应力波传播与屈曲耦合情况下结构动力屈曲控制方程探讨

从应力波作用下结构动力屈曲的特点出发,指出应力波作用下结构动力屈曲与结构中应力波传播的耦合导致时间成为结构动力屈曲的参变量,从而应力波作用下结构动力屈曲问题中结构的真实运动与邻近运动是不同时刻、不同扰动区域的比较,这使得其动力屈曲控制方程的建立不宜采用传统的等时积分变分原理;以压应力波作用下弹性直杆为例,应用能量守恒原理,根据屈曲时刻结构能量的转换关系,建立了弹性压应力波作用下半无限长直杆的动力屈曲控制方程,并得到了波前附加约束条件;最后,讨论了波前附加约束条件的物理意义,指出波前附加约束条件出现的根本原因是轴向应力波的传播与屈曲不能解耦。     

应力波传播与屈曲耦合情况下结构动力屈曲控制方程及波前边界条件的探讨

从应力波作用下结构动力屈曲的特点出发,指出应力波作用下结构屈曲与应力波传播的耦合导致时间成为结构屈曲的参变量,从而应力波作用下结构屈曲的真实运动与邻近运动是不同时刻、不同扰动区域的比较,这使得其控制方程的建立不宜采用传统的等时积分变分原理;以压应力波作用下弹性直杆为例,应用能量守恒原理,根据屈曲时刻结构能量的转换关系,建立了其屈曲控制方程,并实际推导得到了波前边界条件为横向位移,转角和曲率为零;其中,波前边界第三个条件出现的原因是轴向应力波的传播与屈曲的耦合.     

含纤维搭桥的正交各向异性材料非线性矩形脱层屈曲分析

本文基于用挠度和应力函数表示的考虑含纤维搭桥影响的正交各向异性材料矩形脱层屈曲非线性方程组,采用伽辽金法获得了非线性矩形脱层屈曲的理论解,给出了屈曲载荷随脱层中心挠度、纤维搭桥因子及脱层几何和材料参数变化的解析关系式.通过理论计算与有限元数值结果的对比,验证了解的正确性.本文解可有效用于分析材料参数和几何参数以及纤维搭桥作用对结构非线性脱层屈曲行为的影响,对于复合材料抗压屈曲强度设计具有重要参考价值.     

预应力杂交结构的屈曲分析

含有预应力索的半刚性大跨度空间结构是一种非常有生命力的杂交钢结构形式,对应用日益广泛的空间杂交结构的正确分析是保证结构安全设计的前提,屈曲分析通常是这类结构分析的主要内容之一,结构的屈曲分析可分为特征值屈曲分析和非线性屈曲分析。论文首先阐述了结构特征值屈曲分析和非线性屈曲分析中的分枝屈曲分析的基本理论,提出了含有恒定荷载的预应力结构特征值的求解方法,明确正确应用屈曲理论对保证工程安全设计的重要性,然后应用有限元软件ANSYS对待建的安徽大学体育馆新型弦支网壳屋盖结构进行了特征值屈曲分析和分枝屈曲分析,提出应用通用有限元程序跟踪结构分枝屈曲路径的方法,本文结论对预应力杂交结构的屈曲分析具有指导意义。     

海底管道的弹塑性稳定性和屈曲传播

本文根据我国南海海底输油气铺管的要求系统分析了海底管道在弯曲与外水压力共同作用下的弹塑性稳定性和屈曲传播.研究了管道的极值型屈曲和分枝型屈曲.在考虑管道的初始非圆度和材料的物理非线性的情况下提出了临界屈曲载荷的计算方法.综述和评论了屈曲传播现象的本质和各种计算方法.介绍了我们所进行的全尺寸管道实验.在分析理论结果时与现行的有关设计规程进行了比较和评论.     

跨中集中荷载作用下弹性约束圆弧拱的稳定性分析

研究了跨中集中荷载作用下两端由不同转动刚度弹性约束的铰支圆弧拱的面内稳定性。由变形几何关系、变分原理得到了拱的非线性平衡方程,建立了外荷载、结构内力、径向位移的对应关系,通过定义拱的深浅参数和约束刚度参数进行分析,并得到了跳跃屈曲和分岔屈曲的发生条件及存在区间。通过数值分析可知本文方法所得屈曲路径和屈曲荷载与有限元法所得结论吻合良好,极值点、临界荷载相对差值在1%左右。对不同结构参数区间圆弧拱在集中荷载作用下的屈曲路径和临界荷载进行了分析,结果表明约束刚度对屈曲路径和临界荷载起决定性的作用,深浅参数决定屈曲发生条件、屈曲形式、极值点对数。     

非线性地基上弹性梁屈曲传播抑制的动力有限元分析

基于非线性地基弹性梁屈曲传播的动态控制方程，考虑梁质量惯性的影响，用有限元和时间积分相结合的方法，计算了分析了止屈器对梁屈曲传播抑制的作用，止屈器是通过局部加大地基刚度加以模拟。研究表明：考虑动态得到的止屈效果和前人以准静态为前提的结果相比有明显不同。     

压电板屈曲和后屈曲的有限元分析

采用板的一附剪切理论,并考虑结构的几何非线性,基于Ｔｏｔａｌ Ｌａｇｒａｎｇｅ方法,建立了在弱非线性耦合假设下压电智能的有限元控制方法,分析了没边界条件下压电板的屈曲和后屈曲,计算结果表明,在单向压力作用下,材料的压电效应和外加电压对板的屈曲载荷及后屈曲影响很小;而电场对位移加载简支板的屈曲影响较显著。该文为压电材料的工程应用提供了理论指导,同时提供了一种有效的有限元分析方法。     

非线性弹性地基梁在随动载荷作用下的屈曲和振动

基于可伸长梁的几何非线性理论,建立了非线性弹性地基上梁在随动载荷作用下的屈曲问题和振动问题控制方程,分别采用打靶法分析了弹性地基梁的后屈曲行为以及后屈曲构形上的振动问题。给出了不同非线性弹性地基系数下,梁在随动载荷作用下的过屈曲平衡路径曲线以及过屈曲附近前三阶频率随载荷变化的曲线。研究表明:立方刚度系数K_2对梁的屈曲和振动影响较小,而线性刚度系数K_1对梁的过屈曲性态和固有频率都有影响。     

冲击扭矩作用下碳纳米管动力屈曲的研究

为了研究碳纳米管在冲击扭矩作用下的动力屈曲,采用了连续模型将碳纳米管模拟成半无限长的弹性连续圆柱壳。将冲击扭矩作用下碳纳米管的动力屈曲问题归结为由于扭转应力波传播导致的分叉问题,此分叉问题被化为一个非线性方程组的求解。最后进行了数值分析,讨论了碳纳米管的不同参数对动力屈曲的影响,发现碳纳米管有极强的抗冲击性,临界屈曲剪应力可高达几百吉帕。     

DYNAMIC ANALYSIS OF ARREST OF BUCKLE PROPAGATION ON A BEAM ON A NONLINEAR ELASTIC FOUNDATION BY FEM

Based on the dynamic governing equation of propagating buckle on a beam on a nonlin-ear elastic foundation,this paper deals with an important problem of buckle arrest by combining theFEM with a time integration technique.A new conclusion completely different from that by the quasi-static analysis about the buckle arrestor design is drawn.This shows that the inertia of the beam cannotbe ignored in the analysis under consideration,especially when the buckle propagation is suddenlystopped by the arrestors.     

页岩水力压裂中多簇裂缝扩展的全耦合模拟

水平井和水力压裂是页岩气开发中的关键技术。对水力压裂中多簇裂缝同时扩展的物理过程进行了数值模拟。采用扩展有限元法(XFEM)模拟岩石中裂缝沿着任意路径扩展,采用有限体积法(FVM)模拟裂缝中流体的流动,并且考虑井筒中流体流动以及在各簇裂缝间的流量动态分配。通过牛顿迭代对全耦合物理过程进行数值求解,重点研究了初始长度不同的两条裂缝的扩展过程,证明较大的射孔摩阻能促进两条裂缝的同时扩展。并通过算例证明了本方法的精度和有效性。     

深海保温输油管后屈曲及屈曲传播的有限元分析

本文运用ABAQUS有限元软件模拟深海输油管道的后屈曲及屈曲传播现象．将深海输油管道视为内、外层为合金钢材,夹心为聚氨酯泡沫的输油管道．采用线弹性-线性硬化的本构关系,运用Riks分析法获得后屈曲平衡路径,以此模拟管道中的屈曲传播过程,并获得屈曲传播压力．通过数值算例,综合讨论了不同初始缺陷、不同径厚比、不同夹层与夹心厚度比对、不同的材料弹性模量对屈曲传播过程和压力的影响．最后将输油管退化为单层管,将传播压力的有限元结果与实验结果、 Palmer理论解比较．结果表明有限元值、实验结果、理论值三者比较吻合．验证了有限元分析的正确性．     

Wave propagation in a fluid wedge over a solid half-space – Mesh-free analysis with experimental verification

Interaction between a bounded ultrasonic beam and a liquid wedge over a solid half-space is studied. A semi-analytical technique called distributed point source method (DPSM) is adopted for modeling the ultrasonic field in a wedge shaped fluid structure over a solid half space. This study is important for analyzing the ultrasonic waves used for the non-destructive inspections of partially immersed structures. It is also useful for studying the effect of underwater ultrasonic or acoustic wave experiments on marine lives near the shore. The problem geometry considers a bounded acoustic beam striking a fluid–solid interface between a fluid wedge and a solid half-space at steady-state. Solution of this problem is beyond the scope of the currently available analytical methods when the beam is bounded. Only numerical method (boundary element method (BEM) or finite element method (FEM)) based packages (e.g. PZFlex) are in principle capable of modeling ultrasonic fields in such structures. At high frequencies FEM and BEM based packages require huge amount of computation memory and time for their executions that DPSM technique can avoid. Effect of the angle of strike and the fluid wedge angle variation on the wave propagation characteristics is studied. Theoretical predictions are compared with some experimental results.     

Numerical investigation of ice breaking by a high-pressure bubble based on a coupled BEM-PD model

In this paper, by combining the boundary element method (BEM) and peridynamics (PD), a bubble-ice interaction model is established, which can investigate the dynamic interactions between a high-pressure bubble and an ice plate with particular focus on the mechanical behaviors of ice breaking. The bubble dynamics are solved by BEM based on the potential flow theory. Ice cracks initiation and propagation are simulated by the bond-based peridynamics which is validated by a three-point bending test. The fluid–structure interaction (FSI) is achieved by matching the normal velocity and hydrodynamic loads at the fluid–structure interface. To validate the proposed FSI model, an experiment is carried out in which an oscillating bubble is generated under an ice plate by underwater discharge system. The whole interaction process is captured by a Phantom V711 high-speed camera. Qualitative agreements are achieved between the numerical and experimental results. The underlying mechanism of cracks initiation, propagation, branching, and coalescence of the ice plate is found to highly depend on three parameters, i.e., bubble–ice distance, ice thickness and bubble size. The present study is expected to provide further assists in the understanding of ice breaking problems.     

A spectrally formulated finite element for wave propagation analysis in functionally graded beams

In this paper, spectral finite element method is employed to analyse the wave propagation behavior in a functionally graded (FG) beam subjected to high frequency impulse loading, which can be either thermal or mechanical. A new spectrally formulated element that has three degrees of freedom per node (based upon the first order shear deformation theory) is developed, which has an exact dynamic stiffness matrix, obtained by exactly solving the homogeneous part of the governing equations in the frequency domain. The element takes into account the variation of thermal and mechanical properties along its depth, which can be modeled either by explicit distribution law like the power law and the exponential law or by rule of mixture as used in composite. Ability of the element in capturing the essential wave propagation behavior other than predicting the propagating shear mode (which appears only at high frequency and is present only in higher order beam theories), is demonstrated. Propagation of stress wave and smoothing of depthwise stress distribution with time is presented. Dependence of cut-off frequency and maximum stress gradient on material properties and FG material (FGM) content is studied. The results are compared with the 2D plane stress FE and 1D Beam FE formulation. The versatility of the method is further demonstrated through the response of FG beam due to short duration highly transient temperature loading.     

Thermo‐hydrodynamic‐mechanical multiphase flow model for CO2 sequestration in fracturing porous media

In this paper, we introduce a fully coupled thermo‐hydrodynamic‐mechanical computational model for multiphase flow in a deformable porous solid, exhibiting crack propagation due to fluid dynamics, with focus on CO₂ geosequestration. The geometry is described by a matrix domain, a fracture domain, and a matrix‐fracture domain. The fluid flow in the matrix domain is governed by Darcy's law and that in the crack is governed by the Navier–Stokes equations. At the matrix‐fracture domain, the fluid flow is governed by a leakage term derived from Darcy's law. Upon crack propagation, the conservation of mass and energy of the crack fluid is constrained by the isentropic process. We utilize the representative elementary volume‐averaging theory to formulate the mathematical model of the porous matrix, and the drift flux model to formulate the fluid dynamics in the fracture. The numerical solution is conducted using a mixed finite element discretization scheme. The standard Galerkin finite element method is utilized to discretize the diffusive dominant field equations, and the extended finite element method is utilized to discretize the crack propagation, and the fluid leakage at the boundaries between layers of different physical properties. A numerical example is given to demonstrate the computational capability of the model. It shows that the model, despite the relatively large number of degrees of freedom of different physical nature per node, is computationally efficient, and geometry and effectively mesh independent. Copyright © 2017 John Wiley & Sons, Ltd.     

A non-linear analysis of non-isothermal wave propagation in linear-elastic fluid-saturated porous media

The non-isothermal dynamic behaviour of saturated porous media is analysed numerically employing the finite element method and taking energy convection due to large pore fluid displacements into account. A different pore fluid reference temperature is introduced in order to allow properly for heat convection: this concept is usually neglected in the literature and is discussed and analysed herein. The numerical procedure is validated in a simple problem of hot fluid injection in a steady seepage flow and by comparing the numerical results, neglecting energy convection, with those obtained with a novel solution of the linearised equations, presented herein, which is based on the transfer functions and Fourier transforms method. Finally, the effects of energy convection in wave propagation are analysed: in a pervious porous medium the flux of energy due to energy convection is much greater than the one due to heat conduction; in any case, wave propagation can be considered completely adiabatic even when energy convection is taken into account. Thus the validity of the results presented in the literature and based on the linearised theory is demonstrated.     

基于势流理论的内孤立波与立管作用数值研究

内孤立波是一种发生在水面以下的在世界各个海域广泛存在的大幅波浪, 其剧烈的波面起伏所携带的巨大能量对以海洋立管为代表的海洋结构物产生严重威胁, 分析其传播演化过程的流场特征及立管在内孤立波作用下的动力响应规律对于海洋立管的设计具有重要意义. 本文基于分层流体的非线性势流理论, 采用高效率的多域边界单元法, 建立了内孤立波流场分析计算的数值模型, 可以实时获得内孤立波的流场特征. 根据获得的流场信息, 采用莫里森方程计算内孤立波对海洋立管作用的载荷分布. 将内孤立波流场非线性势流计算模型与动力学有限元模型结合来求解内孤立波作用下海洋立管的动力响应特征, 讨论了内孤立波参数、顶张力大小以及内部流体密度对立管动力响应的影响. 发现随着内孤立波波幅的增大, 海洋立管的流向位移和应力明显增大. 由于上层流体速度明显大于下层, 且在所研究问题中拖曳力远大于惯性力, 因此管道顺流向的最大位移发生在上层区域. 顶张力通过改变几何刚度阵的值进而对立管的响应产生明显影响. 对于弱约束立管, 内部流体的密度对管道的流向位移影响较小.