线弹性土壤中埋设悬跨管道的屈曲分析

建立了两端埋设在线弹性土壤中的悬跨管道的屈曲方程。利用细长梁小挠度理论,建立了含有轴向压力的悬跨段和埋设段管道的弯曲控制方程。基于埋设段管道的刚度和变形特性,建立了符合悬跨段管道实际情况的边界条件。导出了悬跨段管道对称屈曲和反对称屈曲的屈曲载荷方程,通过数值求解给出了不同土壤刚度系数条件下悬跨段管道屈曲载荷。研究表明:悬跨段管道的屈曲载荷系数依赖于土壤刚度系数,简支梁模型只在特定的土壤刚度系数下适用于悬跨管道;在土壤刚度系数很大时,两端固支梁模型才能反映悬跨管道的屈曲特性。建议采用该方法进行埋设悬跨管道的屈曲分析。     

轴向力作用下埋设于线弹性土壤中的悬跨管道振动分析

利用细长梁的小挠度理论,建立了两端埋设在线弹性土壤中的含轴向力的悬跨管道自由振动方程。基于埋设段的刚度约束特性,建立了悬跨段管道的边界条件。解析求解得到了悬跨段管道频率方程,数值求解了不同土壤刚度和轴向力条件下悬跨段管道的固有频率。研究表明:悬跨段管道振动特性取决于轴向力系数和土壤刚度系数,工程上推荐使用的简支梁和两端固支梁模型只在几个特殊参数点上适用,建议采用该方法进行悬跨管道振动分析。     

刚性土壤上含有轴向力的悬跨管道的静弯曲和固有频率

针对翘起情况的裸露悬跨管道,建立考虑轴向力影响的刚性土壤支承的悬跨管道模型。利用小挠度梁理论,推导出脱离土壤的翘起段和悬跨段管道在自重作用下的变形和内力公式。以静弯曲挠度为振型函数,用能量法给出第1阶固有频率。对简支梁、固支梁和文本模型在含有轴向力情况下的静变形和第1阶振动频率进行了对比研究。研究表明：该文模型与考虑土...     

部分悬跨海底管道多点输入地震反应分析

对部分悬跨海底管道在空间变化地震动作用下的反应进行了分析.建立了含有悬跨段的长距离埋设海底管道多点输入计算模型,据此推导了多点输入运动方程,采用了一种改进的多点地震动模拟方法生成了空间相关多点地震动时程并对海底管道进行了3维多点输入地震反应时程分析.比较了海底管道在不同地震输入模型(多点输入、行波输入、一致输入)作用下的地震响应.同时进一步分析了地震动空间变化特性、模型计算长度、悬跨段长度、管道外径、钢管壁厚、混凝土配重层厚度以及海床坡度对海底管道多点输入反应的影响.分析结果显示地震动的空间变化特性能显著增大海底管道的地震反应,其他因素也在不同程度上对海底管道多点输入地震反应产生影响.     

水下悬跨管道动力响应分析

水下悬跨输流管道在内外流作用下引起涡流振动和波激振动,对于地震较频繁地区,还将受到地震位移和加速度及地震引起的动水压力的作用,确保水下悬跨管道在各种冲击截荷作用下的安全,是管道可靠性设计及安全运行评估的重要内容。以水下管道悬跨段为研究对象,考虑内外流体与管道间的流固耦合作用,将管跨处理成等截面的直梁模型,两端入土端的约束等效为弹性支承,采用模态叠加法对其进行动态响应研究,通过算例分析了涡激频率、地震频率和管外流速对管跨振动响应特性的影响。从计算结果看出,跨长、管径对冲击的动态响应有着重要影响。本文分析方法对水下管跨的动态设计和可靠性分析评估具有参考价值。     

海底悬跨输流管道固有特性的DQ解法

研究在复杂的海洋环境和管内流体的耦合作用下,水下管跨振动的固有特性.将水下管跨模拟成两端受土弹簧支承和约束的一般支承输流管道,综合考虑管内外流体和管截面轴向力对管跨固有特性的影响,采用求解边值/初值问题的微分求积法(DQ法)分析其固有特性,建立了微分求积法的模拟方程和边界条件.数值仿真分析结果表明,管跨固有频率随两端入土端土弹簧刚度系数和管截面轴向拉力的增加而增大,随管内流体流速和压强及管截面轴向压力的增加而减小.本文所建立的模型更接近工程实际,DQ法用于水下管跨的工程设计和分析是可行的.     

楼板系统对去柱后钢框架梁的轴向约束刚度研究

钢梁两端约束刚度对其悬链线效应影响很大,因此钢梁悬链线效应中约束刚度的研究是一个重要的内容。该文研究“双跨钢梁”两端的钢梁、楼板以及栓钉连接件对钢梁的轴向约束作用。首先,提出提供约束的钢梁、楼板以及栓钉连接件的非线性位移和变形函数。其次,利用最小势能原理,推导楼板系统对去柱钢框架梁轴向约束刚度的计算公式。考虑提供约束的楼板总是局限在一定范围内,提出并使用楼板“临界长度”对理论公式进行了修正。最后,采用20 个有限元算例对理论公式进行算例验证,证明了该文研究结论的可靠性。     

基于整体分析的钢悬链线立管触地点动力响应分析

在立管动力平衡系统的力学模型中考虑浮式平台的惯性作用和管-土相互作用,研究在不同参数激励下钢悬链线立管触地点动力响应。基于大挠度柔性索理论,分别采用具有弯曲刚度的大挠度细长梁、弹性地基梁模拟立管的悬垂段和流线段,考虑触地点处的大曲率,建立了立管的三维有限元模型,利用Galerkin方法对运动方程离散为一组非线性二阶常微分方程,运用Newmark-β法求解离散方程。通过在立管的动力方程中引入δ函数来体现浮式平台对立管的惯性和水动力影响,将悬链线立管与浮式平台作为一个整体进行动力分析,以工程中实际使用的1800m水深的钢悬链线立管为例,通过对立管顶部进行谐波激励,分别就水动力系数、管内流体密度和海床土体刚度对立管特征点动力分析的影响进行分析,研究表明:水动力系数的改变对立管触地点的动力响应的影响较为显著,主要体现在弯矩和张力幅值的增加;管内流体密度不同,触地点位置不同,表明立管在输送不同液体或气体可能发生疲劳破坏的位置也不同;而海床土刚度对立管触地点区域的弯曲应力影响较大,对轴向应力则影响不大,其结果对SCR设计具有重要的指导意义。     

组合梁挠度计算的改进折减刚度法

该文总结了部分抗剪连接组合梁挠度计算的不同方法,并通过对均布荷载作用下两端简支组合梁跨中挠度的对比分析,讨论了各种方法的特点。针对现行规范中采用的折减刚度法所存在的问题,进行了分析研究,提出了组合梁挠度计算的改进折减刚度法。理论分析和数值结果表明,改进的折减刚度法克服了规范中的折减刚度法所存在的抗剪连接程度增大,组合梁抗弯刚度反而减小导致挠度增大的矛盾,同时考虑了边界条件对折减刚度的影响,且与精确解相比,两者吻合较好。     

钢-混凝土预制混合梁变形性能研究

基于两端固定边界条件下预制混合梁的静力受弯试验,研究了此类预制构件在跨中集中荷载作用下的变形性能。采用奇异函数法建立了预制混合梁的挠曲线计算公式,分析了钢梁与混凝土梁抗弯刚度比、长跨比以及高跨比对变形性能的影响。结果表明:各试件考虑剪切变形影响的挠度计算值与试验值吻合较好,与预制混凝土梁相比,剪切变形对预制混合梁变形性能影响更为显著;由剪切变形引起的附加挠度与总挠度比值随长跨比增加呈线性增长趋势,相同长跨比下其比值随高跨比的增加而增大;建议预制混合梁在高跨比大于1/12时考虑剪切变形的影响。     

基于二阶理论的弹性约束变截面悬臂梁刚度与稳定性分析

从计入二阶效应的挠曲微分方程出发,对惯性矩沿轴向二次变化的变截面Bernoulli-Euler梁在弹性约束下的刚度和稳定性进行了分析,推导了在弹性约束下变截面悬臂梁在复合载荷作用下的挠度和稳定性的精确表达式,给出轴向压力引起的挠度影响系数。在极端情况下,该文公式可相应退化为根部固支的变截面梁及等截面梁之刚度与稳定表达式。将该文的计算结果与用ANSYS软件密分单元的计算结果进行分析比较,分析比较结果验证了该文推导的刚度和稳定性表达式的正确性,该文方法可广泛应用于弹性约束下变截面悬臂梁的刚度和稳定性分析。     

State space formulation for composite beam-columns with partial interaction

A state space formulation is established for analyzing static responses of composite members with partial shear interaction under the combined action of an arbitrary transverse load and a constant axial force. Three generalized displacements (deflection, rotation angle, and interface slip) and three generalized forces (bending moment, shear force, and axial force) are combined into a state vector, which satisfies a state equation whose solution is easily obtained using matrix theory. The interfacial normal contact stress between the two subelements of a composite member is derived in order to check the validity of the basic assumption of identical deflection (or curvature) possessed by the two subelements. We find that, when a concentrated load alone acts on clamped–clamped or clamped–free beam-columns, tensile normal contact stress does appear at certain part of the interface. The formulation is then readily extended to analyze continuous composite beam-columns and inhomogeneous composite beam-columns. In particular, a non-continuous model of slip stiffness along the interface with discrete rectangular pulses is incorporated into the analysis, and the numerical results indicate a significant effect of slip stiffness ununiformity on the critical axial load as well as internal actions of the composite members.     

ACCURATE CALCULATION OF ELASTIC BUCKLING LOADS FOR SPACE FRAMES BUILT UP OF UNIFORM BEAMS WITH OPEN THIN-WALLED CROSS-SECTION

A so-called exact static stiffness matrix for a uniform beam element with open thin-walled cross-section carrying an axial compressive load is derived. This stiffness matrix is useful in an accurate calculation of bifurcation loads and corresponding buckling modes of space frames built up of such beam elements. One may also calculate displacements and sectional forces caused by external joint loads taking into account the second-order effect of the axial beam loads. The exact stiffness matrix is derived by use of the general solution to a set of three coupled differential equations. This means that no preselected shape functions need be introduced and that discretization errors are avoided. The differential equations model coupled Euler–Bernoulli bending in the two principal planes and Saint-Venant/Vlasov torsion and warping with respect to the shear centre axis. No cross-sectional symmetries are assumed. Numerical examples are given. One application will be to loaded pallet racks. The ‘effective length’ for a rack column is calculated.     

Stress State of Bent Buried Pipelines

The authors consider edge effects in buried pipelines that occur in the region of joining of a straight buried pipe and a bent insert (factory bend, elbow, or an elastically bent segment). The action of those effects results in the appearance of additional bending moments, which are proportional to the difference between the axial force in an infinite straight pipeline and that in a closed-end pipe, and depend on the geometrical parameters of the pipeline and physical-mechanical characteristics of the soil. Specific examples of analysis of elastic interaction of a pipeline with the soil for pipe bends with various radii of the bend arc are offered. It is shown that additional bending stresses may exceed appreciably the stresses from the axial force, and therefore, they should be taken into account when designing and building pipelines. The solution for an elastically bent segment has been obtained and analyzed.     

埋地钢管局部悬空的挠度和内力分析

在地质灾害作用下,埋地钢管下方的土壤下陷或流失会造成管道悬空,这给管道长期的安全运行构成了严重的威胁。对于埋地钢管在悬空时的失效问题曾有文献进行过研究,但均未推导出此种状态下埋地钢管的挠度和内力计算公式。该文基于Winkler假设的弹性地基梁理论,建立了埋地钢管在局部悬空时管道与土相互作用的力学模型。利用埋地钢管悬空段与非悬空段之间的变形协调性,通过求解管轴挠曲线微分方程,得出了埋地钢管在局部悬空时的挠度和内力计算公式。通过算例与有限元方法的结果进行了比较,结果表明:该方法在精度方面可满足工程要求。     

基于正交异性材料的预应力梁频率的试验研究

进行了一根无粘结预应力简支梁的动力试验,结果表明:预应力梁的固有频率随着预应力的增加而增加,这与Clough提出的轴力作用下各向同性材料梁的理论分析结果相反。其原因是传统的结构分析方法将混凝土视为各向同性、均质的线弹性材料。但是对预应力混凝土结构进行动力分析和检测,要求计算结果必须具有相对高的计算精度。为此该文从混凝土的微观结构入手,将预应力混凝土梁看作各向异性复合材料梁,采用正交异性的线弹性本构模型进行分析,将复合材料梁的刚度视为钢筋混凝土梁的刚度与预应力筋等效刚度之和,然后对预应力混凝土梁的频率与预应力的关系进行分析计算,计算结果与试验结果吻合较好。同时,利用该文提出的分析方法对Saiidi等人的试验梁进行了分析对比,其计算结果与其试验值也符合较好。     

Power series expansion of the general stiffness matrix for beam elements

The general stiffness matrix for a beam element is derived from the Bernoulli–Euler differential equation with the inclusion of axial forces. The terms of this matrix are expanded into a power series as a function of the two variables: the axial force, and; the vibrating frequency. It is shown that the first three terms of the resulting series, which are derived in the technical literature from assumed static displacement functions, correspond respectively to the elastic stiffness matrix, the consistent mass matrix, and the geometric matrix. Higher order terms up to the second order terms of the series expansion are obtained explicitly. Also a discussion is presented for establishing the region of convergence of the series expansion for the dynamic stiffness matrix, the stability matrix, and the general stiffness matrix.     

Elastic buckling analysis of 3-D trusses and frames with thin-walled members

 A finite element method is presented for the determination of the elastic buckling load of three-dimensional trusses and frames with rigid joints. The beam element stiffness matrix is constructed on the basis of the exact solution of the governing equations describing the coupled flexural-torsional buckling behaviour of a three-dimensional beam with an open thin-walled section in the framework of a small deformation theory. Large deformation effects are taken into account approximately through consideration of P−Δ effects. The structural stiffness matrix is obtained by an appropriate superposition of the various element stiffness matrices. The axial force distribution in the members is obtained iteratively for every value of the externally applied loading and the vanishing of the determinant of the structural stiffness matrix is the criterion used to numerically determine the elastic buckling load of the structure. The effect of initial member imperfections is also included in the formulation. Comparisons of accuracy and efficiency of the present exact finite element method against the conventional approximate finite element method are made. Cases where the axial force distribution determination can be done without iterations are also identified. The effect of neglecting the warping stiffness of some mono-symmetric sections is also investigated. Numerical examples involving simple and complex three-dimensional trusses and frames are presented to illustrate the method and demonstrate its merits. Received: 2 May 2000 / Accepted: 15 July 2002