Network-distributed finite element analysis

The widespread availability of local-area networks has made the combined processing power of workstations a viable approach for compute-intensive analyses. In this paper, we describe several distributed algorithms for structural analysis using finite element methods, and we assess their performance on a conventional Ethernet-connected workstation network. Direct, iterative and hybrid equation solvers are evaluated for their performance on plane-elasticity problems, and are contrasted with respect to overall solution time and efficiency in distributing computations over a network. Equations modeling the costs of network communication and structural analysis computations are derived, and are subsequently used to predict the performance of several variations on the implemented algorithms. Our results show that each of the methods performs well on network architectures, and in particular that, while direct methods usually minimize network communication, certain iterative and hybrid methods can often be used to minimize overall solution time.     

Support system for finite element analysis

This paper describes work aimed at developing an intelligent support system for finite element modeling and a methodology for managing input data model. Analyzing various statement structures of input data, three structural interface models — the hierarchical browser, the spread sheet and the model generator — are proposed for advanced representation and editing. Two knowledge models composed of macro visual data representation (user oriented model) and micro regularized data representation (processor oriented model) are revealed in conformity with the approach of object-orientation. Moreover, an extended relational schema composed of a composite object (assembly of functional elements) and several abstracted scalar indexes has been implemented for case retrieval.     

Geometric uncertainties in finite element analysis

This paper demonstrates the use of automatic differentiation in solving finite element problems with random geometry. In the area of biomechanics, the shape and size of the domain is often known only approximately. Stochastic finite element analysis can be used to compute the variability in the structural response as a result of variability in the shape of the structural domain. Automatic differentiation can be used to compute the shape sensitivites accurately and effortlessly. Unlike randomness in material properties, the response variability can be the same as or greater than the variability in the input. When both the Young's modulus and geometry are random, it is likely that randomness in geometry will dominate randomness in Young's modulus.     

Solution errors in finite element analysis

The development of the finite element method so far indicates that it is a discretization technique especially suited for positive definite, self-adjoint, elliptic systems, or systems with such components. The application of the method leads to the discretized equations in the form of $\text{u}\text{?}\text{=}\text{f(u)}$, where u lists the response of the discretized system at n preselected points called nodes. Instead of explicit expressions, vector function f and its Jacobian f,_u are available only numerically for a numerically given u. The solution of $\text{u}\text{?}\text{=}\text{f(u)}$ is usually a digital computer. Due to finiteness of the computer wordlength, the numerical solution $\text{u}{}_{\mathrm{c}}$ is in general different from u. Let $\text{u}\text{(}\text{x}\text{, t)}$ denote the actual response of the system in continuum at points corresponding to those of u. In the literature. $\text{u}\text{(}\text{x}\text{, t)-}\text{u}$ is called the discretization errors, $\text{u}\text{-}\text{u}{}_{\mathrm{c}}$ the round-off errors, and the s is. $\text{u}\text{(}\text{x}\text{, t)-}\text{u}{}_{\mathrm{c}}$ is called the solution errors. In this paper, a state-of-the-art survey is given on the identification, growth, relative magnitudes, estimation, and control of the components of the solution errors.     

Stochastic finite element analysis of shells

In the present paper the stochastic formulation of the triangular composite (TRIC) facet shell element is presented using the weighted integral and local average methods. The elastic modulus of the structure is considered to be a two-dimensional homogeneous stochastic field which is represented via the spectral representation method. As a result of the proposed derivation and the special features of the element, the stochastic stiffness matrix is calculated in terms of a minimum number of random variables of the stochastic field giving a cost-effective stochastic matrix. Under the assumption of a pre-specified power spectral density function of the stochastic field, it is possible to compute the response variability of the shell structure. Numerical tests are provided to demonstrate the applicability of the proposed methodologies.     

Knowledge-based control for finite element analysis

This paper shows that control logic may be separated from analysis software and that a knowledge-based expert system can use this logic to perform interactive computation. Heuristics that control a simple interactive finite element analysis program are represented using a rule-based format and are used by a goal-driven logic processor to invoke analysis activity.Traditional algorithm-oriented control and the proposed knowledge-based control are compared in a simple displacement computation scenario to identify the advantages/disadvantages of the two approaches. General activities and constraints, practical methods of reasoning and representation, and knowledge-based expert systems are discussed with emphasis on applications to interactive finite element analysis.An analysis control expert system has been developed for use in the numerical analysis of two-dimensional linear problems in solid and structural mechanics. An example problem is used to clarify the methods used to direct activity and to identify the problems associated with conditional task processing for interactive analysis.The main difference between the analysis program described in this paper and conventional analysis programs is related to the control architecture. The general conclusion of this paper is that knowledge-based control is more effective and flexible than algorithm-oriented control.     

Concepts and implementation of parallel finite element analysis

The design of complex engineering systems such as advanced aircraft structures and offshore platforms requires continually increasing levels of detail in supporting analysis. The finite element method is widely used as a computational method with which to model physical systems in various engineering problems. For detailed analyses of complex designs, structural models composed of several thousands of degrees of freedom are no longer uncommon. Such design activities require large order finite element and/or finite difference models and excessive computation demands in both calculation speed and information management. The computer simulation of the nonlinear dynamic response of structures and the implementation of parallel FEM systems on a high speed multiprocessor have received considerable attention in recent years. The driving forces of these activities included the reliable simulation of automotive and aircraft crash phenomena, and the increased performance of computers. Most existing major structural analysis software systems were designed 10–20 years ago and have been optimized for current sequential computers. Such systems often are not well structured to take maximum advantage of the recent and continuing revolution in parallel vector computing capabilities. These parallel vector computer architectures not only occur in the form of large supercomputers, but are now also occurring for minicomputers and even engineering workstations. To benefit from advances in parallel computers, software must be developed which takes maximum advantage of the parallel processing feature.     

Mixed finite element models for plate bending analysis: A new element and its applications

With a few exceptions, finite element packages available in today's commercial software environment contain in their libraries displacement-type elements only. The present paper aims to demonstrate the feasibility that properly formulated mixed-type elements compete most favorably with displacement-type elements and should, therefore, be considered as potential candidates for inclusion in general purpose finite element packages. In doing so, the development of a new triangular doubly—curved mixed-hybrid shallow shell element and its extensive testing in carefully chosen example problems are reported on.     

Nonlinear finite element analysis of elastic frames

A very simple and effective formulation and numerical procedure to remove the restriction of small rotations between two successive increments for the geometrically nonlinear finite element analysis of in-plane frames is presented. A co-rotational formulation combined with small deflection beam theory with the inclusion of the effect of axial force is adopted. A body attached coordinate is used to distinguish between rigid body and deformational rotations. The deformational nodal rotational angles are assumed to be small, and the membrane strain along the deformed beam axis obtained from the elongation of the arc length of the deformed beam element is assumed to be constant. The element internal nodal forces are calculated using the total deformational nodal rotations in the body attached coordinate. The element stiffness matrix is obtained by superimposing the bending and the geometric stiffness matrices of the elementary beam element and the stiffness matrix of the linear bar element. An incremental iterative method based on the Newton-Raphson method combined with a constant arc length control method is employed for the solution of the nonlinear equilibrium equations. In order to improve convergence properties of the equilibrium iteration, a two-cycle iteration scheme is introduced. Numerical examples are presented to demonstrate the accuracy and efficiency of the proposed method.     

High-precision finite element analysis of cylindrical shells

This paper presents the finite element formulation to study the free vibration of cylindrical shells. The displacement function for the high-precision shell element with 16 degrees of freedom is approximated by a Hermitian polynomial of beam function type. The explicit formulation for the high-precision element is extremely efficient. For the purpose of comparison, the subject element is used to study the sample case of free vibration of a shell structure. The results are in good agreement with those published. The study shows that solution accuracy with fewer elements is assured and that accurate solutions are obtainable in the high-frequency range.     

Nonlinear finite element analysis of curved beams

Mixed curved-beam finite elements are developed for the geometrically nonlinear analysis of deep arches. The analytical formulation is based on a form of the nonlinear deep-arch theory with the effects of transverse shear deformation and bending-extensional coupling included. The fundamental unknowns consist of the six internal forces and generalized displacements of the arch. The generalized stiffness matrix is obtained by using a modified form of the Hellinger-Reissner mixed variational principle. Numerical studies are presented to demonstrate the high accuracy of the solutions obtained by the mixed models and to show that their performance is considerably less sensitive to variations in the arch geometry than that of the displacement models.     

加速度传感器的有限元分析

为了分析加速度传感器的动态特性,对其进行了模态分析、频响和瞬态分析。通过模态分析得到传感器的前六阶固有频率和振型,频响分析和瞬态分析得到传感器的幅频特性,得出传感器动态维间耦合情况。仿真实验的结果表明:传感器一阶和二阶、四阶和五阶振型相同,频率相近;传感器受到轴向载荷的时候,轴向与水平方向存在较大的动态耦合;受到水平方向载荷作用时轴向耦合较大,而与另一水平方向耦合较小。     

Dynamic finite element analysis of nonaxisymmetric structures

A dynamic finite element method of analysis is developed for structural configurations which are derived from axisymmetric geometries but contain definite nonaxisymmetric features in the circumferential direction. The purpose of the analysis is to develop a method which will take into consideration the fact that the stress and strain conditions in these geometries will be related to the corresponding axisymmetrie solution. This analysis is an extension of previously published work in which a similar approach was developed for static structural problems. The analysis is developed in terms of a cylindrical coordinate system r, θ and z. As the first step of the analysis, the geometry is divided into several segments in the r-θ plane. Each segment is then divided into a set of quadrilateral elements in the r-z plane. The axisymmetric displacements are obtained for each segment by solving a related axisymmetric configuration. A perturbation analysis is then performed to match the solutions at certain points between the segments, and obtain the perturbation displacements for the total structure. The total displacement is then the axisymmetric displacement plus the perturbation displacement. The analysis allows for elastic-plastic materials with orthotropic yield criterion based on Hill's yield function and kinematic strain hardening. The finite element dynamic equations are solved by finite differences by dividing the time domain into incremental steps. The solution has been programmed on a computer and applied to a number of examples.     

Automatic mesh generation for finite element analysis

The finite element analysis in engineering applications comprises three phases: domain discretization, equation solving and error analysis. The domain discretization or mesh generation is the pre-processing phase which plays an important role in the achievement of accurate solutions. In this paper, the improvement of one particularly promising technique for generating two-dimensional meshes is presented. Our technique shows advantages and efficiency over some currently available mesh generators.     

Non-linear finite element analysis of flexible pavements

A research study is being undertaken to incorporate the realistic material properties of the pavement layers and the moving traffic load, in the analysis of flexible pavements, using the finite element theory. As a preliminary step taken herein in this direction, a pavement structure where field measurements have been carried out when subjected to a cyclic loading, is selected and modelled as a finite element model. The analysis is being carried out using the finite element computer package ABAQUS/STANDARD, when this pavement model is subjected to static and cyclic loading while considering the linear and non-linear material properties of the pavement layers. The results indicate that displacements under cyclic loading when non-linear materials are present, are the closest to field measured deflections.     

利科有限元分析软件开发

针对现有的通用CAE分析软件不能满足水工结构和岩土工程领域数值分析的需求,国内外还没有一款功能较完备的水工结构和岩土工程通用的CAE软件的问题,开发出面向水工结构和岩土工程设计、咨询、科研与高等教育的专业有限元分析软件——利科有限元分析软件(LinkFEA).计算模块的设置主要满足该领域中坝、闸、隧道和地下洞室、各类岩质土质边坡等中的渗流场、温度场、应力场(或位移场)及这3个场之间的耦合计算和结构安全性分析需求.前处理模块的功能有几何建模、有限元网格生成以及材料参数、载荷、初始条件和边界条件的设定等;后处理模块包括强度分析、渗透稳定性分析、边坡稳定分析和洞室围岩稳定性分析等,有限元计算结果和分析结果都能以等值线图或云图显示.LinkFEA已经过国内多个工程的渗流和应力(变形)计算的检验.     

旋转式FBG粘度计设计与有限元分析

设计了一种用于测量液体粘度的旋转式光纤布拉格光栅(FBG)粘度计.对旋转式FBG粘度计的主体结构进行有限元分析,有限元分析表明:在转速同为44 r/min的条件下,当设置液体粘度参数分别为0.5,0.75,1.5Pa·s时,传感元件的最大应变量分别为2.578×10-6,3.836 × 10-6,7.502×10-6,扭转角度分别为1.32°,2.04°,3.83°.结果显示:改变液体的粘度值能够对测扭传感器扭转形变产生影响,并且呈一定的线性关系.有限元分析为研究传感器的工作原理和改进传感器的结构性能提供了依据.