top/bottom/web plates and their ribs, which leads to accurate modeling of structural properties of the girder. The simulation of the computation results compared well with the experimental results. It is illustrated that the finite element analysis is an effective method to predict properties of this class of bridges.