边界层理论中非稳态流体方程的数值解

非稳态流体方程是边界层流问题中的一个典型方程,是一个定义在半无限区间上的一维三阶非线性方程,采用有限差分法求解它的数值解.方法是通过将半无限区间上的三阶非线性微分方程转化成有限区间上的二阶微分形式,并构造出相应的有限差分方程来求得数值解.结果表明该方法是有效的.     

非线性阻尼吸振器应用于主系统受迫振动的一阶近似解

研究利用非线性阻尼吸振器应用于主系统受迫振动的情形，运用伽辽金法求出系统运动和微分方程的近似解。     

摄动Wadati-Segur-Ablowitz方程的精确行波解

利用G′/G展开方法求解摄动的Wadati-Segur-Ablowitz（WSA）方程的解,并得到该方程推广形式的行波解,这几组行波解对Schrdinger方程的适定性的研究、可变为Lienard方程形式的一类非线性偏微分方程行波解的求解都有重要意义.为了更好的理解这几组行波解,给出了解的数值模拟图,通过数值模拟图可以直观的了解WSA方程中摄动项对方程波幅的影响.     

固体含源导热问题的Hamilton原理及其解析方法

变分原理的推导一般采用试凑法或Lagrange乘子法.基于固体瞬态热传导的微分方程,利用奥奇西克分部积分法建立固体含源导热问题的Hamilton原理.该原理可以用于构建新的有限元数值算法,也可以用于获得一些复杂边界问题的新解析解.分析Hamilton原理在热传导问题解析解方面的应用,利用康托洛维奇—里茨杂交法给出2个算例的近似解析解和精确解析解,从而证明建立的Hamilton原理及其解析解法的正确性和有效性.讨论基于热质理论的Hamilton原理存在的问题.     

求解二阶线性常微分方程的一个显式差分格式

在求解常微分方程的方法中,有限差分法是使用最广泛的方法之一。考虑一个二阶线性常微分方程的边值问题,利用有限差分法,建立了一个具有二阶精度的显式差分格式。首先,通过讨论该显式差分格式的系数矩阵,证明了该显式差分格式解的存在性。然后,通过定义的3种不同范数之间的关系,证明了显式差分格式解的收敛性和稳定性。最后,通过计算机编程对实例的计算,验证了该显式差分格式的数值结果具有二阶精度,并且该显式格式数值结果绘制的图形稳定、光滑,与解析结果吻合较好。     

求解二阶线性常微分方程的一个显式差分格式

在求解常微分方程的方法中,有限差分法是使用最广泛的方法之一。考虑一个二阶线性常微分方程的边值问题,利用有限差分法,建立了一个具有二阶精度的显式差分格式。首先,通过讨论该显式差分格式的系数矩阵,证明了该显式差分格式解的存在性。然后,通过定义的3种不同范数之间的关系,证明了显式差分格式解的收敛性和稳定性。最后,通过计算机编程对实例的计算,验证了该显式差分格式的数值结果具有二阶精度,并且该显式格式数值结果绘制的图形稳定、光滑,与解析结果吻合较好。     

一种基于预估校正法的解常微分方程的方法

由预估校正法，构造了一个收敛加速的解微分方程的方法，即所谓的二阶Ｃ变换法。此法的稳定域与校正法的相同，数值检验表明此新方法很有用。     

等参数水均衡有限元法及与其它方法的比较

本文按局部质量守恒原则,采用非线性基函数,导出了求解渗流问题的又一种数值法——等参数水均衡有限元法。在一般情况下,它克服了采用线性基函数的有限元方法的某些理论缺陷。与采用同样非线性基函数的等参数里茨有限元法或伽辽金有限元法相比,也具有物理意义明确、计算公式简单及易于接受使用等优点。     

计算Darcy流速时第一类边界的处理

提出了一种求解Darcy流速时一类边界的处理方法.该法利用有限元方程得出一类边界节点的水力坡度和渗流速度,并且模拟了一个理想算例,结果显示解析解与数值解吻合地很好,这表明了该法的有效性.     

应用有限元方法分析负荷潮汐倾斜效应

本文简要回顾了负荷潮汐倾斜效应的研究方法及意义。利用有限元法计算了沿海台站的负荷效应并与Boussinesq解进行了一般对照,认为有限元数值计算方法是负荷潮汐问题分析中的一个强有力的工具。     

Adaptive finite element modeling of marine controlled-source electromagnetic fields in two-dimensional general anisotropic media

In this paper, we extend the scope of numerical simulations of marine controlled-source electromagnetic (CSEM) fields in a particular case of anisotropy (dipping anisotropy) to the general case of anisotropy by using an adaptive finite element approach. In comparison to a dipping anisotropy case, the first order spatial derivatives of the strike-parallel components arise in the partial differential equations for generally anisotropic media, which cause a non-symmetric linear system of equations for finite element modeling. The adaptive finite element method is employed to obtain numerical solutions on a sequence of refined unstructured triangular meshes, which allows for arbitrary model geometries including bathymetry and dipping layers. Numerical results of a 2D anisotropic model show both anisotropy strike and dipping angles have great influence on the marine CSEM responses.     

Study of numerical simulation on dual-frequency IP method with FEM

Using the finite element method and Cole-Cole model for dual-frequency IP method to research numerical simulation, the authors introduced the fundamental principle of the dual-frequency IP method and the boundary value problem and variational equations, then replaced the complex resistivity of the model with the Cole-Cole model's parameters under ignoring the EM effect. Through solving the last linear equations, electric potentials of all the model's points were obtained. With changing model's parameters, the authors got different curves of the Fs and phases. According to the results of the simulation, the algorithm is proved to be correct and adaptable.     

Dynamic responses of top tensioned riser under combined excitation of internal solitary wave, surface wave and vessel motion

An investigation on the dynamic response of a top tensioned riser (TTR) under combined excitation of internal solitary wave, surface wave and vessel motion is presented in this paper. The riser is idealized as a tensioned slender beam with dynamic boundary conditions. The KdV-mKdV equation is chosen to simulate the internal solitary wave, and the vessel motion is analysed by using the method proposed by Sexton. Using finite element method, the governing equation is solved in time domain with Newmark-β method. The computation programs for solving the differential equations in time domain are compiled and numerical results are obtained, including dimensionless displacement and stress. The action of internal solitary wave on the riser is like a slow powerful impact, and is much larger than those of surface wave and vessel motion. When the riser is under combined excitation, it vibrates at frequencies of both surface wave and vessel motion, and the vibration is dominated by internal solitary wave. As the internal solitary wave crest passes by the centre of the riser, the maximum displacement and stress along the riser occur. Compared to the lower part, the displacement and stress of the riser in the upper part are much larger.     

Comparative Analysis of Seismic Response Characteristics of Pile-Soil-Stnicture Interaction System

The study on the earthquake-resistant performance of a pile-soil-structure interaction system is a relatively complicated and primarily important issue in civil engineering practice. In this paper, a computational model and computation procedures for pile-supported structures, which can duly consider the pile-soil interaction effect, are established by the finite element method. Numerical implementation is made in the time domain. A simplified approximation for the seismic response analysis of pile-soil-structure systems is briefly presented. Then a comparative study is performed for an engineering example with numerical results computed respectively by the finite element method and the simplified method. Through comparative analysis, it is shown that the results obtained by the simplified method well agree with those achieved by the finite element method. The numerical results and findings will offer instructive guidelines for earthquake-resistant analysis and design of pile-supported structures.     

A LAYERED NUMERICAL MODEL FOR SIMULATING THE GENERATION AND PROPAGATION OF INTERNAL TIDES OVER CONTINENTAL SLOPE II STABILITY ANALYSIS

INTRODUCTIONAsoneofthemethodsenablingnumericalsolutionofdifferentialequations,thefinite differ encemethodiswidelyacceptedinthestudyofphysicaloceanography.Afinite differenceschememusthavepropertiesofconvergence ,consistencyandstabilitytoyieldusefulapproximatesolutionoftherelevantdifferentialequations.However,thepropertiesneednotbeverifiedonebyonebecausethewell knownLaxLawassuresthattheconvergenceisequivalenttothestabilityforafinitediffer enceschemewithconsistence .Twomainmethodsforstudyin…     

Stability analysis of slope in strain-softening soils using local arc-length solution scheme

Soils with strain-softening behavior — manifesting as a reduction of strength with increasing plastic strain — are commonly found in the natural environment. For slopes in these soils,a progressive failure mechanism can occur due to a reduction of strength with increasing strain. Finite element method based numerical approaches have been widely performed for simulating such failure mechanism,owning to their ability for tracing the formation and development of the localized shear strain. However,the reliability of the currently used approaches are often affected by poor convergence or significant mesh-dependency,and their applicability is limited by the use of complicated soil models. This paper aims to overcome these limitations by developing a finite element approach using a local arc-length controlled iterative algorithm as the solution strategy. In the proposed finite element approach,the soils are simulated with an elastoplastic constitutive model in conjunction with the Mohr-Coulomb yield function. The strain-softening behavior is represented by a piece-wise linearrelationship between the Mohr-Coulomb strength parameters and the deviatoric plastic strain. To assess the reliability of the proposed finite element approach,comparisons of the numerical solutions obtained by different finite element methods and meshes with various qualities are presented. Moreover,a landslide triggered by excavation in a real expressway construction project is analyzed by the presented finite element approach to demonstrate its applicability for practical engineering problems.     

基于谱-有限元法的SNERI地球模型固体潮形变计算

基于谱-有限元法计算一个球型、非自转、完全弹性、各向同性(SNERI)的地球固体潮形变,其中地球固体部分潮汐形变的弱解用哈密顿变分原理给出,液核部分的弱解采用静态中性分层的流体近似。计算过程中把SNERI地球进行等间距球层剖分,球面上对解函数和试探函数采用球谐展开,径向上采用线性插值。比较数值计算结果与同质地球模型的解析解结果得出,1 km径向等距剖分即可获得10~(-8)精度量级的低阶Love数。基于PREM地球模型的计算结果表明,谱-有限元法计算的固体潮2～3阶Love数与Runge-Kutta法的计算值差异在10~(-4)量级;与武汉台超导重力仪8个主潮波的实测重力潮汐因子相比,本方法计算的理论重力潮汐因子相差平均约0.15%。研究结果说明,谱-有限元法具有较好的收敛性与较高的计算精度,比传统Runge-Kutta法更适用于高精度地计算复杂地球模型的固体潮形变。     

Comparative Analysis of Seismic Response of Pile-Soil-Structure Interaction System

The study on the earthquake-resistant performance of a pile-soil-structure interaction system is a relatively complicated and primarily important issue in civil engineering practice. In this paper, a computational model and computation procedures for pile-supported structures, which can duly consider the pile-soil interaction effect, arc established by the finite clement method. Numerical implementation is made in the time domain. A simplified approximation for the seismic response analysis of pile-soil-structure systems is briefly presented. Then a comparative study is performed for an engineering example with numerical results computed respectively by the finite clement method and the simplified method. Through comparative analysis, it is shown that the results obtained by the simplified method well agree with those achieved by the finite element method. The numerical results and findings will offer instructive guidelines for earthquake-resistant analysis and design of pile-supported structures.