Finite element modelling of the effective elastic properties of partially saturated rocks

Simulation of effective physical properties from microtomographic 3D images of porous structures allows one to relate properties of rocks directly to their microstructure. A static FEM code has been previously used to estimate effective elastic properties of fully saturated monomineralic (quartz) rock under wet and dry conditions. We use the code to calculate elastic properties under partially saturated conditions. The numerical predictions are compared to the Gassmann theory combined with Wood's formula (GW) for a mixture of pore fluids, which is exact for a monomineralic macroscopically homogeneous porous medium.Results of the numerical simulations performed for two Boolean sphere pack distributions show significant deviation from the GW limit and depend on the spatial distribution of fluids. This is shown to be a numerical artefact caused by incomplete equilibration of fluid pressure, which is primarily due to insufficient spatial resolution.To investigate the effect of pore-size and pore geometry, we perform FEM simulations for a model with regular pore geometry, where all pore channels have the same size and shape. Accuracy of these simulations increases with the total cross-section area of the channels and the size of individual channels. For the case where the total cross-section of the channels is large enough (on the same order as total porosity), there is a minimum of 4 voxels per channel diameter required for adequate fluid pressure equilibration throughout the pore space. Increasing the spatial resolution of the digital models reduces the discrepancy between the simulations and theory, but unfortunately increases the memory and CPU requirements of the simulations.     

动态海缆机械性能有限元分析

为探究动态海缆在剧烈交变环境载荷下的疲劳寿命,基于环境载荷响应,开展动态海缆系统的整体分析。基于有限元方法,研究海水中悬浮的动态海缆在服役过程中承受的极端载荷,分析破断力和侧压力工况,提取关键部位的应力、应变分布并进行校核。研究结果可为动态海缆材料选型、结构优化以及疲劳分析和测试提供理论依据。     

纳米孔单分子传感器电导特性有限元分析

主要从纳米孔结构角度,考虑生物分子在纳米孔内的位阻效应影响.运用有限元模拟方法分别模拟了3类常见纳米孔的电导,并比较了3种不同纳米孔在检测纳米杆通过纳米孔时的相对堵塞电流值大小.研究了纳米杆上带有亚结构时,在3种纳米孔内的电流堵塞效应的差异.研究方法有助于进一步理解纳米孔结构对检测生物分子的影响.     

Finite element analysis

Current use of the finite element method in engineering practice is considered. The increasing use of finite element analysis in a CAD environment and factors influencing it are discussed.The technological state of the art is briefly reviewed. Special consideration is given to shell elements and solution methods, illustrating the progress being made in these and other areas of finite element technology. Future trends are predicted.     

Finite element costs

This paper describes an extension to the classical finite element analysis methods. Using the same data inherent in the stiffness matrix, and adding cost parameters as input, a finite element structural analysis program is shown to output cost data. The basic concept is that the material costs are only a fraction of the total costs, which include labor and overhead. It is theorized that the labor and overhead costs may be dominant, and are related to structural complexity and numbers of joints.Two examples are given: a simple four-member truss illustrates the method, and a transmission tower example is offered to demonstrate the principle.     

Finite element elastic-plastic-creep analysis of two-dimensional continuum with temperature dependent material properties

A technique is presented for performing finite element elastic-plastic-creep analysis of two-dimensional continuum composed of material with temperature dependent elastic, plastic, and creep properties. The plastic analysis utilizes the Prandtl-Reuss flow equations assuming isotropic material properties and linear strain-hardening. A power creep flow law formulated by Odquist is used to determine the steady state creep strain rate. The plastic and creep flow laws are employed to derive a ‘softened’ plastic-creep stress-strain matrix. These modified stress-strain relations are then used to formulate the element stiffness matrix in the usual manner. The differences in the elastic, plastic, and creep properties of the material due to the temperature change during the increment result in the formation of pseudo stresses, which in turn lead to load terms that appear on the right hand side of the equilibrium equations. The load terms resulting from these pseudo stresses not only keep the solution on the temperature dependent stress-strain curve of the material, but also correct for the elastic ‘overshoot’ that occurs when an element changes from an elastic to a plastic state. The effect of large displacements is included by the formulation of the geometric stiffness matrix for each element being used in the computer code. With this procedure it becomes economically feasible to perform elastic-plastic-creep stress analysis of two-dimensional continuum subjected to transient thermal and mechanical loadings. Several examples of both elastic-plastic and creep analyses are presented, and the finite element solutions are compared to either other theoretical solutions or experiment.     

Finite element optimisation on the DAP

In this paper we report on our experience solving steady two dimensional sets of nonlinear simultaneous partial differential equations on the ICL-DAP computer. Results are reported for the heat conduction equation, a nonlinear pde in one variable and for the Navier Stokes equations. In each case the parallel implementation of finite element optimisation on the DAP solved coarse grid problems much more rapidly than the sequencial code and also enabled much fine grids to be used.     

Finite element mesh generation

The capabilities of a geometric modeller are extended towards finite element analysis by a mesh generator which extracts all its geometric and topological information from the model. A coarse mesh is created and subsequently refined to a suitable finite element mesh, which accomodates material properties, loadcase and analysis requirements. The mesh may be optimized by adaptive refinement, ie according to estimates of the discretization errors.A survey of research and development in geometric modelling and finite element analysis is presented, then an implementation of a mesh generator for 3D curvilinear and solid objects is described in detail.     

SiC/Al梯度功能材料蠕变性能有限元分析

为研究SiC／Al梯度功能材料（Functionally Gradient Material,FGM）的性能,采用ANSYS分别对具有4个梯度层的该种材料的3点弯曲试样和紧凑拉伸试样,在热载荷和机械载荷热载荷共同作用下的蠕变性能进行数值模拟分析,得到不带微裂纹、带垂直梯度方向微裂纹和平行梯度方向微裂纹的SiC／A1FGM试样在这两种工况下的蠕变应变随坐标位置及时间变化曲线．结果发现：（1）蠕变应变主要发生在铝合金富集层,横向裂纹对试件蠕变影响不大;（2）在有机械载荷作用时,裂纹位置对最大蠕变应变值有较大影响;（3）考察紧凑拉伸试件,发现随着远离裂纹尖端,其蠕变应变值也随之迅速减小,在有机械载荷作用下,蠕变减小趋势比只受热载荷作用明显,变化趋势反映出蠕变应变与材料的应力分布有很大关系．     

Finite element analysis of the captive column structure

A linearly elastic finite element computer model is developed for analyzing the behavior of a structural member concept known as the “captive column.” This concept has the potential for combining high-strength and lightweight materials in optimum configurations to produce structural components fora variety of applications. Experimental verification of the computer model is presented for the case of static flexural loading of captive column members acting as beams. Both deflection and stress results are compared. The computer model is shown to hold promise as a useful design tool for specific applications of the captive column concept.     

Finite element analysis of the shear vane test

Finite element analyses of the standard shear vane test to measure the in situ undrained shear strength of soil are presented. The mobilization of shear stresses on the vertical and horizontal faces of the vane has been studied up to failure and compared with analytical solutions. This has been achieved by the use of 2-D and quasi-3-D analyses. Good agreement between the computed and analytical solutions was achieved provided the soil strength was isotropic. The influence of soil strength anisotropy was considered by the use of a simple model in which the undrained shear strength was related to direction. The effect of strain softening was also incorporated into the analyses. When combined with the quasi-3-D analysis, these features allowed more realistic models to be made of the shear strength mobilization on all parts of the cylindrical failure surface.     

Finite element programming and C

In finite element programming, data have to be dealt with which are of different types but belong together in a logical sense. It would be very effective, with respect to program readability and maintainability, to store these data as a single unit. Effcient software design requires that all parts of information, which belong together logically, are stored as a single data unit. This can be accomplished utilizing structured data types.

Dynamic memory allocation allows the definition of dynamic variables which can be created and destroyed during run-time. Dynamic memory management is handled in C by pointers. In other conventional languages, e.g. Fortran 77, the programmer has the responsibility to select adequate array sizes for the largest problem to be solved. This often leads in engineering practice to array oversizing and to memory wasting. By allocating memory dynamically during program execution according to actual problem size, wasting can be avoided.

The combination of structured data and pointers along with the dynamic memory allocation capabilities of C allows the creation of linked lists. Utilizing these concepts, an effective and easy-to-read C program has been written for finite element analysis. The C program presented demonstrates the use of these techniques for interactive finite mesh generation. The strengths of C are compared to that of Fortran 77 and Fortran 90. It has been found that for finite element programming C is in many aspects superior to Fortran 77. However, it has some disadvantages in comparison with Fortran 90 concerning array processing.     

A Partitioned finite element method for dynamical systems

A new analytical method is described for deriving the equations of motion of dynamical systems. The concept is to consider the displacements of the domain to be composed of rigid and elastic components. In contrast to other reduction methods, the domain modeled by finite number of degrees of freedom is discretized into two distinctive types of subdomains. Rigid and elastic subdomains are generated by consistent lumping of the domain properties under unique kinematic constraint relations. Equations of motion of the disjoint subdomains are derived by Lagrange's equations, in conjunction with the shape function matrix represented in partitioned form. This allows reduced sizes of matrices and avoids their possible singularities. Based on the invariance of energies under a compatible partitioned procedure, a simple analytical method is introduced for building the equations of motion of the whole domain from those of the subdomains. The dynamic analysis of a two-node domain with application to a blade-shaft combination is presented to illustrate the method.     

Finite element analysis of shell structures

Summary A survey of effective finite element formulations for the analysis of shell structures is presented. First, the basic requirements for shell elements are discussed, in which it is emphasized that generality and reliability are most important items. A general displacement-based formulation is then briefly reviewed. This formulation is not effective, but it is used as a starting point for developing a general and effective approach using the mixed interpolation of the tensorial components. The formulation of various MITC elements (that is, elements based on Mixed Interpolation of Tensorial Components) are presented. Theoretical results (applicable to plate analysis) and various numerical results of analyses of plates and shells are summarized. These illustrate some current capabilities and the potential for further finite element developments.     

Finite element analysis of stiffened plates

A finite element method is presented in which the constraint between stiffener and member is imposed by means of Lagrange multipliers. This is performed on the functional level, forming augmented variational principles. In order to simplify the initial development and implementation of the proposed method, two-dimensional stiffened beam finite elements are developed. Several such elements are formulated, each showing monotonic convergence in numerical tests. In the development of stiffened plate finite elements, the bending and membrane behaviors are treated seperately. For each, the stiffness matrix of a standard plate element is modified to account for an added beam element (representing the stiffener) and additional terms imposing the constraint between the two. The resulting stiffened plate element was implemented in the SAPIV finite element code. Exact solutions are not known for rib-reinforced plated structures, but results of numerical tests converge monotonically to a value in the vicinity of an approximate “smeared” series solution.     

Finite element analysis of suspension bridges

A finite element analysis of static and dynamic response of suspension bridges is presented in this paper. Several finite element models of the three-dimensional bridge structure, with varying degrees of complexity and accuracy, are discussed. The formulation takes into account the geometric nonlinearities of the cables and some elements of the girders-bracingsdeck system as well as the nonlinear material properties of the components. Special attention is given to the effects of steady and unsteady wind forces. Examples of application include calculations of the static and dynamic response of a bridge subjected to wind and moving loads.