Finite difference method for dynamic response analysis of anchorage system

Based on some assumptions, the dynamic analysis model of anchorage system is established. The dynamic governing equation is expressed as finite difference format and programmed by using MATLAB language. Compared with theoretical method, the finite difference method has been verified to be feasible by a case study. It is found that under seismic loading, the dynamic response of anchorage system is synchronously fluctuated with the seismic vibration. The change of displacement amplitude of material points is slight, and comparatively speaking, the displacement amplitude of the outside point is a little larger than that of the inside point, which shows amplification effect of surface. While the axial force amplitude transforms considerably from the inside to the outside. It increases first and reaches the peak value in the intersection between the anchoring section and free section, then decreases slowly in the free section. When considering damping effect of anchorage system, the finite difference method can reflect the time attenuation characteristic better, and the calculating result would be safer and more reasonable than the dynamic steady-state theoretical method. What is more, the finite difference method can be applied to the dynamic response analysis of harmonic and seismic random vibration for all kinds of anchor, and hence has a broad application prospect.

Nonlinear finite element analysis of effect of seismic waves on dynamic response of Shiziping dam

Many high earth-rockfill dams are constructed in the west of China. The seismic intensity at the dam site is usually very high, thus it is of great importance to ensure the safety of the dam in meizoseismal area. A 3D FEM model is established to analyze the seismic responses of Shiziping earth-rockfill dam. The nonlinear elastic Duncan-Chang constitutive model and the equivalent viscoelastic constitutive model are used to simulate the static and dynamic stress strain relationships of the dam materials, respectively. Four groups of seismic waves are inputted from the top of the bedrock to analyze the dynamic responses of the dam. The numerical results show that the calculated dynamic magnification factors display a good consistency with the specification values. The site spectrum results in larger acceleration response than the specification spectrum. The analysis of relative dynamic displacement indicates that the displacement at the downstream side of the dam is larger than that at the upstream side. The displacement response reduces from the center of river valley to two banks. The displacement responses corresponding to the specification spectrum are a little smaller than those corresponding to the site spectrum. The analysis of shear stress indicates that a large shear stress area appears in the upstream overburden layer, where the shear stress caused by site waves is larger than that caused by specification waves. The analysis of dynamic principal stress indicates that the minimum dynamic stresses in corridor caused by specification and site waves have little difference. The maximum and minimum dynamic stresses are relatively large at two sides. The largest tensile stress occurs at two sides of the floor of grouting corridor, which may result in the crack near the corridor side. The numerical results present good consistency with the observation data of the grouting corridor in Wenchuan earthquake.

Numerical Simulation of Elastic Stress Wave Refraction at Air-Solid Interfaces

Elastic wave refraction at the air-solid interface and wave propagations in the vicinity of the air-solid interface are numerically studied.The modified ghost fluid method(MGFM)and isobaric fix methods are combined to solve the fluid and solid statuses at the air-solid interface and construct a continuous boundary condition for the air-solid interface.The states in the ghost domain are evaluated by the MGFM-algorithm.The solid governing equations are solved with second order spatial discretization.Numerical tests verify the correctness of the presented continuous boundary condition and show that the combined method is convergent in the vicinity of the air-solid interface.The 3D numerical results by the combined method are close to those of the ArbitraryLagrangian-Eulerian(ALE)method.The combined method is robust when applied for multi-dimensional problems.A compression stress wave impacting on the air-solid interface result in a compression wave in air.A tension stress wave impacting on the air-solid interface result in an expansion wave in air.

Solution of a problem of thermal stresses in a non-homogeneous thermoelastic infinite medium of isotropic material by finite difference method

The present work deals with a new problem of thermoelasticity for an infinitely long and isotropic circular cylinder of temperature dependent physical properties.The inner and outer curved surfaces of the cylinder are subjected to both the mechanical and thermal boundary conditions.A finite difference model is developed to derive the solution of the problem in which the governing equations are uncoupled linear partial differential equations.The transient solution at any time can be evaluated directly from the model.In order to demonstrate the efficiency of the present model we consider a suitable material and obtain the numerical solution of displacement,temperature,and stresses inside the cylinder for the homogeneous-dependent material properties of the medium.The results are analyzed with the help of different graphical plots.

A symplectic finite element method based on Galerkin discretization for solving linear systems

We propose a novel symplectic finite element method to solve the structural dynamic responses of linear elastic systems.For the dynamic responses of continuous medium structures,the traditional numerical algorithm is the dissipative algorithm and cannot maintain long-term energy conservation.Thus,a symplectic finite element method with energy conservation is constructed in this paper.A linear elastic system can be discretized into multiple elements,and a Hamiltonian system of each element can be constructed.The single element is discretized by the Galerkin method,and then the Hamiltonian system is constructed into the Birkhoffian system.Finally,all the elements are combined to obtain the vibration equation of the continuous system and solved by the symplectic difference scheme.Through the numerical experiments of the vibration response of the Bernoulli-Euler beam and composite plate,it is found that the vibration response solution and energy obtained with the algorithm are superior to those of the Runge-Kutta algorithm.The results show that the symplectic finite element method can keep energy conservation for a long time and has higher stability in solving the dynamic responses of linear elastic systems.

Influence of the Radial Inertia Effect on the Propagation Law of Stress Waves in Thin-Walled Tubes

This investigation focused on the influence of the radial inertia effect on the propagation behavior of stress waves in thin-walled tubes subjected to combined longitudinal and torsional impact loads.Generalized characteristics theory was used to analyze the main features of the characteristic wave speeds and simple wave solutions in thin-walled tubes.The incremental elastic-plastic constitutive relations described by the rate-independent plasticity were adopted,and the finite difference method was used to investigate the evolution and propagation behaviors of combined elasticplastic stress waves in thin-walled tubes when the radial inertial effect was considered.The numerical results were compared with those obtained when the radial inertia effect was not considered.The results showed that the speed of the coupled stress wave increased when the radial inertia effect was considered.The hardening modulus of the material in the plastic stage had a greater impact on the coupled slow waves than on the coupled fast waves.

LARGE EDDY SIMULATION (LES) OF TURBULENT FLOW BY FINITE DIFFERENCE METHOD

A Large Eddy Simulation (LES) technique was applied to solve the turbulentchannel flow for Re_τ = 150 . Three types of turbulence models are employed, such as theSmagorinsky model, the Dynamic Sub-Grid Scale(SGS) model and the Generalized Normal Stress (GNS)model. The simulated data in time series for the LES were averaged in both time and space to carryout the statistical analysis. Results of LES were compared with that of a DNS. As an application, aLES technique was used for 2D body in order to check the validation by investigating the turbulentvortical motion around the afterbody with a slant angle.

Computation on pipe dynamic response induced by deflagration of H_2 and air mixture

Computation is devoted to evaluating structural safety of a heat exchanger inside a reactor whose geometry can be simplified as outer and inner pipes as well as a chamber. This paper has numerically studied deflagration of hydrogen air mixture and pipe dynamic responses. The Navier-Stokes equations coupled with multi-species mass equation are solved by TVD scheme to get flow-field solution based on MPI and multi-block methods. Combustion is described by a 11-species and 23-step reaction model. The source term is treated implicitly to involve species production and depletion. Ignition is approximated by input energy CpT per unit mass in a specified period and zone. Finally,contours of pressure and OH mass fraction at different time pe-riods and pressure histories at fixed points are obtained. When loading is specified as wall pressure,virtual work theorem in Lagrangian frame which describes pipe response is solved by FEM to obtain stress and strain distributions. Results show that shock waves can be generated and reflected on the walls of the chamber and pipes. The shock waves and flame can not be dis-sipated in a narrow gap spanning 2 mm. Meanwhile,stress waves are generated. They propagate outwards on the inner and outer pipe walls. At the gap exit,shock wave diffracts and impacts on the inner pipe walls. Coupled with hot jet from the gap,reignition occurs on the inner pipe wall surfaces. Then,flame catches up the leading shock and shock front deforms into a planar one although the shock front passes through a short divergent section downstream. Also,stress concentrates along the intersected lines among the top,bottom and side walls. This means that the chamber is an easily damaged component. The methods provided in this paper can be used to evaluate structural safety.

DYNAMIC RESPONSE OF LAMINATED ORTHOTROPIC SPHERICAL SHELLSINCLUDING TRANSVERSE SHEAR DEFORMATION AND ROTATORY INERTIA

In this paper.the equations of motion of axisymmetrically laminated cylindrical orthotropic spherical shells are derived.Theeffects of transverse shear deformation and rotatory inertia are considered.On this basis,the dynamic response of spherical shells under axisymmetric dynamic load is calculated using the finite difference method The effects of material parameters.structural parameters and transverse shear dgformation are discussed.

内孤立波作用下缓波形立管动力特性研究

我国南海活跃着大量内孤立波,严重威胁海洋工程作业的安全。本文采用向量式有限元方法分析内孤立波作用下深海缓波形钢悬链立管动力特性,建立考虑触地段土反力和内孤立波载荷的缓波形钢悬链立管动力模型,根据mKdV方程求解内孤立波载荷,基于向量式有限元梁单元编制Fortran计算程序。分析不同入射角内孤立波作用下立管的位移极值、张力及弯矩变化趋势,并比较缓波形立管与简单钢悬链立管在内孤立波作用下的动力特性。结果表明:内孤立波作用下,缓波形钢悬链立管会有较大的位移响应,特别是顶部悬垂段会有较大的水平位移;缓波形立管比简单钢悬链立管有更显著的张力变化幅值,有更加复杂的弯矩变化趋势。

西北季节性冻土场地地震反应特性研究

我国西北地区被季节冻土全覆盖,且近年来该区域地震频发。为研究我国西北地区季节性冻土场地的地震反应特性,开展了季节性冻土场地振动台试验,并建立了不同冻结深度的三维实体有限差分模型,对比分析了不同地震激励作用下的季节性冻土场地的地震反应特征和土体的动剪应力—动剪应变规律。结果表明:在地震激励下,冻土层的存在虽然有效抑制了地震动能量,但冻结期场地的水平位移与非冻结期相比明显较大,且竖向位移呈显著的层状震陷特征;冻土场地的峰值放大系数呈先增大后减小然后再增大的规律,并且冻土层深度越大其峰值放大系数越小。此外,通过土体的动剪应力—动剪应变关系可以发现,冻土场地地震反应具有明显的非线性特征,且冻土层的存在对地震能量具有一定的削弱作用。

滚动轴承内圈不同曲率初始次表面裂纹的扩展仿真研究

滚动轴承内圈次表面裂纹的动态扩展将影响轴承工作的稳定性,继而影响轴承的剩余使用寿命。针对这一问题,研究了滚动轴承内圈上不同曲率的初始次表面裂纹对应力分布和裂纹扩展的影响规律。首先,基于扩展有限元方法,构建了承受径向载荷的圆柱滚子轴承有限元模型;然后,基于滚动轴承次表面裂纹的形态特征,模拟了滚道次表面不同曲率的初始裂纹在径向载荷下的动态扩展过程;最后,基于模拟结果,在相同工况下,分析并讨论了次表面裂纹尖端应力随裂纹曲率的变化规律,以及裂纹尖端应力对裂纹扩展的影响。研究结果表明:在径向载荷作用下,次表面裂纹尖端出现应力集中现象;裂纹的扩展主要受水平方向应力(S_(11))的影响;相同工况下,0.25 mm^(-1)~1.67 mm^(-1)曲率范围内的次表面裂纹,曲率较大的裂纹两端的应力较小;次表面裂纹的曲率越大,裂纹的扩展长度和角度均越小;通过比较相同径向载荷下不同曲率次表面裂纹的扩展长度、扩展角度等,发现曲率较大的次表面裂纹对轴承的损伤程度以及寿命的影响较小。这些研究结果可以为更好地理解和预防轴承损伤提供理论依据和参考。

Time-Domain Nonlinear Wave-Current Interaction with A Steep Wave Riser Considering Internal Flow Effect

The nonlinear dynamic response induced by the wave-current interaction on a deepwater steep wave riser(SWR)is numerically investigated based on a three-dimensional(3 D)time-domain finite element method(FEM).The governing equation considering internal flow is established in the global coordinate system.The whole SWR consists of three segments:the decline segment,buoyancy segment and hang-off segment,in which the buoyancy segment is wrapped by several buoyancy modules in the middle section,leading to the arch bend and sag bend.A Newmark-β iterative scheme is adopted for the accurate analysis to solve the governing equation and update the dynamic response at each time step.The proposed method is verified through the published results for the dynamic response of steel catenary riser(SCR)and static configuration of steel lazy wave riser(SLWR).Simulations are executed to study the influence of wave height,current velocity/direction,internal flow density/velocity and top-end pressure on the tension,configuration and bending moment of the SWR.The results indicate that the influence of the current on the configuration and mechanical behavior of the SWR is greater than that of the wave,especially in the middle section.With increasing current velocity,the suspending height of the middle section drops,meanwhile,its bending moment decreases accordingly,but the tension increases significantly.For a fixed external load,the increasing internal flow density induces the amplification of the tension at the hang-off segment and the mitigation at the decline segment,while the opposite trend occurs at the bending moment.

Stochastic Response Analysis of Piled Offshore Platforms to Earthquake Load

In this paper, using the theory of stochastic analysis of the response to earthquake load, a stochastic analysis method of the response of piled platforms to earthquake load has been established. In the method, the strong ground motion is considered as three dimensional stationary white noise process and the pile-soil interaction and water-structure interaction are considered. The stochastic response of a typical platform to earthquake load has been computed with this method and the results compared with those obtained with the response spectrum analysis method. The comparison shows that the stochastic analysis method of the response of piled platforms to earthquake load is suitable for this kind of analysis.

Mathematical Simulation of Dynamic Heat Transfer in a Human-Clothing-Environment System

A mathematical model has been developed to describe the dynamic heat transfer in the clothing microclimate under transient wear conditions. This model is solved numerically by the implicit finite difference method. If the physical activity and ambient conditions are specified, the model can predict the thermoregulatory response of the body. Experimental measurements with garments made of fibers with different levels of hygroscopicity are compared with predictions by the model. There is good agreement between prediction and experiment for the temperature of the clothing microclimate.

基于谱元法考虑层间接触状态的Rayleigh波频散特征正演计算

为了提升Rayleigh波应用于成层土基勘探的精细化水平,本文基于谱元法原理,通过Goodman模型和Matsui层间滑移系数建立了可考虑层间不同接触状态的Rayleigh波理论频散方程。针对典型土基成层结构,运用谱元法和快速矢量传递解析法对比计算了层间完全连续状态下土基的Rayleigh波多阶模态频散曲线,结果显示谱元法计算结果与解析法相应结果之间的平均相对误差在0.3%以下,具有较高的计算精度。在此基础上,通过改变层间接触状态和敏感性分析,揭示了层间接触状态对Rayleigh波基阶频散特征的影响。最后,结合速度-应力有限差分数值计算,验证了谱元法计算层间不同接触状态下R波频散特征的可靠性。

海上吸力基础式风机结构动力响应研究

由于海上风机受到风浪流荷载的长期作用,因而其动力响应问题成为风机结构设计的关键问题。针对上述情况,以5 MW吸力基础固定式海上风机为研究对象,充分考虑风机基础与土的相互作用等非线性荷载,利用有限元方法建立了综合考虑空气动力、水动力和土壤约束力作用的海上风机整体动力耦合分析模型,在多荷载工况组合下进行了海上风机结构的动力响应分析。研究结果表明,海上风机整体结构位移最大区域在塔筒顶部,应力最大区域在吸力基础与风机塔架的连接处。通过对线性叠加法和Turkstra准则的对比分析验证可以看出,采用Turkstra准则能更准确地获得对风机结构动力响应最不利的荷载组合方式。

应力波在有地下复合结构的岩石介质中传播规律研究

复合结构在抗动荷载方面具有明显的优势,它比一般的结构能够吸收更多的冲击能量。根据f 2.5 m爆炸模拟器上所做的实验结果和动力有限元方法对应力波的传播进行的计算,对应力波在有软回填层的地下复合圆形结构的介质中传播规律及与复合结构体系的相互作用进行了分析研究,给出了应力波在有软回填层的地下复合圆形结构的介质中传播规律。

交变载荷作用下大型振动筛的应力分析

采用ANSYS建立了某型号大型振动筛的有限元模型,仿真分析了振动筛处于不同交变载荷作用下的谐响应.结果表明:振动筛无论做直线运动还是做椭圆运动,其结构薄弱处均出现在入料口端加强板与侧板三角区域,如将加强板向振动筛入料口端延伸,则可以降低筛箱最大应力幅值,实现延长振动筛寿命的目的.所用建模方法与分析思路亦可为其他振动机械装备的研究提供参考。

挤压油膜阻尼器转子系统非线性动力特性分析

为了对挤压油膜阻尼器 (SFD) 转子系统非线性动力特性进行分析 ,提出了油膜力数据库方法 ,即将挤压油膜阻尼器轴颈沿径向和周向的速度变化范围从 (-∞ ,+∞ )转化到 (- 1,+ 1) ,给定阻尼器的长径比 ,用有限差分法建立了挤压油膜阻尼器轴颈在各离散运动状态下的油膜力数据库 ,直接或通过插值求得对应运动状态下的非线性油膜力 ,从而有效地解决了非线性油膜力的快速计算问题。实际算例计算结果表明 ,该方法无论在速度还是在精度上都能满足要求 ,对实际转子系统的动力特性分析及优化设计具有一定的应用价值。