动支座对拱结构抗爆承载力的影响

建立了具有动支座拱的计算模型,该模型考虑了竖向的弹性支承和阻尼支承、水平向弹性支承和扭转约束等柔性支承形式。基于大变形动力微分方程并利用有限差分方法，研究了动支座拱在爆炸荷载作用下的动力响应，并分析动支座对结构承载力的影响。研究表明:动支座对拱的抗爆承载能力有较大影响，不同形式的柔性支承对拱承载力的影响截然不同，竖向弹性支承能够使爆炸荷载作用下拱的弯矩峰值减小,并且使到达峰值的时间增加,提高了拱的抗爆或承受瞬态荷载的能力。而水平弹性支承使拱的内力值和相对位移值增大，对结构的承载力不利。     

基于三阶剪切变形理论的悬臂输流管道自由振动

采用三阶剪切变形理论,结合有限元法研究了悬臂输流管道的自由振动问题．利用虚功原理建立了输流管系统的有限元方程,同时将悬臂端弹性支承以势能的形式引入到系统方程中,求解了系统前三阶的复频率．分别探讨了流体速度和弹簧刚度对系统复频率实部和虚部的影响,重点分析了弹簧刚度与前三阶固有频率间的关系．在弹性支承刚度为零的特例下,对比了本文结果与Timoshenko梁理论的结果,证明了本文方法的可靠性．研究发现系统固有频率的实部恒为负值,表明一端带有弹性支承的约束形式有利于提高悬臂输流管道自由振动的稳定性;流体的流动对管道振动起到了阻尼作用,在流动速度足够大的情况下,各阶振动固有频率均趋于零;当弹簧刚度为无穷大,且流体速度足够大时,输流管道将发生失稳．     

用强迫力法求解弹性支承梁的固有振动

本文将强迫力法引入弹性支承梁固有振动的计算问题，把具有多个弹性支承的梁按自由粱米处理，而将支承反力看作作用于梁上的强迫力。最后利用各支承点的位移约束条件建立了系统的频率方程和以各支反力为基本未知量的线性方程组．     

提高强冲击荷载作用下平板式防护门门框墙抗力的方法

在强冲击波荷载作用下门框墙转角处会产生明显的应力集中，影响门框墙体系甚至整个防护结构的安全。为解决该问题，提出在迎爆面门框墙和衬砌结合部位设置薄弱层的构造方法，从而减小冲击荷载引起的过大的拉应力。运用考虑了剪切变形的悬臂梁理论分析表明，梁端部约束刚度的变化可以影响结构的破坏形态以及结构的内力分布，降低端部的约束刚度可以有效降低端部区域的内力峰值，延缓结构发生破坏的时间。利用有限元模拟的方法，分析了在出入口门框墙位置设置薄弱层对门框墙动力响应和破坏规律的影响。分析结果表明，设置薄弱层可以有效降低门框墙转角处的应力，降低门框墙结构破坏的风险，进而提高门框墙的抗力水平。     

轴向扩散不可压饱和多孔弹性梁的拟静态弯曲

建立了横观各向同性不可压饱和多孔弹性梁拟静态弯曲的数学模型,并给出了一般的求解方法。作为例子,研究了端部不同渗透条件对梁中点承受突加常集中载荷作用的饱和多孔悬臂梁拟静态弯曲的影响,给出了挠度和孔隙流体压力等效力偶沿梁轴线的分布以及随时间的响应曲线。结果表面:端部渗透条件对饱和多孔弹性梁的弯曲行为有显著的影响,梁的弯曲挠度既可随时间单调递增、亦可单调递减,其性态依赖于梁端部的渗透条件。同时发现不同于经典单相弹性梁,由于孔隙流体压力的作用,不承受载荷作用的梁段亦发生弯曲,并且Man-del-Cryer效应亦存在于不可压饱和多孔弹性梁的拟静态响应中,这些结果有助于揭示传热管道、植物根茎等力学行为的机理。     

弹性支承滑动轴承系统的上稳定性理论及应用

建立了考虑支承阻尼和转子外阻尼的弹性支承滑动轴承系统模型,通过对该模型的油膜稳定性计算,确立了第１和第２稳定性界限并划分了稳定区,从而进一步证实了上稳定区的存在．同时提出了可以通过保证上稳定区工作条件来解决滑动轴承油膜失稳问题,并通过实例验证了该方法的有效性．     

弹性支承圆弧梁内力分析

以现代桥梁及房屋结构为工程背景,提出弹性支承曲线梁计算模型,按结构力学方法推导出弹性支承圆弧梁的内力计算公式,分析讨论了竖向和抗扭弹性支承对内力的影响．     

研究带有附加质量和弹性支承的弹性体动态特性的新方法

本文把梁的振动问题表示成第二类Fredholm型积分方程的特征值问题,然后用一种新的方法探讨了附加质量、弹性支承和截面形状变化对梁的动态特性的影响.     

弹性支承条件下车-桥体系的振动分析

本文研究弹性支承条件下车-桥体系的动力分析方法。给出了弹性支承桥梁和车体的振动方程并通过对具有弹性支座简支梁主振动的分析，得出了梁主振型的解析公式。分析计算了上海高架轨道交通典型区段具有弹性支座高架梁的主振型，并利用龙格-库塔法分析计算了车-桥体系在列车通过时的桥梁和车体的振动。计算结果表明，在上海高架轨道交通实际计算参数条件下，考虑支座弹性后桥梁和车体的振动与刚性支承梁的情况相比变化不明显。本文还计算分析了不同橡胶减震支座的刚度及考虑减震支座后系统阻尼比增大等因素对高架梁振动反应的影响，得出一些有益的结论。     

高精度石英振梁加速度计挠性支承设计研究

分析了石英振梁加速度计的工作原理和结构设计,确定出挠性支承的结构形式.根据力学原理给出了挠性支承的设计计算公式,并依据挠性支承的结构设计原则,确定了加速度计基本结构参数.利用有限元分析软件对该加速度计建模并进行整体的位移分布、应力特性等有限元力学分析,软件仿真结果与理论计算的摆片端部位移相差小于3%,支承在极限范围内不会断裂,证明了所建立的支承力学模型正确,这为优化结构设计提供了理论依据和方法.     

Structural modeling of beams on elastic foundations with elasticity couplings

A new simplified structural model and its governing equations for beams on elastic foundations with elastic coupling are proposed. This modeling system is simple but appropriate for the initial structural design of large-scale submerged floating-beam structures moored by tension legs spaced at uniform interval along the beam. The model is actually for beam on discrete elastic supports rather than on continuous elastic foundations. Therefore, the governing equations are based on finite difference calculus and solutions for beams on discrete elastic supports with elasticity coupling are also proposed. To clarify the applicability limit of the proposed model, the equivalence between a beam on discrete elastic supports and that on continuous elastic foundation is investigated by comparisons of characteristic solutions.     

起波配筋RC梁抗爆作用机理及抗力动力系数的理论计算方法

针对钢筋混凝土(RC)梁，提出了一种通过对抗拉纵筋进行局部弯折，形成钢筋起波，从而提高RC梁抗爆能力的高效新方法。结合已有的实验结果和有限元模型计算，分析了起波配筋RC梁的受荷破坏全过程，揭示了其抗爆作用机理。分析结果表明，在RC梁底部适当位置设置纵筋起波，能增大RC梁在爆炸荷载作用下的允许变形，有效吸收爆炸能量，大幅度提高RC梁的抗爆性能。基于能量法，建立了起波配筋RC梁在爆炸荷载作用下的理论计算模型，给出了抗力动力系数的显示计算公式；讨论了平屈抗力比、平弹变形比以及屈弹变形比3个关键设计参数对起波配筋RC梁抗爆性能的影响规律，以便为进一步工程应用提供理论依据。     

功能梯度变曲率曲梁的几何非线性模型及其数值解

基于弹性曲梁平面问题的精确几何非线性理论,建立了功能梯度变曲率曲梁在机械和热载荷共同作用下的无量纲控制方程和边界条件,其中基本未知量均被表示为变形前的轴线坐标的函数.以椭圆弧曲梁为例,采用打靶法求解非线性常微分方程的两点边值问题,获得了两端固定功能梯度椭圆弧曲梁在横向非均匀升温下的热弯曲变形数值解,分析了材料梯度指数、温度参数、结构几何参数等对曲梁受力及变形的影响.     

Initial thermo-mechanical post-buckling of beams with temperature-dependent physical properties

The objective of this work is to analyze the elastic buckling and initial post-buckling behavior of slender beams subjected to uniform heating. The beams are assumed to be double-hinged with fixed ends, preventing thermal expansion. Consequently, destabilizing compressive forces arise that may lead to beam buckling. When the temperature is further increased, the beam experiences finite displacements, with the result that the analysis is geometrically non-linear. The modulus of elasticity and the thermal induced strain, key material properties for this problem, are temperature-dependent. Thus, the coefficients of the governing equations are not constant. This suggests the physical non-linearity of the mathematical model. Hence, the analysis is geometrically and physically non-linear. The analysis is sensitive to the beam initial temperature, as the thermal strain is a function of the initial and final temperatures. The material is considered to be linear elastic, and consequently viscoelastic and plastic effects are not taken into account. Furthermore, the beam cross-section properties are assumed to be constant, which is consistent with the small strain formulation. A perturbation method is applied to the governing non-linear differential equations so that the initial post-buckling behavior may be analytically determined when temperatures above the critical temperature are applied to the beam. To illustrate the application of the formulation we present a case study for the aluminum 7075-T6 alloy, a material commonly used in aerospace and naval industries. Nonetheless, it is expected similar behavior for other metallic materials. The curves that define the variation of the modulus of elasticity, the thermal strain and the yield stress with temperature are considered in our analysis. The change in length, reaction forces at the supports and geometric configurations are obtained as a function of temperature and the beam slenderness ratio. The critical buckling loads and temperatures and the initial post-buckling analysis are also calculated in the context of the temperature-independent physical properties. Our results emphasize the importance of modeling the material's non-linearity if accuracy is required. However, from a practical application point of view results are acceptable if temperature-independent physical properties are employed, especially for large slenderness ratios.     

Dynamic stability analysis of shear-flexible composite beams

Dynamic stability behavior of the shear-flexible composite beams subjected to the nonconservative force is intensively investigated based on the finite element model using the Hermitian beam elements. For this, a formal engineering approach of the mechanics of the laminated composite beam is presented based on kinematic assumptions consistent with the Timoshenko beam theory, and the shear stiffness of the thin-walled composite beam is explicitly derived from the energy equivalence. An extended Hamilton’s principle is employed to evaluate the mass-, elastic stiffness-, geometric stiffness-, damping-, and load correction stiffness matrices. Evaluation procedures for the critical values of divergence and flutter loads of the nonconservative system with and without damping effects are then briefly introduced. In order to verify the validity and the accuracy of this study, the divergence and flutter loads are presented and compared with the results from other references, and the influence of various parameters on the divergence and flutter behavior of the laminated composite beams is newly addressed: (1) variation of the divergence and flutter loads with or without the effects of shear deformation and rotary inertia with respect to the nonconservativeness parameter and the fiber angle change, (2) influence of the internal and external damping on flutter loads whether to consider the shear deformation or not.     

部分共同作用组合梁单元刚度矩阵改进

以钢-混凝土组合梁平衡微分方程的齐次解作为组合梁单元的位移函数，取消了 要求单元两端滑移量为零的假定,给出了钢、混凝土和弹性夹层合而为一的组合梁单元刚度矩 阵和等效节点荷载，为更好地分析由组合梁组成的复杂结构提供了有力的分析工具.     

热载荷作用下梯度多孔材料梁弯曲及过屈曲力学行为的研究

基于Bernoulli-Euler梁理论,引入物理中面解耦了复合材料结构的面内变形与横向弯曲特性,研究了梯度多孔材料矩形截面梁在热载荷作用下的弯曲及过屈曲力学行为．假设沿梁厚度方向材料的性质是连续变化的,利用能量法推导了矩形截面梁的控制微分方程和边界条件,并用打靶法对无量纲化的控制方程进行数值求解．利用计算得到的结果分析了材料的性质、热载荷、边界条件对矩形截面梁非线性力学行为的影响．结果表明,对称材料模型下,固支梁与简支梁均显示出了典型的分支屈曲行为特征,而其临界屈曲热载荷值均会随着孔隙率系数的增加而单调增加．非对称材料模型下,固支梁仍显示出分支屈曲行为特征,但其临界屈曲热载荷不再随着孔隙率系数的变化而单调变化;而对于两端简支梁,发生了弯曲变形,弯曲挠度随载荷的增大而增大．     

横向荷载作用下弹性地基上梁的主共振分析

基于Winkler地基模型及Euler-Bernoulli梁理论,建立了弹性地基上有限长梁的非线性运动方程.运用Galerkin方法对运动方程进行一阶模态截断,并利用多尺度法求得该系统主共振的一阶近似解.分析了长细比、地基刚度、外激励幅值和阻尼系数等参数对系统主共振幅频响应的影响,然后通过与非共振硬激励情况对比分析主共振对其动力响应的影响.结果表明:主共振幅频响应存在跳跃和滞后现象;阻尼对主共振响应有抑制作用;主共振显著增大系统稳态动力响应位移.