关节软骨两相多孔介质非线性模型的有限元方法

基于混合物理论的两相多孔介质模型可以准确描述关节软骨的力学行为，关节软骨的渗透率与固体相体积应变相关。本文研究这一模型的非线性有限元法。具体采用伽辽金加权残值法得到有限元平衡方程，编制了有限元程序，进而对关节软骨围限压缩蠕变和应力松弛行为进行了数值模拟。与视渗透率为常数的线性模型的计算结果比较表明，在变形较大时，渗透率随固体相体积应变变化这一非线性效应不容忽视。     

饱和多孔介质大变形分析的一种有限元-有限体积混合方法

建立了饱和多孔介质大变形分析的一种有限元-有限体积混合计算方法.将饱和多孔介质视为由固体骨架和孔隙水组成的两相体,其基本方程包括动力平衡方程和渗流连续方程.基于u-p假定和更新的Lagrange方法,饱和多孔介质的动力平衡方程在空间域内采用有限元方法进行离散,而渗流连续方程在空阃域内则采用有限体积法进行离散.通过两个数值算例,一维有限弹性固结和动力荷载作用下堤坝动力响应的计算,验证了该方法的有效性.     

Quasi-Static and Dynamic Behavior of Saturated Porous Media with Incompressible Constituents

In this paper the field equations governing the dynamic response of a fluid-saturated elastic porous medium are analyzed and built up for the study of quasi-static and dynamical problems like the consolidation problem and wave propagation. The two constituents are assumed to be incompressible. A numerical solution is derived by means of the standard Galerkin procedure and the finite element method.     

Some generic capillary-driven flows

This paper deals with numerical simulations of some capillary-driven flows. The focus is on the wetting phenomenon in sintering-like flows and in the imbibition of liquids into a porous medium. The wetting phenomenon is modeled using the coupled Cahn–Hilliard/Navier–Stokes system. The Cahn–Hilliard equation is treated as a system where the chemical potential is solved first followed by the composition. The equations are discretised in space using piecewise linear functions. Adaptive finite element method is implemented with an ad hoc error criterion that ensures mesh resolution along the vicinity of the interface. In the 3D case we use parallel adaptive finite element method. First, a basic wetting of a liquid drop on a solid surface is shown and is established the independence of the dynamic contact angle on the interface width. In addition, the dependence of the dynamic contact angle on the Capillary number is matched with experimental data. Next, some generic sintering-like flows with a fixed matrix is presented. Different geometries in 2D and 3D are considered. We observed rapid wetting, precursor films, coalescence, breakup of melt drops as well as pore migration and elimination that are all microstructural characteristics of a liquid phase sintering. Finally, the effect of equilibrium contact angles on imbibition of liquid into a porous medium is studied.     

基于显式有限元方法的两相介质弹塑性动力反应计算分析

针对增量形式的流体饱和两相多孔介质弹塑性波动方程组,运用基于显式逐步积分格式的时域显式有限元方法对该波动方程组进行求解,并应用基于SMP破坏准则的弹塑性动力本构模型描述两相介质的动力反应性质,对两相介质在输入地震波作用下的弹塑性动力反应进行计算和分析,将计算结果与相应的弹性动力反应的计算结果进行对比;对本文应用的弹塑性...     

The effect of numerical methods on the simulation of mid-ocean ridge hydrothermal models

This work considers the effect of the numerical method on the simulation of a 2D model of hydrothermal systems located in the high-permeability axial plane of mid-ocean ridges. The behavior of hot plumes, formed in a porous medium between volcanic lava and the ocean floor, is very irregular due to convective instabilities. Therefore, we discuss and compare two different numerical methods for solving the mathematical model of this system. In concrete, we consider two ways to treat the temperature equation of the model: a semi-Lagrangian formulation of the advective terms in combination with a Galerkin finite element method for the parabolic part of the equations and a stabilized finite element scheme. Both methods are very robust and accurate. However, due to physical instabilities in the system at high Rayleigh number, the effect of the numerical method is significant with regard to the temperature distribution at a certain time instant. The good news is that relevant statistical quantities remain relatively stable and coincide for the two numerical schemes. The agreement is larger in the case of a mathematical model with constant water properties. In the case of a model with nonlinear dependence of the water properties on the temperature and pressure, the agreement in the statistics is clearly less pronounced. Hence, the presented work accentuates the need for a strengthened validation of the compatibility between numerical scheme (accuracy/resolution) and complex (realistic/nonlinear) models.     

Numerical and experimental study on the dynamic behavior of a sea-star tension leg platform against regular waves

This paper describes an experimental work on a 1: 100 scaled model of a miniature sea-star tension leg platform (TLP) in a wave flume. Two different numerical models are developed: finite element model (FEM) based on the Morison equation and boundary element model (BEM) based on a 3D diffraction/radiation theory. The developed codes are used to calculate hydrodynamic forces and related coefficients. The nonlinear hull/tendon coupled dynamic equation of a mini seastar TLP is solved by using a modified Euler method (MEM). The results of numerical modeling of the motion response behavior of the platform in different degrees of freedom are compared with experimental data. This comparison shows good agreement between the results. Furthermore, this modeling reveals that the first-order diffraction method and quasi-static tendon modeling are sufficient in general for the hydrodynamic analysis of the sea-star TLP.     

前进式U形通风采空区风流与自燃的数值模拟

基于渗流方程、多组分气体渗流-扩散方程和多孔介质渗流传热方程,建立前进式开采U型 通风采空区自然发火模型. 通过迭代方法计算沿空巷道的侧漏风量,以此边界条件数值模拟 计算出前进式开采U型通风采空区的漏风规律;根据瓦斯-Ohttp://d.wanfangdata.com.cn/Periodical_lxysj200804005.aspx前进式开采U型通风;采空区;风流规律;自燃温度场;有限元; 基于渗流方程、多组分气体渗流-扩散方程和多孔介质渗流传热方程,建立前进式开采U型 通风采空区自然发火模型. 通过迭代方法计算沿空巷道的侧漏风量,以此边界条件数值模拟 计算出前进式开采U型通风采空区的漏风规律;根据瓦斯-Ohttp://d.wanfangdata.com.cn/Periodical_lxysj200804005.aspx前进式开采U型通风;采空区;风流规律;自燃温度场;有限元; 基于渗流方程、多组分气体渗流-扩散方程和多孔介质渗流传热方程,建立前进式开采U型 通风采空区自然发火模型. 通过迭代方法计算沿空巷道的侧漏风量,以此边界条件数值模拟 计算出前进式开采U型通风采空区的漏风规律;根据瓦斯-Ohttp://d.wanfangdata.com.cn/Periodical_lxysj200804005.aspx前进式开采U型通风;采空区;风流规律;自燃温度场;有限元;基于渗流方程、多组分气体渗流-扩散方程和多孔介质渗流传热方程,建立前进式开采U型通风采空区自然发火模型.通过迭代方法计算沿空巷道的侧漏风量,以此边界条件数值模拟计算出前进式开采U型通风采空区的漏风规律;根据瓦斯-O2-CO浓度和温度分布状态及其变化来描述自燃过程.在计算中,采空区非均质性按自然冒落考虑,兼顾瓦斯涌出对自燃的耦合作用;模拟得到,在前进式开采特有的3面漏风边界条件下,采空区自燃位置(最高温点)在开切眼冒落区进风一侧,自燃产生的有害气体和瓦斯随漏风流从回风边界渗出.在前进开采U型通风形式下,通风量在到达工作面时衰减很大,因此,前进开采布置一次推进距离不易过大;解决好沿空留巷的封堵材料和正确的堵漏措施,是保证前进式开采顺利进行的技术关键.     

非线性随机结构动力可靠度的密度演化方法

建议了一类新的非线性随机结构动力可靠度分析方法。基于非线性随机结构反应分析的概率密度演化方法,根据首次超越破坏准则对概率密度演化方程施加相应的边界条件,求解带有初、边值条件的概率密度演化方程,可以给出非线性随机结构的动力可靠度。研究了数值计算技术,建议了具有自适应功能的TVD差分格式。以具有双线型恢复力性质的8层框架结构为例进行了地震作用下的动力可靠度分析,与随机模拟结果的比较表明,所建议的方法具有较高的精度和效率。     

以DIASS程序为基础的饱和土与防护结构相互作用动力分析研究

介绍了新开发的防护结构动力有限元分析程序DIASS系统。该系统装有空爆冲击波荷载数值自动生成器,并可将基础土壤模拟为饱和多孔介质模型,采取多重子结构技术进行结构与土体相互作用的动力分析。文中利用该程序系统进行数值试验,给出若干初步结论。     

Nonlinear numerical simulation method for galloping of iced conductor

Based on the principle of virtual work, an updated Lagrangian finite element formulation for the geometrical large deformation analysis of galloping of the iced conductor in an overhead transmission line is developed. In numerical simulation, a three-node isoparametric cable element with three translational and one torsional degrees-of-freedom at each node is used to discretize the transmission line. The nonlinear dynamic system equation is solved with the Newmark time integration method and the Newton-Raphson nonlinear iteration. Numerical examples demonstrate the efficiency of the presented method and the developed finite element program. A new possible galloping mode, which may reflect the saturation phenomenon of a nonlinear dynamic system, is discovered under the condition that the lowest order of vertical natural frequency of the transmission line is approximately two times of the horizontal one.     

Fluid–structure interaction modelling of nonlinear aeroelastic structures using the finite element corotational theory

The application of the finite element corotational theory to model geometric nonlinear structures within a fluid–structure interaction procedure is proposed. A dynamic corotational approximately-energy-conserving algorithm is used to solve the nonlinear structural response and it is shown that this algorithm's application with a four-node flat finite element is more stable than the nonlinear implicit Newmark method. This structural dynamic algorithm is coupled with the unsteady vortex-ring method using a staggered technique. These procedures were used to obtain aeroelastic results of a nonlinear plate-type wing subjected to low speed airflow. It is shown that stable and accurate numerical solutions are obtained using the proposed fluid–structure interaction algorithm. Furthermore, it is illustrated that geometric nonlinearities lead to limit cycle oscillations.     

考虑空气耦合的薄膜结构动力分析

假定空气是可压缩、无粘性和有势的,推导了薄膜结构的非线性刚度矩阵和空气与薄膜结构耦合作用的气动力表达式。根据薄膜结构的受力特点,建立了薄膜结构与空气耦合系统的运动方程。采用有限元方法对无限域的空气进行简化,建立了空气与薄膜结构的耦合有限元模型,模拟了空气对薄膜结构的附加质量和声致阻尼影响。考虑薄膜结构的几何非线性,对结构在空气中的自由振动和受迫简谐振动进行了系统分析,同时探讨了流体环境对薄膜结构动力响应的影响因素。     

不确定非线性结构动力响应的区间分析方法

研究多自由度非线性不确定参数系统的动力响应问题. 以区间数学为基础，将不确定 性参数用区间进行定量化，借助一阶Taylor级数，给出了近似估计非线性振动系统动力响 应范围的区间分析方法. 从数学证明和数值算例两方面，将其与概率摄动有限元法进行了比 较，结果显示区间分析方法对不确定参数先验信息具有要求较少、精度较高的优点.     

简谐载荷下嵌入式单壁碳纳米管动态响应的Magnus方法

基于两端固支的弹性梁模型,研究嵌入式单壁碳纳米管在横向简谐载荷作用下的非线性振动问题。利用Galerkin方法对运动微分方程进行近似处理,将原方程从非线性动力学系统转化到二阶动力学系统,对于二阶动力学方程采用Magnus级数方法进行求解。通过数值实验,分析了嵌入式单壁碳纳米管非线性振动幅频特性,根据非线性动力学理论分析了碳纳米管动态响应,结果表明倍周期分岔产生混沌。     

Analysis of interlaminar stress and nonlinear dynamic response for composite laminated plates with interfacial damage

By considering the effect of interfacial damage and using the variation principle, three-dimensional nonlinear dynamic governing equations of the laminated plates with interfacial damage are derived based on the general sixdegrees-of-freedom plate theory towards the accurate stress analysis. The solutions of interlaminar stress and nonlinear dynamic response for a simply supported laminated plate with interfacial damage are obtained by using the finite difference method, and the results are validated by comparison with the solution of nonlinear finite element method. In numerical calculations, the effects of interfacial damage on the stress in the interface and the nonlinear dynamic response of laminated plates are discussed.     

基于互补理论和扩展有限元法的摩擦接触裂纹应力强度因子计算

从虚功方程出发，结合扩展有限元离散技术与接触条件的非线性互补表述，建立了摩擦接触裂纹问题的扩展有限元非线性互补模型，将不等式接触条件转化为非线性互补类的非光滑方程组，并采用基于广义导数的非光滑阻尼牛顿法求解方程组，无需引入任何额外人工变量以及迭代求解。以含中心倾斜裂纹平板和边裂纹平板为例，运用相互作用积分法计算摩擦接触裂纹的应力强度因子，将其结果与理论解进行对比分析，该方法都能给出精确的计算结果；基于扩展有限元方法对单轴压缩作用下倾斜裂纹扩展过程进行了数值模拟，计算结果表明，受压裂纹数值结果与实验结果比较吻合，从而验证了本文方法的有效性与正确性。     

一种三维饱和土-基础-结构动力相互作用分析方法

地震波入射时土与结构动力相互作用分析是地震工程领域的重要问题.由于问题的复杂性,以往的研究大多考虑地基土为干土情形.而实际工程中,土体中经常充满孔隙水,土层往往是含水层或部分含水层.孔隙水对土层的地震反应影响较大,进而影响支撑于其上的基础和上部结构的响应.因此,有必要考虑饱和土-基础-结构动力相互作用问题.基于此,土体采用Biot模型,利用集中质量显式有限元方法并结合多次透射人工边界进行模拟;结构经有限元离散后,采用Newmark隐式时步积分方法进行分析,可通过ANSYS等有限元软件实现;基础假定为刚性,采用显式时步积分进行求解;土体和结构(及基础)可分别采用不同的时间步距;通过FORTRAN程序实现了三维饱和土-基础-结构系统在地震作用下的整体分析.从饱和多孔介质动力微分方程出发可知,干土是饱和土的特殊情形,通过将流体体积模量及孔隙率置为零,可将饱和土退化到干土,从而将干土统一到饱和土的计算框架中,通过土-结构相互作用算例对此进行了验证,进一步实现了干土与饱和土混合情形时的土-结构动力相互作用分析,使得问题的模拟更贴近实际工程(如考虑地下水位情形).通过算例对比了饱和土地基、干土地基、干土覆盖饱和土地基(考虑地下水位)情形时,土-结构相互作用对基础和结构响应的影响,结果表明地下水位对基础和结构响应的影响较大.     

Simulation of Coupled Viscous and Porous Flow Problems

Theoretical and numerical formulations are presented for the conjugate problem involving incompressible flow and flow in a saturated porous medium. The major focus of the work is the development of a generally applicable finite element method for the simulation of both fixed interface and evolving porous interface problems. The available alternatives for coupling Darcy and non-Darcy models to the Navier-Stokes equations have been studied and evaluated in a mixed finite element framework. Questions regarding convergence of the finite element method for porous flow models have been addressed. Numerical experiments on simple flow geometries have revealed the shortcomings of both the Darcy and Brinkman models. Application of the more realistic models to practical, multidimensional, flow studies has also been demonstrated.     

冲击波和气泡作用下舰船结构动态响应的数值模拟

针对水下爆炸载荷、瞬态流固耦合效应在舰船水下爆炸数值模拟中的困难,在现有水下爆炸载荷计算模型(Geers and Hunter)的基础上,结合边界元法,修正水下爆炸气泡载荷计算方法.针对用二阶双渐近法(the second-order doubly-asymptotic approximation,DAA2)在处理低频...