一个改进的平面梁单元

根据有限单元法基本原理 ,提出了一个变截面平面梁单元 ,推导了其单元钢度矩阵。这一改进的梁单元用于分析梁高呈线性变化及二次抛物线变化的矩形截面梁 ,将得到准确解。文中给出了一个变截面悬臂梁算例 ,计算表明 ,这一改进的梁单元使变截面梁的分析大大简化     

基于有限元分析的特征值反问题求解的逆摄动方法

本文研究特征值反问题的求解方法,根据广义特征值反问题理论和有限元法的特点,以转子系统平面梁单元有限元模型结构分析的特征值反问题求解为例,给出一种新的逆摄动方法,给出了本逆摄动法较完整的理论基础,给出了其逆摄动参数的显式计算公式及相应的取值方法,本逆摄动法也可推广到其他单元类型的有限元模型特征值反问题的求解。     

On the convergence of elastoplastic boundary element analysis

Iterative process is a main component of boundary element method in plasticity. In this paper, the convergence of elastoplastic boundary element analysis has been discussed in detail and studied theoretically.     

Stochastic finite element analysis of non-linear plane trusses

—This study considers the responses of geometrically and materially non-linear plane trusses under random excitations. The stress-strain law in the inelastic range is based on an explicit differential equation model. After a total Lagrangian finite element discretization, the nodal displacements satisfy a system of stochastic non-linear ordinary differential equations with right-hand-sides given by random functions of time. The exact solution of the above stochastic differential equation is generally difficult to obtain. To seek an approximate solution with good accuracy and reasonable computational effort, the stochastic linearization method is used to find the first and second statistical moments (i.e. the mean vector and the one-time covariance matrix) of the nodal displacements. Results of simple structures under Gaussian white-noise excitation indicate that the proposed method has good accuracy (generally underestimates the r.m.s. stationary response by 5–14%) and requires only a small fraction of the computation time of the time-history Monte-Carlo method.     

A constitutive model and elastoplastic analysis of structures under cyclic loading

A constitutive model for cyclic plasticity is briefly outlined. Then the model is implemented in a finite element code to predict the response of cyclic loaded structural components such as a double-edge-notched plate, a grove bar and a nozzle in spherical shell. Comparision with results from other theories and experiments shows that the results obtained by using the present model are very satisfactory.The Project Supported by National Natural Science Foundation of China.     

A finite element method on the plane elastic material analysis

Based on the finite element displacement method, a finite element method on the analysis of mechanical behaviour of plane elastic materials is proposed in this paper. By using this method and the corresponding computational program, the material behaviour of any unknown plane elastic material can be determined and all the elastic constants can be calculated.     

Free-form shell analysis by a mixed-hybrid finite element approach

Summary A novel finite element scheme is proposed for the linear elasto-static analysis of free-form thinwalled shells. On the basis of a modified version of the variational theorem due to Hellinger and Reissner, a doubly curved triangular element is developed with six degrees-of-freedom (three translations plus three rotations) per nodal point. For each element, separate trial functions are introduced in order to approximate the displacements and the stress resultants. It is shown that by properly choosing these interpolants, an element is obtained which (i) is capable of exactly representing the rigid body and constant strain modes; (ii) does not possess any spurious kinematic modes; (iii) fulfils C ¹ interelement continuity and (iv) satisfies exactly the interior domain static equilibrium conditions. Two representative examples have been solved in order to illustrate the advantages of the proposed scheme over existing ones.

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Berechnung dünnwandiger elastischer Schalen mit Hilfe eines gemischt-hybriden Finite-Element-Verfahrens

Übersicht Die vorliegende Arbeit beschäftigt sich mit der numerischen Berechnung des linearen Trag- und Deformationsverhaltens dünnwandiger Schalentragwerke beliebiger Geometrie. Auf der Grundlage eines modifizierten Funktionals vom Typ Hellinger/Reissner wird ein doppeltgekrümmtes Dreieckselement mit insgesamt achtzehn Freiheitsgraden entwickelt. Im Vergleich mit existierenden Elementen zeichnet sich das hier vorgeschlagene dadurch aus, daß es (i) keine fiktiven Kinematikzustände (spurious modes) besitzt; (ii) in der Lage ist, Starrkörperzustände sowie Zustände konstanter Verzerrungen exakt darzustellen; (iii) einen C ¹-stetigen Verschiebungsverlauf an den Zwischenelementrändern garantiert, und (iv) die a-priori-Erfüllung der Gleichgewichtsbedingungen im Elementinneren gewährleistet. Eine Vielzahl von ausgesuchten Testbeispielen sind mit Hilfe des hier vorgestellten Elementeverfahrens gerechnet worden, um sein Konvergenzverhalten sowie seine Zuverlässigeit zu überprüfen. Einige charakteristische Resultate werden im Schlußteil der Arbeit präsentiert.

     

Vibration modelling of structural networks using a hybrid finite element/wave and finite element approach

The vibration modelling of waveguide structures is considered. These structures comprise waveguides connected via joints. Traditionally, analytical models of the wave behaviour of such structures can be developed if they are simple (beams or rods connected at point joints, etc.). However, if the waveguides are of complicated constructions (truss-like, layered media, etc.) or the joints are complicated (e.g. of significant physical dimensions), obtaining the wave characteristics might be a formidable task. In this paper, such structures are modelled using a hybrid finite element/wave and finite element (FE/WFE) approach. The waveguides are modelled using the WFE method and thus their wave characteristics are obtained regardless of the complexity of their cross-section. The joints are modelled using standard FE, and the WFE and FE models are coupled to yield the scattering properties of the joints. The propagation and scattering models are assembled to describe the behaviour of the structure using relatively small models, while also providing information for other applications such as structure-borne sound, statistical energy analysis, etc. Numerical examples are presented to illustrate the approach.     

Nonlinear finite element analysis of no-tension masonry structures

A numerical approach for structural analysis of masonry walls in plane stress conditions is presented. The assumption of a perfectly no-tension material (NTM) constitutive model, whose relevant equations are in the form of classical rate-independent associated flow laws of elastoplastic material, allows one to adopt numerical procedures commonly used in computational plasticity. An accuracy analysis on the integration algorithm employed in the solution of constitutive relations has been carried out. The results obtained for some relevant case-studies and their comparison with data, available in the literature show the effectiveness of the proposed method.

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Sommario Si presenta un approccio numerico per l'analisi strutturale di pareti in muratura in stato piano di tensione. L'assunzione di un modello costitutivo per materiale perfettamente non resistente a trazione (NTM), le cui equazioni sono esprimibili nella classica forma incrementale delle leggi dello scorrimento plastico di tipo associato per materiali elastoplastici, consente di adottare procedure numeriche comunemente utilizzate in plasticità computazionale. Si conduce un'analisi di accuratezza dell'algoritmo utilizzato nell'integrazione delle equazioni costitutive del modello esaminato. I risultati ottenuti per alcuni casi analizzati ed il confronto effettuato con esempi riportati in letteratura mostrano l'efficienza dell'approccio proposto.

     

Lower bound limit analysis of three-dimensional elastoplastic structures by boundary element method

IntroductionThelimitanalysisofstructuresisoneofthemostpracticalandusefulbranchesinplasticity .Ithasimportantapplicationbackgroundforproblemssuchasthedeterminationofloadcarryingcapacityandplasticformingofmetal.Thepurposeofthelimitanalysisofstructuresistoprovidereliabletheoreticalbasesforengineeringdesignandsafetyassessment.Asasimplifiedmethodforelastoplasticproblems,limitanalysisneednotrequirethehistoryofloadandcancomputethelimitloadsdirectlyinsteadofelastoplasticincrementalcomputationwhichisus…     

On strain localization analysis of elastoplastic materials at finite strains

The problem of strain localization into planar bands of rate-independent elastoplastic solids with smooth yield surface and plastic potential is analyzed reconsidering the work of Rice and Rudnicki in 1980. It is shown that strain localization with elastic unloading on one side of the band first becomes possible either at localization in the comparison solid corresponding to the loading branch of the constitutive equation or at the snap-back threshold. The elastic unloading is shown to start from the condition of neutral loading, occurring in fact at the onset of localization. The case of localization with elastic unloading into the band and plastic loading outside that was not considered by Rice and Rudnicki is taken into account.     

基于混合编码遗传算法和有限元分析的压电结构载荷识别

与传统的优化算法相比,遗传算法不需要计算目标函数的导数信息,便于迭代,可实现全局寻优.因此,本文提出一种采用混合编码的遗传算法与有限元分析相结合,对复合材料层合板、壳进行载荷识别的新方法.在遗传算法求解过程中,设计变量的编码方法选择是其重要环节,二进制编码容易产生连续函数离散化时的映射误差,且其求解精度与染色体的编码长度紧密相关,过长的染色体描述虽可提高精度,但会显著降低算法的求解效率.为此,本文提出采用混合编码的方法进行载荷识别,即用二进制编码表征载荷作用位置,浮点数编码表示载荷的大小.这一方法大大降低了染色体的长度,并显著提高了计算效率和精度.     

Buckling of structures with finite prebuckling deformations—a perturbation,finite element analysis

In some technically important structures, finite prebuckling displacements have a profound effect on the bifurcation load. To ignore these displacements, as is done in most instability analyses, is to invite major errors, usually on the unsafe side. A method is presented which approximates this effect without the necessity of solving nonlinear equations. The general theory is developed for any elastic body under conservative loads. The governing equations are subsequently discretized by a finite element approach and it is shown that for planar framed structures, the second order approximation to the buckling load can be found in terms of the standard linear and geometric stiffness matrices of structural analysis; the solution procedure does not require iterations. For illustrative purposes, a computer program was developed for planar structures and the results are compared to the exact solution for the buckling of shallow circular arches.     

Crack parameter estimation in structures using finite element modeling

This paper addresses the problem of linear crack quantification, crack depth estimation and localization, in structures. An optimization technique based on a finite element model for cracked structural elements is employed in the estimation of crack parameters for beam, truss and two-dimensional frame structures. The modal data for the cracked structures are obtained by solving the corresponding eigenvalue problem. The error in the modal data is simulated by an additive noise that follows the normal distribution. The simulated reduced modal data is expanded using the eigenvector projection method. Numerical examples showed that this technique gives good results for cracks with high depth ratio. The accuracy of the estimated crack parameters depends on (1) the number of modes used, (2) the error level in the cracked structure modal data and (3) the number of measured degrees of freedom in the case of reduced modal data.     

Determination of stress intensity factor with direct stress approach using finite element analysis

In this article,a direct stress approach based on finite element analysis to determine the stress intensity fac-tor is improved.Firstly,by comparing the rigorous solution against the asymptotic solution for a problem of an infinite plate embedded a central crack,we found that the stresses in a restrictive interval near the crack tip given by the rigorous solution can be used to determine the stress intensity fac-tor,which is nearly equal to the stress intensity factor given by the asymptotic solution.Secondly,the crack problem is solved numerically by the finite element method.Depending on the modeling capability of the software,we designed an adaptive mesh model to simulate the stress singularity.Thus, the stress result in an appropriate interval near the crack tip is fairly approximated to the rigorous solution of the corre-sponding crack problem.Therefore,the stress intensity factor may be calculated from the stress distribution in the appro-priate interval,with a high accuracy.     

On the finite element analysis of woven fabric impact using multiscale modeling techniques

Finite element modeling of the impact of flexible woven fabrics using a yarn level architecture allows the capturing of complex projectile-fabric and yarn–yarn level interactions, however it requires very large computational resources. This paper presents a multiscale modeling technique to simulate the impact of flexible woven fabrics. This technique involves modeling the fabric using a yarn level architecture around the impact region and a homogenized or membrane type architecture at far field regions. The level of modeling resolution decreases with distance away from the impact zone. This results in a finite element model with much lower computational requirements. The yarns are modeled using both solid and shell finite elements. Impedances are matched across all interfaces created between the various regions of the model to prevent artificial reflections of the longitudinal strain waves. A systematic approach is presented to determine geometric and material parameters of the homogenized zone. The multiscale model is extensively validated against baseline models. The limitations of using shell elements to model the yarn level architecture underneath the projectile are addressed.     

Two-dimensional modeling of heterogeneous structures using graded finite element and boundary element methods

In the present work, graded finite element and boundary element methods capable of modeling behaviors of structures made of nonhomogeneous functionally graded materials (FGMs) composed of two constituent phases are presented. A numerical implementation of Somigliana’s identity in two-dimensional displacement fields of the isotropic nonhomogeneous problems is presented using the graded elements. Based on the constitutive and governing equations and the weighted residual technique, effective boundary element formulations are implemented for elastic nonhomogeneous isotropic solid models. Results of the finite element method are derived based on a Rayleigh–Ritz energy formulation. The heterogeneous structures are made of combined ceramic–metal materials, in which the material properties vary continuously along the in-plane or thickness directions according to a power law. To verify the present work, three numerical examples are provided in the paper.     

A FINITE ELEMENT METHOD FOR STRESS ANALYSIS OR ELASTOPLASTIC BODY WITH POLYGONAL LINE STRAIN——HARDENING

In this paper, the stress-strain curve of material is fitted by polygonal line composed of three lines. According to the theory of proportional loading in elastoplasticity, we simplify the complete stress-strain relations, which are given by the increment theory of elastoplasticity. Thus, the finite element equation with the solution of displacement is derived. The assemblage elastoplastic stiffness matrix can be obtained by adding something to the elastic matrix, hence it will shorten the computing time. The determination of every loading increment follows the von Mises yield criteria. The iterative method is used in computation. It omits the redecomposition of the assemblage stiffness matrix and it will step further to shorten the computing time. Illustrations are given to the high-order element application departure from proportional loading, the computation of unloading fitting to the curve and the problem of load estimation.