STUDY ON THREE-DIMENSIONAL FINITE BODIES CONTAINING CRACKS USING THE FINITE ELEMENT METHOD OF LINES

The three-dimensional finite element method of lines is presented, and the basic processing description of 3D FEMOL in cracking questions is given in detail. Applications to 3D bodies with cracks indicate that good accuracy can be obtained with relatively coarse girds. In particular, application to the tension specimen shows very good agreement with the evaluation of stress intensity factors, which is better than the results of other methods. This implies a considerable potential for using this method in the 3D analysis of finite geometry solids and suggests a possible extension of this technique to nonlinear material behavior.

Cracking analysis of fracture mechanics by the finite element method of lines(FEMOL)

The Finite Element Method of Lines （FEMOL） is a semi-analytic approach and takes a position between FEM and analytic methods. First, FEMOL in Fracture Mechanics is presented in detail. Then, the method is applied to a set of examples such as edge-crack plate, the central-crack plate, the plate with cracks emanating from a hole under tensile or under combination loads of tensile and bending. Their dimensionless stress distribution, the stress intensify factor （SIF） and crack opening displacement （COD） are obtained, and comparison with known solutions by other methods are reported. It is found that a good accuracy is achieved by FEMOL. The method is successfully modified to remarkably increase the accuracy and reduce convergence difficulties. So it is a very useful and new tool in studying fracture mechanics problems.

COMPUTATION OF STRESS INTENSITY FACTORS BY THE SUB-REGION MIXED FINITE ELEMENT METHOD OF LINES

Based on the sub-region generalized variationM principle, a sub-region mixed version of the newly-developed semi-analytical ＇finite element method of lines＇ （FEMOL） is proposed in this paper for accurate and efficient computation of stress intensity factors （SIFs） of two-dimensional notches/cracks. The circular regions surrounding notch/crack tips are taken as the complementary energy region in which a number of leading terms of singular solutions for stresses are used, with the sought SIFs being among the unknown coefficients. The rest of the arbitrary domain is taken as the potential energy region in which FEMOL is applied to obtain approximate displacements. A mixed system of ordinary differential equations （ODEs） and algebraic equations is derived via the sub-region generalized variational principle. A singularity removal technique that eliminates the stress parameters from the mixed equation system eventually yields a standard FEMOL ODE system, the solution of which is no longer singular and is simply and efficiently obtained using a standard general-purpose ODE solver. A number of numerical examples, including bi-material notches/cracks in anti-plane and plane elasticity, are given to show the generally excellent performance of the proposed method.

OBJECT-ORIENTED FINITE ELEMENT ANALYSIS AND PROGRAMMING IN VC++

The design of finite element analysis program using object-oriented programming (OOP) techniques is presented. The objects, classes and the subclasses used in the programming are explained. The system of classes library of finite element analysis program and Windows-type Graphical User Interfaces by VC + + and its MFC are developed. The reliability, reusability and extensibility of program are enhanced. It is a reference to develop the large-scale, versatile and powerful systems of object-oriented finite element software.

A stable implicit nodal integration-based particle finite element method(N-PFEM)for modelling saturated soil dynamics

In this study,we present a novel nodal integration-based particle finite element method(N-PFEM)designed for the dynamic analysis of saturated soils.Our approach incorporates the nodal integration technique into a generalised Hellinger-Reissner(HR)variational principle,creating an implicit PFEM formulation.To mitigate the volumetric locking issue in low-order elements,we employ a node-based strain smoothing technique.By discretising field variables at the centre of smoothing cells,we achieve nodal integration over cells,eliminating the need for sophisticated mapping operations after re-meshing in the PFEM.We express the discretised governing equations as a min-max optimisation problem,which is further reformulated as a standard second-order cone programming(SOCP)problem.Stresses,pore water pressure,and displacements are simultaneously determined using the advanced primal-dual interior point method.Consequently,our numerical model offers improved accuracy for stresses and pore water pressure compared to the displacement-based PFEM formulation.Numerical experiments demonstrate that the N-PFEM efficiently captures both transient and long-term hydro-mechanical behaviour of saturated soils with high accuracy,obviating the need for stabilisation or regularisation techniques commonly employed in other nodal integration-based PFEM approaches.This work holds significant implications for the development of robust and accurate numerical tools for studying saturated soil dynamics.

A Numerical Method for Rigid-plastic FEM Analysis Basing on Mathematical Programming

The rigid-plastic analysis of mental forming simulation is formulated as a discrete nonlinear mathematical programming problem with equality and inequality constraints by means of the finite element technique. An iteration algorithm is used to solve this formulation, which distinguishes the integration points of the rigid zones and the plastic zones and solves a series of the quadratic programming to overcome the difficulties caused by the nonsmoothness and the nonlinearity of the objective function. This method has been used to carry out the rigid-plastic FEM analysis. An example is given to demonstrate the effectiveness of this method.

AN OPTIMAL DESIGN OF RING SPINNING SPINDLES USING PROGRAM SAP84

In this paper, natural frequencies and vibration modes of spindl D1203 are calculated by us-ing structural analysis program SAP84. It is found that the second natural frequency of D1203spindle is too close to the range of working speed. In order to raise the second natural frequencyand to reduce the vibration noise, simple optimal design of several structural parameters are alsodiscussed by means of the orthogonal design method. It is shown that the better design is toshorten the length of the spindle blade appropriately and to increase the elasticity of its uppersupport.

Static and Dynamic Analysis of Mooring Lines by Nonlinear Finite Element Method

This study has focused on developing numerical procedures for the static and dynamic nonlinear analysis of mooring lines. A geometrically nonlinear finite element method using isoparametric cable element with two nodes is briefly presented on the basis of the total Lagrangian formulation. The static and dynamic equilibrium equations of mooring lines are established. An incremental-iterative method is used to determine the initial static equilibrium state of cable systems under the action of self weights, buoyancy and current. Also the Newmark method is used for dynamic nonlinear analysis of ocean cables. Numerical examples are presented to validate the present numerical method, and examine the effect of various parameters.

The use of the node-based smoothed finite element method to estimate static and seismic bearing capacities of shallow strip footings

The node-based smoothed finite element method(NS-FEM)is shortly presented for calculations of the static and seismic bearing capacities of shallow strip footings.A series of computations has been performed to assess variations in seismic bearing capacity factors with both horizontal and vertical seismic accelerations.Numerical results obtained agree very well with those using the slip-line method,revealing that the magnitude of the seismic bearing capacity is highly dependent upon the combinations of various directions of both components of the seismic acceleration.An upward vertical seismic acceleration reduces the seismic bearing capacity compared to the downward vertical seismic acceleration in calculations.In addition,particular emphasis is placed on a separate estimation of the effects of soil and superstructure inertia on each seismic bearing capacity component.While the effect of inertia forces arising in the soil on the seismic bearing capacity is non-trivial,and the superstructure inertia is the major contributor to reductions in the seismic bearing capacity.Both tables and charts are given for practical application to the seismic design of the foundations.

A MATHEMATICAL PROGRAMMING ALGORITHM FOR LIMIT ANALYSIS

This paper deals with the limit analyses of perfect rigid-plastic continua.Based on the kinematic theorem of the limit analysis theory,a mathematical programming finite element formula for determining the upper bound load multiplier has been established,and an iteration algorithm proposed accordingly.In this algorithm the plastic and rigid zones are distinguished for every iteration step,and the goal function is modified gradually.The difficulties caused by the nonsmoothness of the goal function are over- come.Some examples solved by this algorithm are presented.

PARAMETRIC VARIATIONAL PRINCIPLE BASED ELASTIC-PLASTIC ANALYSIS OF HETEROGENEOUS MATERIALS WITH VORONOI FINITE ELEMENT METHOD

The Voronoi cell finite element method （VCFEM） is adopted to overcome the limitations of the classic displacement based finite element method in the numerical simulation of heterogeneous materials. The parametric variational principle and quadratic programming method are developed for elastic-plastic Voronoi finite element analysis of two-dimensional problems. Finite element formulations are derived and a standard quadratic programming model is deduced from the elastic-plastic equations. Influence of microscopic heterogeneities on the overall mechanical response of heterogeneous materials is studied in detail. The overall properties of heterogeneous materials depend mostly on the size, shape and distribution of the material phases of the microstructure. Numerical examples are presented to demonstrate the validity and effectiveness of the method developed.

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.

Object-Oriented Finite Element Analysis of Metal Working Processes

Recently an object-oriented approach has been applied in the fields of finite element analysis with a view to treating the various complexities within these. It has been demonstrated that finite element software designed using an object-oriented approach can be significantly more robust than traditional codes. This paper describes a special kind of implementation of object-oriented programming which is rather hybrid in nature, in the development of a finite element code for engineering analysis of metal working problems using C++, and discusses the advantages of this approach.

Finite Element Analysis of the Dynamic Behaviour of Transmission Line Conductors Using MATLAB

The dynamic behaviour of power line cables have been a source of interest to researchers ever since the phenomenon was first noticed in the 1920s. Conductor oscillation is mostly caused by the dynamic forces of nature such as wind loading. This imposes a periodic force on the conductors which is highly undesirable. It is therefore important for engineers to account for the possible effect of the wind loading when designing the power line. Investigations have shown that modeling the exact dynamic behaviour of a conductor is very difficult. Based on this fact, getting the exact analytical solution to conductor vibration is difficult, which is almost impossible, hence the numerical approximation becomes an option. This paper presents the developed finite element method used to analyse the dynamic behaviour of transmission line conductors. The developed FEM （finite element method） is implemented on MATLAB. The numerical analysis using MATLAB that is presented in this paper is used to simulate the response of the conductor when subjected to external loading in the time domain. The simulation is used to analyse the transverse vibration of the conductor. The formulation of the stiffness matrix and load vector is done and the results obtained are used to evaluate the conductor＇s internal energy dissipation. This finite element solution is compared with the results documented in literature. This numerical simulation is also used to investigate the effects of varying the axial tension on energy dissipation within the strands. Hence, this evolved in physically appropriate energy characterization process that can be used to evaluate the conductor self-damping with respect to line contact.

Nonlinear dynamical response of high-voltage transmission lines based on cable dropping

In order to study the dynamic response of high-voltage transmission lines under mechanical failure, a finite element model of a domestic 500-kV high-voltage transmission line system is established. The initial equilibrium condition of the coupling system model is verified by nonlinear static analysis. The transient dynamic analysis method is proposed to analyze the variation law of dynamic response under cable or insulator rupture, and the dynamic response of structural elements next to the broken span is calculated. The results show that upper crossarm cable rupture has no effect on cable tension at adjacent suspension points, but it has a significant influence on tension in the insulator and the tower component of the upper crossarm next to the broken span. The peak tension in the conductor of the upper crossarm at the suspension point exceeds the design value under insulator rupture. Insulator rupture has no effect on the tower component of the upper crossarm, but it has a significant influence on insulator tension of the upper crossarm. Insulator rupture should be taken into account in the design of overhead transmission lines. The research results can provide a theoretical basis for the design of transmission lines.

Reduction of electric field strength by two species of trees under power transmission lines

Electrical pollution is a worldwide concern,because it is potentially harmful to human health.Trees not only play a significant role in moderating the climate,but also can be used as shields against electrical pollution.Shielding effects on the electric field strength under transmission lines by two tree species,Populus alba and Larix gmelinii,were examined in this study.The electrical resistivity at different heights of trees was measured using a PiCUS sonic tomograph,which can image the electrical impedance for trees.The electric field strength around the trees was measured with an elf field strength measurement system,HI-3604,and combined with tree resistivity to develop a model for calculating the electric field intensity around trees using the finite element method.In addition,the feasibility of the finite element method was confirmed by comparing the calculated results and experimental data.The results showed that the trees did reduce the electric field strength.The electric field intensity was reduced by 95.6%,and P.alba was better than L.gmelinii at shielding.

Dynamic Analysis of Overhead Transmission Lines under Turbulent Wind Loading

Transmission tower-line systems are designed using static loads specified in various codes. This paper compares the dynamic response of a test transmission line with the response due to static loads given by Eurocode. Finite element design software SAP2000 was used to model the towers and lines. Non-linear dynamic analysis including the large displacement effects was carried out. Macroscopic aspects of wind coherence along element length and integration time step were investigated. An approach is presented to compare the probabilistic dynamic response due to 7 different stochastically simulated wind fields with the response according to EN-50341. The developed model will be used to study the response recorded on a test line due to the actual wind speed time history recorded. It was found that static load from EN overestimated the strength of conductor cables. The response of coupled system considering towers and cables was found to be different from response of only cables with fixed supports.

A NEW METHOD FOR SOLUTION OF 3D ELASTIC-PLASTIC FRICTIONAL CONTACT PROBLEMS

The solution of 3 D elastic-plastic frictional contact problems belongs to the un specified boundary problems where the interaction between two kinds of nonlinearities should occur. Considering the difficulties for the solution of 3 D frictional contact problems, the key part is the determination of the tangential slip states at the contact points, and a great amount of computing work is needed for a high accuracy result. A new method based on a combination of programming and iteration methods, which are respectively known as two main kinds of methods for contact analysis, was put forward to deal with 3 D elastic-plastic contact problems. Numerical results demonstrate the efficiency of the algorithm illustrated here.

Finite Element Structural Analysis UsingObject-Oriented Techniques

This paper describes the object-oriented implementational method of finite element structural analysis, gives the basic concepts of the object-oriented method and objectoriented programming, develops a complete class hierarchy structure of object-oriented finite element structural analysis, and gives a part C+ + code description.

Application of Program Generation Technology in Solving Heat and Flow Problems

Based on a new DIY concept for software development, an automatic program-generating technology attached on a software system called as Finite Element Program Generator （FEPG） provides a platform of developing programs, through which a scientific researcher can submit his special physico-mathematical problem to the system in a more direct and convenient way for solution. For solving flow and heat problems by using finite element method, the stabilization technologies and fraction-step methods are adopted to overcome the numerical difficul- ties caused mainly due to the dominated convection. A couple of benchmark problems are given in this paper as examples to illustrate the usage and the superiority of the automatic program generation technique, including the flow in a lid-driven cavity, the starting flow in a circular pipe, the natural convection in a square cavity, and the flow past a circular cylinder, etc. They are also shown as the verification of the algorithms.