bluuebunny/crossref_metadata_2025 huggingface dataset:
Finite element model for the analysis of a building
Authors: Bouberguig A.
Published: February 2008

Many problems are identified in the static analysis of a building based on ‘slabs, walls, columns’ by the classical method consisting of isolating the corresponding slab at each level and of subdividing it into finite elements by replacing walls and columns by localized fixed bearing points. Better adapted methods are indicated, particularly modelling the whole structure using ‘shell’ elements. A specially developed ‘slab, wall, column’ model is defined based on simplifying hypotheses which break down the effects of horizontal and vertical loads. The scope is precisely outlined and practical examples are given integrating the soil‐structure interaction and the placing of prestressing.
Analysis of three‐dimensional prestressed concrete structures using a non‐linear material model
Authors: Majorana C. , Natali A. , Vitaliani R.
Published: February 2008

The aim of the present work is to describe a numerical approach to the analysis of three‐dimensional reinforced concrete structures subject to prestressing. The finite element approach developed is described, with particular regard to the configuration of finite elements in relation to numerical model generation. An elasto‐viscoplastic material law is adopted. The non‐linear formulation is discussed, pointing out theoretical and numerical aspects. The computational examples, carried out using a specially developed code, aim at illustrating the characteristic aspects of the proposed approach.
Which parallel finite element algorithm for which architecture and which problem?
Authors: Farhat Charbel
Published: February 2008

The various forms of parallel numerical algorithms that speed up finite element computations are as numerous as the number of researchers working on the problem. In this paper, we review some of these parallel computational strategies and assess their adequacy for a given architecture and a given problem. We also report on the performance of both extreme parallel hardware technologies on real‐life structural problems.
A boundary element method to calculate the fluid hydrodynamic mass matrix in structural analysis including free surface waves
Authors: Rangette A.
Published: February 2008

A boundary element method has been developed to calculate the added mass matrix of fluid coupled structures in the case when the fluid is assumed to be compressible and inviscid. The potential flow is represented by a double layer density with linear interpolation functions. A linear set of equations for the fluid motion is obtained by Galerkin's procedure. The added mass matrix is not symmetric but a symmetrization procedure is established. The method has been implemented into a computer code for two‐dimensional geometries, whose results are presented here. A comparison with the analytical results already shows excellent agreement for coarse discretizations.
Edge effects in Mindlin—Reissner plates using adaptive mesh refinement
Authors: Selman A. , Hinton E. , Atamaz‐Sibai W.
Published: February 2008

An adaptive mesh refinement procedure is used in static plate bending finite element analysis to study the edge effects in Mindlin—Reissner plates.
Introduction of anisotropy in the numerical simulation of the forging process
Authors: Bay François , Chenot Jean‐Loup
Published: February 2008

In order to optimize production and save material, numerical simulation is becoming more and more used in industrial forging processes.
Modelling the three‐dimensional fluid flow and heat transfer in a moving weld pool
Authors: Song Wu Chuan , Tsao Keh C.
Published: February 2008

A three‐dimensional model for the fluid convection and heat flow in arc welding is proposed. It extends the previous two‐dimensional model by accounting also for the fluid flow and heat transfer in a travelling rather than a stationary mode. The model can be applied to analyse the heat‐ and fluid‐flow phenomena in welding processes. It is found that the fluid velocity in the pool front is higher than that in the pool rear. The fluid velocity field and the temperature distributions are directly proportional to the welding amperage and inversely to the welding speed. The comparison of the calculated and measured results show that the model is much more accurate than Rosenthal's theory and the pure conduction numerical method. Theoretical predictions based on the model are found to be in good agreement with experimental measurements.
Comparative investigation of sheet metal forming processes by the elastic‐plastic finite element method with emphasis on the effect of bending
Authors: Yang D.Y. , Shim H.B. , Chung W.J.
Published: February 2008

The effect of bending is investigated through the comparison of the membrane analysis and the shell analysis for stretching and deep drawing. An incremental formulation incorporating the effect of shape change and anisotropy is used for the analysis of elastic‐plastic non‐steady large deformation. The deformation during a step is considered using the natural convected coordinate system. Stretching of a square blank with a hemispherical punch and deep drawing of a cyclindrical cup is analysed and the corresponding experiments are carried out. The computational results are compared with the experiments. In stretching, the comparison has shown that both the membrane analysis and the shell analysis are in good agreement with the experiment for punch load and strain distribution. In deep drawing, the computed loads of both the membrane analysis and the shell analysis are generally in good agreement with the experiment. The computed thickness strain of the membrane analysis, however, shows a wide difference with the experiment. In the shell analysis, the thickness strain shows good agreement with the experiment. It has been shown that the membrane approach shows a limitation for the deep drawing process in which the effect of bending is not negligible and more exact informations on the thickness strain distribution are required.
Numerical modelling and non‐linear analysis of the behaviour of maxillary partial denture
Authors: Böhm H.J. , Rammerstorfer F.G. , Schmid R. , Starlinger A. , Slavicek R.
Published: February 2008

The biomechanical problem of investigating the behaviour of a maxillary partial denture is treated by non‐linear finite element analyses. The finite element models developed allow the solution of an inverse problem to find material data of the palatal tissue and the computation of pressure distributions between the palatal plate of the denture and the palatal tissue as well as the determination of the forces acting on the anchoring teeth. This information is essential from the physiological point of view in order to avoid configurations causing pain to the patient and to prevent the natural teeth from becoming slack. Such analyses can serve as a basis for the computer aided design of proper palatal dentures.
THREE‐DIMENSIONAL NON‐LINEAR ANALYSIS OF REINFORCED CONCRETE BEAMS
Authors: SUN ZHEFENG , BREYSSE DENYS
Published: February 2008

Simplified methods are often employed for the analysis of reinforced concrete beams (R‐C beams). A three‐dimensional problem (3D) is often transformed into a two‐dimensional problem (2D) with some assumptions which are usually established in static. The essential reason for this simplification lies in the fact that the 3D finite element analysis is so expensive that it is impossible to study directly the non‐linear behaviour of R‐C beams in many cases. Our purpose is to present a specific method which allows the direct 3D analysis of R‐C beams with a suitable numerical cost. First, the 3D linear heterogeneous beam theory is briefly recalled as well as the continuum damage model used for concrete. Second, the non‐linear behaviour of concrete is introduced in the 3D beam theory. Several numerical examples illustrate the effectiveness of the method.
DYNAMIC STABILITY ANALYSIS OF A COMPOSITE MATERIAL CONNECTING ROD BY THE FINITE ELEMENT METHOD
Authors: CHEN LIEN‐WEN , KU DER‐MING
Published: February 2008

The Euler beam theory is used to study the dynamic stability of a composite material slider‐crank mechanism with an elastic connecting rod. The Ritz finite element procedure is applied to derive the governing equations of motion of the mechanism. Based on the assumption that the slider‐crank mechanism is subjected to a sinusoidal input torque and the operation condition is at a steady dynamic state, the governing equations represent a system of second order differential equations with periodic coefficients of the Mathieu‐Hill type. Making use of the Bolotin method, the boundaries between stable and unstable solutions of the elastic connecting rod are constructed. The advantages of using composite materials in the design of mechanisms are demonstrated.
ERROR ESTIMATION AND MESH OPTIMIZATION FOR CLASSICAL FINITE ELEMENTS
Authors: LADEVÈZE P. , PELLE J.‐P. , ROUGEOT PH.
Published: February 2008

We present several applications for 2D or axisymmetric elasticity problems of a method to control the quality of a finite element computation, and to optimize the choice of meshes. The method used, which is very general, is based (i) on the concept of error in constitutive relation and (ii) on explicit techniques to construct admissible fields. Illustrative examples are shown for several 2D or axisymmetric elements (3 or 6 node triangles, 4 or 8 node quadrilaterals). They have been achieved with our code ESTEREF, a post‐processor of error computation and mesh optimization which can be interfaced with any finite element code.
OBJECT ORIENTED PROGRAMMING IN SCIENTIFIC COMPUTATIONS: THE BEGINNING OF A NEW ERA
Authors: SERGIO RODRIGUES ALVES FILHO JOSÉ , REMY BERNARD DEVLOO PHILIPPE
Published: February 2008

Undoubtedly, Fortran dominates the field of scientific computing from commercial packages to university programs. Although Pascal and C have managed to seduce some programmers with their newer design, the majority of users still favours Fortran into which most of those new features are eventually incorporated. The innovative programming tools offered by new languages have not been able to justify the time and cost required for the training of programmers and the porting of existent code.
THREE DIMENSIONAL SOIL‐STRUCTURE INTERACTION ANALYSIS: DEFORMABLE STRUCTURES IN MULTILAYERED SOIL MASS
Authors: KUNDU T. , MATHUR R.P. , DESAI C.S.
Published: February 2008

A new hybrid method based on three‐dimensional finite element idealization in the near field and a semi‐analytic scheme using the principles of wave propagation in multilayered half space in the far field is proposed for the dynamic soil‐structure interaction analysis. The distinguishing feature of this technique from direct or indirect boundary integral techniques is that in boundary integral techniques a distribution of sources are considered at the near field boundary. Strengths of these sources are then adjusted to satisfy the continuity conditions across the near‐field/far‐field interface. In the proposed method unknown sources are placed not at the near field boundary but at the location of the structure. Then the Saint‐Venant's principle is utilized to justify that at a distant point the effect of the structure's vibration can be effectively modelled by an equivalent vibrating point force and vibrating moment at the structure's position. Thus the number of unknowns can be greatly reduced here. For soil‐structure interaction analysis by this method one needs to consider only three unknowns (two force components and one in‐plane moment) for a general two‐dimensional problem and six unknowns (three force components and three moment components) for a general three‐dimensional problem. When a vertically propagating elastic wave strikes a structure which is symmetric about two mutually perpendicular vertical planes the structure can only vibrate vertically for dilatational waves and horizontally for shear waves. Under this situation the number of unknowns is reduced to only one whereas in boundary integral and boundary element techniques the number of unknowns is dependent on the number of nodes at the near field boundary, which is generally much greater than six. Several example problems are solved in this paper using this technique for both flexible and rigid structures in multilayered soil media.
THREE‐DIMENSIONAL TRANSIENT ANALYSIS OF A SINGLE SUBMERGED CYLINDRICAL SHELL
Authors: SINGH R.K. , KANT T. , KAKODKAR A.
Published: February 2008

Three‐dimensional transient analysis of a submerged cylindrical shell is presented. Three‐dimensional trilinear eight‐noded isoparametric fluid element with pressure variable as unknown is coupled to a nine‐noded degenerate shell element. Staggered solution scheme is shown to be very effective for this problem. This allows significant flexibility in selecting an explicit or implicit integrator to obtain the solution in an economical way. Three‐dimensional transient analysis of the coupled shell fluid problem demonstrates that inclusion of bending mode is very important for submerged tube design—a factor which has not received attention, since most of the reported results are based on simplified two‐dimensional plane strain analysis.
FINITE ELEMENT COMPUTATION OF SPREAD IN HOT FLAT AND SHAPE ROLLING WITH A STEADY STATE APPROACH
Authors: CHENOT J.L. , MONTMITONNET P. , BUESSLER P. , FAU F.
Published: February 2008

A technique for computing free surfaces by a steady state approach has been included in the hot rolling code ROLL3. It has been described in a previous paper, along with applications to some simple rolling passes. In the present text, new developments are included to deal with more complex geometries, in particular when several potentially free surfaces exist. The problem of contact with flanks of grooves is given special care. Application to dog bone formation and flattening is presented. Then a case with two free surfaces is computed and compared to experiments. An application is then performed to beam roughing passes.
IMPROVEMENT OF THREE‐DIMENSIONAL HYBRID HEXAHEDRAL ELEMENTS BY USING ORTHOGONAL APPROACH
Authors: CHEN WANJI , CHEUNG Y.K.
Published: February 2008

Based on the orthogonal approach for hybrid element methods, refined three‐dimensional isoparametric hybrid hexahedral elements have been developed. The behaviour of the proposed models are discussed in respect of coordinate invariance, spurious zero energy modes and the ability to pass the patch test. By adopting the orthogonality of strain energy, the element stiffness matrix can be decomposed into a series of stiffness matrices in which the implementational effectiveness can be improved. A number of examples is used to demonstrate the implementation efficiency, accuracy and distortion insensitivity of the proposed elements, and its capacity of handling nearly incompressible materials
ELASTO‐VISCOPLASTIC ANALYSIS OF FIBRE‐REINFORCED COMPOSITES
Authors: KWON Y.W.
Published: February 2008

An analysis model has been developed for the elasto‐viscoplastic analysis of continuous fibre‐reinforced composite structures. Elastic deformation of fibre and elasto‐viscoplastic deformation of matrix are considered in the analysis model because the yield strength of matrix is, in general, substantially lower than that of fibre. A finite element formulation is derived for the proposed analysis model. If matrix is assumed homogeneous and isotropic, the von Mises yield criterion is used for viscoplastic yielding. As numerical examples, a parametric study has been performed for elasto‐viscoplastic analysis of unidirectional composite plates subjected to inplane loads.
ADDING THE TIME‐DEPENDENT TERMS TO A SEGREGATED FINITE ELEMENT SOLUTION OF THE INCOMPRESSIBLE NAVIER—STOKES EQUATIONS
Authors: SHAW C.T.
Published: February 2008

To‐date, several segregated finite element algorithms have been proposed that solve the Navier—Stokes equations. These have considered only steady‐state cases. This paper describes the addition of the time‐dependent terms to one such segregated solution scheme. Several laminar flow examples have been computed and comparisons made to predictions obtained with both finite difference and finite volume solution schemes. The finite element results compare very well with the results from the other schemes, both in terms of accuracy and the qualitative behaviour of the iterative schemes.
INCIPIENT FLOW OF ELASTICO‐VISCOUS FLUID IN A PIPE
Authors: SINGH TEJWANT
Published: February 2008

The theoretical derivation of the start‐up laminar flow of incompressible viscous fluid in a long pipe as suggested by Szymanski, could not be verified experimentally. This leads to the checking of assumption of constant pressure gradient across the ends of the pipe, on the basis of which the theoretical development was made. Recently, the problem was again investigated for viscous fluid by Otis. In the present paper, the laminar start‐up flow of elastico‐viscous fluid in a pipe, without assuming constant pressure gradient across its ends, has been investigated. The non‐linear governing equations are solved numerically and the effects of start‐up flow parameters and elastico‐viscous parameter on the velocity distribution have been studied.
NUMERICAL MODELLING OF DISCONTINUA
Authors: CUNDALL PETER A. , HART ROGER D.
Published: February 2008

Discrete element methods are numerical procedures for simulating the complete behaviour of systems of discrete, interacting bodies. Three important aspects of discrete element programs are examined: (1) the representation of contacts; (2) the representation of solid material; and (3) the scheme used to detect and revise the set of contacts. A proposal is made to define what constitutes a discrete element program, and four classes of such programs are described: the distinct element method, modal methods, discontinuous deformation analysis and the momentum‐exchange method. Several applications and examples are presented, and a list is given of suggestions for future developments.
DISCRETE MODELLING OF STRESS‐STRAIN BEHAVIOUR OF GRANULAR MEDIA AT SMALL AND LARGE STRAINS
Authors: DOBRY RICARDO , TANG‐TAT NG AND
Published: February 2008

A general overview is presented on applications of the discrete element method (DEM) to granular media. A literature survey is performed of static and dynamic simulations using random arrays of compliant particles, and forty‐two references published mostly in the last ten years are identified and categorized according to a number of relevant criteria. It is concluded that the interest in the use of the technique is rapidly increasing in the research and engineering community, with applications concentrated in soil mechanics, rock mechanics, grain flow and engineering problems. Additional studies and verifications of some numerical aspects of the DEM technique are suggested including parametric studies and comparisons. Program CONBAL‐2 (CONTACT + TRUBAL in 2D) developed by the authors based on TRUBAL created by Strack and Cundall, is described. CONBAL‐2 uses the complete Mindlin solution for the contact between two spheres and thus can be used for small strain and cyclic loading. The program is applied to study the cyclic response of uniform, medium dense to dense rounded quartz sand. Cyclic strain‐controlled loading at constant volume is applied to isotropically consolidated, random arrays of 531 spheres, using cyclic strains ranging from 10–4% to 10–1%. The calculated shear modulus, Gmax, constrained modulus, D, and Poisson's ratio at small strains are correlated with the confining pressure, the porosity of the array, and the coordination number. The calculated variations of secant modulus and damping ratio with cyclic strain compare favourably with the experimental results on sands compiled by Seed and Idriss. Finally, ‘pore water pressure buildup’ and cyclic stiffness degradation of the material with number of cycles is calculated at a cyclic strain of 10–1%, and the prediction is found to represent closely cyclic undrained experiments on sands. The existence of a threshold strain, yt ≈ 10–2%, found experimentally, is also predicted by the simulations.
THE DISCRETE ELEMENT METHOD FOR ANALYSIS OF FRAGMENTATION OF DISCONTINUA
Authors: HOCKING GRANT
Published: February 2008

This paper is concerned with the determination of the transient stress and deformational state of plate‐like discontinua subject to flexural cracking. Such a phenomenon can be easily visualized as the type of fragmentation to floating sea ice impacted by an ice‐breaker or offshore platform. The discrete element method is used to solve the dynamic equilibrium equations for each distinct deformable body and the interaction between bodies. Each body may deform elastically and fracture into further pieces if a brittle failure criterion for flexure is exceeded. The discrete plate element is a hybrid thin‐plate (Kirchhoff) mode lumped at element boundaries with transverse shear deformation computed at element centroids. Errors in computed stresses near point loads and cracks by the current element warrant the use of an improved mixed mode plate element. A three‐dimensional application of the discrete element method is presented for the case of fragmentation of floating sea ice impacting an arctic offshore platform. A semi‐implicit solution scheme is introduced to overcome the stringent explicit time step stability conditions due to stiff members in the discrete element formulation.
APPLICATION OF THE DISTINCT ELEMENT METHOD FOR ROCK MECHANICS PROBLEMS
Authors: CHOI S.K.
Published: February 2008

Some aspects of the distinct element method (DEM) are reviewed. A model for fully grouted reinforcement subjected to axial and/or shear force(s) is proposed. The modelling of some rock mechanics problems, by incorporating the reinforcement model into the DEM is presented. A general discussion on the application of the DEM in rock mechanics, and some of the difficulties that may be encountered, based on the author's experience, are also included.
HYBRID DISCRETE ELEMENT CODE FOR SIMULATION OF MINING‐INDUCED STRATA MOVEMENTS
Authors: O'CONNOR KEVIN M. , DOWDING CHARLES H.
Published: February 2008

To simulate the kinematics associated with mining‐induced subsidence in a blocky rock mass, a hybrid rigid block model was developed by combining a small displacement code with a large displacement code. Gravity was applied to a rigid block mesh using an implicit formulation and the equilibrium displacements are then used as initial conditions for an explicit analysis in which excavation of a longwall mine panel and subsequent subsidence was simulated. A parameter study was performed to evaluate the influence of rigid block contact stiffness, vertical joint density, and contact roughness on mining‐induced strata movements for comparison with previously obtained field measurements. The best agreement between measured and calculated displacements was obtained when a relatively low stiffness value was maintained constant for all contacts. A surprising result was that neither increasing the density of vertical joints nor reducing the rigid block contact roughness improved the agreement between measured and simulated displacements.
DISCRETE FINITE ELEMENT METHOD
Authors: BARBOSA R. , GHABOUSSI J.
Published: February 2008

A numerical technique is described for the analysis of multiple interacting deformable bodies undergoing large displacements and rotations. Each body is considered an individual discrete unit, which is idealized by a finite element model. Discrete finite element models interact with their surroundings through contact stresses, which are continually updated as the elements move and deform. The method of analysis consists of a finite element formulation based on a generalized explicit updated Lagrangian method. This formulation is a general finite element formulation, that permits the large deformation analysis of both continuum and discontinuum systems. Different validations of the proposed method of analysis, including cases that involve very large rotations, as well as some examples that demonstrate the application of the discrete finite element method to problems in rock mechanics are presented and discussed in the paper.
EIGENVALUES OF ELEMENT STIFFNESS MATRICES. PART I: 2‐D PLANE ELEMENTS
Authors: KIDGER D.J. , SMITH I.M.
Published: February 2008

The eigenvalues of element stiffness matrices K and the eigenvalues of the generalized problem Kx = λMx, where M is the element's mass matrix, are of fundamental importance in finite element analysis. For instance, they may indicate the presence of ‘zero energy modes’, or control the critical timestep applicable in temporal integration of dynamic problems. Recently explicit formulae for the eigenvalues of the stiffness matrix of a plane, 4‐node rectangular element have been given, and the authors have extended this approach to deal with 8‐node solid brick elements as well. In the present paper, explicit eigenvalues are given for plane triangular elements and techniques for eigenmode visualization are applied to well‐known triangular and quadrilateral elements. In the companion paper (Part II), the stiffness matrices of solid tetrahedra and bricks are similarly treated.
EIGENVALUES OF ELEMENT STIFFNESS MATRICES. PART II: 3‐D SOLID ELEMENTS
Authors: KIDGER D.J. , SMITH I.M.
Published: February 2008

In Part I, eigenvalues and eigenmodes of typical plane element stiffness matrices were separated and traced. This has important implications for the viability of new elements (presence of zero energy modes) and integrability of dynamic equations (critical time steps). In this part of the paper, similar techniques are applied to well‐known solid element stiffness matrices, and to some new ones.
A FINITE ELEMENT TECHNIQUE FOR THE ULTIMATE STRENGTH ANALYSIS OF TUBULAR JOINTS
Authors: COFER WILLIAM F. , WILL KENNETH M.
Published: February 2008

Offshore structures are generally constructed as frameworks of tubular members. The tubular joints should be designed to allow the full post yield or post buckled capacity of the members. However, design guidelines for ultimate strength capacity of these joints are based exclusively upon compilations of test data for simple configurations under simple loading conditions. A methodology based upon the finite element method is presented for analytically predicting the ultimate strength of arbitrary tubular joints. Eight node, isoparametric, curved shell elements were used for the majority of the tubular joint model. Twenty node, isoparametric, solid elements were used to capture the three‐dimensional stress state at the shell intersection while fifteen node, isoparametric, wedge elements modelled the weld profile. Solid‐shell transition elements provided the connection between the three‐dimensional solid elements and the surface based shell elements. Non‐linearities were included via an elastoplastic material model with isotropic strain hardening and the updated Lagrangian approach for finite deflections and rotations. Several experimental tubular joint analyses were reproduced to validate the analytical procedure. Non‐linear finite element analysis was shown to be a practical approach for the evaluation and extension of current design procedures for tubular joints.
A GENERALIZED CLOSEST‐POINT‐PROJECTION METHOD FOR DEFORMATION‐NEUTRALIZED FORMULATION IN FINITE STRAIN PLASTICITY
Authors: SARAN M.J. , RUNESSON K.
Published: February 2008

An implicit type algorithm for the integration of hypoelastic constitutive equations is proposed for large strain and large rotation conditions. Constitutive relations are derived in a deformation‐neutralized form. This provides the basis for integration in time resulting in an incremental tensor relation. Proposed algorithm can be considered as a generalization of the closest‐point‐projection method in the sense that the projection property applies to a ‘midstep’ rather than the final stress state. Hill's yield criterion under plane stress conditions suitable for metal‐forming applications is used in presented benchmark problems. Numerical results are discussed illustrating the accuracy of the algorithm for different values of the midstep parameter.
AUTOMATIC GENERATION OF BENDING ELEMENT MATRICES FOR FINITE ELEMENT METHOD USING REDUCE
Authors: BARBIER CHRISTINE
Published: February 2008

The formation of the well known element mass, geometric stiffness and stiffness matrices based on Hermite polynomials can be very easily automated using Computer Algebra systems. The algebraic language REDUCE has been used to obtain the algebraic expressions for such matrices in one and two dimensions and to automatically produce FORTRAN code. The program developed can derive the matrices for any number of nodes in the element. The aim is to demonstrate how the Computer Algebra system can greatly reduce the effort in forming these classical matrices. It can thus be used as a teaching aid.
MULTIOBJECTIVE DESIGN OPTIMIZATION OF CONTINUOUS BEAMS BY NUMERICAL METHODS
Authors: KODIYALAM SRINIVAS , ADALI S. , SADEK I.S.
Published: February 2008

The optimal thickness distribution of a two‐span continuous beam is determined with the objectives of minimizing the maximum stress, maximizing the fundamental frequency and frequency separation between adjacent frequencies. The self‐weight of the beam is included in the computations. The multiobjective design problem is solved by using the concept of Pareto optimality. The beam thickness is approximated by constant splines. The stress distribution and the frequencies are determined by the finite element method. The optimization of the beam is carried out by the feasible direction method and by employing a quadratic approximation of the thickness function. Numerical results are given for two‐objective design problems. Optimal trade‐off curves, thickness distributions and stress distributions of optimally designed beams are presented in graphical form. The effects of self‐weight and different design objectives on the thickness distribution are investigated.
COMPUTATION AND ANALYSIS OF MULTI‐EXCITATION RANDOM SEISMIC RESPONSES
Authors: JIAHAO LIN , WILLIAMS F.W.
Published: February 2008

Because of the extensive use of long‐span structures in modern engineering, much attention has been given to the extent to which ground motion phase‐lags affect the internal forces of such structures. In this paper, this problem is studied from the aspect of random seismic analysis, i.e. the random seismic responses of long‐span structures are explored with the phase‐lags of the ground joints of the structures taken into account. The earthquake is regarded as a stationary random process. Formulae for calculating the random responses of the structural displacements and internal forces are derived. Numerical examples are presented which illustrate some basic features of such random response, and also show that the ground motion phase‐lags have considerable effects on structural safety analysis.
SIMULATION OF INDUSTRIAL FORGING OF AXISYMMETRICAL PARTS
Authors: HANS RAJ K. , FOURMENT L. , COUPEZ T. , CHENOT J.L.
Published: February 2008

Numerical modelling and simulation of metal forming is rapidly gaining prominence in many industries all over the world due to its effective saving of production time, effort and economy. In order to meet this need a special finite element code FORGE2 has been developed at CEMEF. In this work the theoretical basis of the FORGE2 along with its features such as thermo‐viscoplastic coupling, material compressibility and automatic mesh regeneration is reviewed and an attempt is made to simulate a few industrial forming processes taking into account the complex friction phenomena and thermal environment.
THERMO‐ELASTOVISCOPLASTIC FINITE ELEMENT PLATE BENDING ANALYSES OF COMPOSITES
Authors: KWON Y.W.
Published: February 2008

A formulation has been developed for thermo‐elastoviscoplastic finite element analyses of continuous fibre‐reinforced composite plates subject to bending loading using a generalized continuum mechanics approach. Such an approach is used to model the non‐homogeneity in a composite, which is constituted by fibres embedded in a matrix material. The present formulation computes the respective stresses occurring in each constituent so that the respective yield criterion and flow rule of each constituent may be used if there is a material yielding in any constituent. Thermo‐elastic deformation of fibre and thermo‐elastoviscoplastic deformation of matrix are considered in the present study because the yield strength of fibre is substantially higher than that of matrix in many cases. Both constituents are assumed to be isotropic so that the von‐Mises yield criterion may be used for viscoplastic yielding of matrix. As numerical examples, a parametric study is performed for thermo‐elastoviscoplastic deformations of laminated composite plates subject to thermal bending loads.
ON THE RANK DEFICIENCY OF AHMAD'S DEGENERATED SHELL ELEMENT
Authors: JENDELE L. , CHAN A.H.C. , PHILLIPS D.V.
Published: February 2008

This paper deals with the well known degenerated shell element of Ahmad. The main concern focuses on the rank of the element stiffness matrix and the zero energy modes. Element formulation includes geometrical and material non‐linearities. The Lagrangian, heterosis and serendipity variants of displacement approximation are studied using full, selective or reduced in‐plane numerical integration. In the third direction the layered concept is adopted. The obtained results do not fully coincide with those published in References 2 and 3. The Figures presented in this paper, showing the displacement modes, clarify in a convenient form some of the element properties associated with particular element formulations. The work also shows the influence of the plastic and cracked material conditions on the stiffness matrix of the element.
A TWO‐FIELD SOLID ELEMENT SUITING THIN‐MESH ANALYSIS BY ADMISSIBLE MATRIX FORMULATION
Authors: SZE K.Y. , GHALI A.
Published: February 2008

An 8‐node solid element applicable for thin structures is presented. The element employs eighteen assumed stress modes and the conventional displacement interpolation. The formulation starts with the hybrid stress element proposed by Pian and Tong. The higher order stress modes are first decomposed into the ones which do and do not lead to thin‐element locking. The recently established methodology of admissible matrix formulation allows the decoupling of the above two categories of stress modes in the flexibility matrix without triggering element instability or failure of the patch test. The element stiffness can thus be decomposed into a series of matrices. Locking can be eliminated by adjusting the magnitude of the pertinent matrices. Accuracy and convergence rate of the present element are found to be competent to many of the existing plate and shell models.
AN EFFICIENT ALGORITHM FOR THE COMPUTATION OF STABILITY POINTS OF DYNAMICAL SYSTEMS UNDER STEP LOAD
Authors: WRIGGERS P. , CARSTENSEN C.
Published: February 2008

Many engineering structures exhibit loss of stability under static and dynamic loading. Due to the significance of these phenomena in engineering design this topic has attracted considerable attention during the last decades. In recent years much effort has been made to devise algorithms within finite element analysis to investigate the static stability behaviour of structures. With these methods stable and unstable paths can be traced, and limit or bifurcation points can be computed efficiently. The associated arc‐length or branch‐switching procedures are today standard tools in existing finite element codes.
NUMERICAL SIMULATION OF CONTINUOUS CHIP FORMATION DURING NON‐STEADY ORTHOGONAL CUTTING
Authors: SEKHON G.S. , CHENOT J.L.
Published: February 2008

A finite element model for numerical simulation of non‐steady but continuous chip formation under orthogonal cutting conditions is described. The problem is treated as coupled thermo‐mechanical. A velocity approach has been adopted for the proposed solution. The computational algorithm takes care of dynamic contact conditions and makes use of an automatic remeshing procedure. The results of simulation yield complete history of chip initiation and growth as well as distributions of strain rate, strain, stress and temperature. The paper includes a detailed presentation of computational results for an illustrative case.
RIGID‐PLASTIC IMPLICIT SCHEME FOR NON‐ AND THREE‐DIMENSIONAL ANALYSIS OF METAL FORMING BY FINITE ELEMENT METHOD
Authors: DE SAXCE G. , FENG Z.Q. , TOUZOT G.
Published: February 2008

This paper is devoted to the analysis of metal forming with assumption of rigid‐plastic behaviour with strain hardening. As opposed to the classical rate problem formulation based on Markov's principle and the explicit scheme, a more satisfactory incremental approach is deduced from Moreau's catching up algorithm. This implicit scheme, although more complicated, gives better results concerning convergence and numerical stability. Using an internal variable representing the strain hardening, an incremental strain energy density is defined which leads to a principle of minimum of the total incremental strain energy. In the numerical approximation using finite elements, the non‐linear equilibrium equations are solved by classical Newton's method. An approximation of Coulomb's criterion is used in order to represent friction with a rigid foundation. The simple compression test is simulated and shows that the implicit scheme is faster than the explicit one.
RANK ANALYSIS OF RECTANGULAR MATRIX AS AN ELEMENT OF CONTINUATION METHOD
Authors: KOWALCZYK MACIEJ
Published: February 2008

This paper is concerned with rank analysis of rectangular matrix of a homogeneous set of incremental equations regarded as an element of continuation method. The rank analysis is based on a known feature that every rectangular matrix can be transformed into the matrix of echelon form. By inspection of the rank, correct control parameters are chosen and this allows not only for rounding limit and turning points but also for branch‐switching near bifurcation points.
DAMAGE SIMULATION IN HETEROGENEOUS MATERIALS FROM GEODESIC PROPAGATIONS
Authors: JEULIN D.
Published: February 2008

We propose a simplified method to simulate damage evolution in heterogeneous media from geodesic propagation calculations. The method introduced for the case of porous media (polycrystalline graphite), was generalized to multiphase media, and then to a continuous variation of local fracture energy. It is based on a minimization of the fracture energy criterion, ignoring the local variations of the stored strain energy. With this simplification, the microcracking process is simulated by very efficient algorithms, involving a low calculation cost, to extract minimal paths on graphs with edges valued according to the local fracture energy. From the simulations, made on micrographs in materials or on random microstructure simulations, we get images of the possible microcracks paths, to be compared with real cracking of materials, and an estimation of the effective toughness of heterogeneous materials. Our approach is illustrated from two‐dimensional simulations corresponding to various types of microstructure involving the following micro‐geometrical distributions of the local fracture energy: isotropic and anisotropic two‐phase media, polycrystal with cleavage and intergranular fracture, material with a continuous distribution of surface energy.
MULTIGRID TECHNIQUE FOR THE COMPRESSIBLE EULER AND NAVIER‐STOKES EQUATIONS
Authors: KANARACHOS A.E. , VOURNAS I.P.
Published: February 2008

An optimized multigrid method (NSFLEX‐MG) for the NSFLEX‐code (Navier‐Stokes solver using characteristic flux extrapolation) of MBB (Messerschmitt Bolkow Blohm GmbH) is described. The method is based on a correction scheme and implicit relaxation procedures and is applied to two‐dimensional test cases. The principal feature of the flow solver is a Godunov‐type averaging procedure based on the eigenvalues analysis of the Euler equations by means of which the inviscid fluxes are evaluated at the finite volume faces. Viscous fluxes are centrally differenced at each cell face. The performance of NSFLEX‐MG is demonstrated for a large range of Mach numbers for compressible inviscid and viscous (laminar and turbulent) flows over a RAE‐2822 airfoil and over a NACA‐0012 airfoil.
PSEUDO‐TRANSIENT LARGE‐DEFLECTION ELASTIC ANALYSIS OF FIBRE REINFORCED COMPOSITE PLATES
Authors: KANT T. , KOMMINENI J.R.
Published: February 2008

A unified approach is presented for the pseudo‐transient (static) linear and geometrically non‐linear analyses of composite laminates. A finite element idealization with a four‐noded linear and a nine‐noded quadrilateral isoparametric elements, both belonging to the Lagrangian family are used in space discretization. An explicit time marching scheme is employed for time integration of the resulting discrete ordinary differential equations with the special forms of diagonal fictitious mass and/or damping matrices. The accuracy of the formulation is then established by comparing the presnt pseudo‐transient analysis results with the present static Newton‐Raphson method results and other available analytical closed‐form two dimensional and finite element solutions. The usefulness and effectiveness of this approach is established by comparing computational time required by this approach and Newton‐Raphson's approach.
NEW ERROR ESTIMATION FOR C° EIGENPROBLEMS IN FINITE ELEMENT ANALYSIS
Authors: AVRASHI JACOB , COOK ROBERT D.
Published: February 2008

This paper presents a new approach for estimating the discretization error of finite element analysis of generalized eigenproblems. The method uses smoothed gradients at nodal points to derive improved element‐by‐element interpolation functions. The improved interpolation functions and their gradients are used in the Rayleigh quotient to obtain an improved eigenvalue. The improved eigenvalue is used to estimate the error of the original solution. The proposed method does not require any re‐solution of the eigenproblem. Results for 1‐D and 2‐D C° eigenproblems in acoustics and elastic vibrations are used as examples to demonstrate the accuracy of the proposed method.
AN ALGORITHM FOR PROFILE AND WAVEFRONT REDUCTION OF SPARSE MATRICES WITH A SYMMETRIC STRUCTURE
Authors: MEDEIROS S.R.P. , PIMENTA P.M. , GOLDENBERG P.
Published: February 2008

A new algorithm for reducing the profile and root‐mean‐square wavefront of sparse matrices with a symmetric structure is presented. Our numerical experiments show an overall better performance than the widely used reverse Cuthill‐McKee, Gibbs‐King and Sloan algorithms. The new algorithm is fast, simple and useful in engineering analysis where it can be employed to derive efficient orderings for both profile and frontal solution schemes.
AUTOMATING FINITE ELEMENT DEVELOPMENT USING OBJECT ORIENTED TECHNIQUES
Authors: RAPHAEL BENNY , KRISHNAMOORTHY C.S.
Published: February 2008

An object oriented finite element model is presented. The main advantage of this model over conventional systems is that, the additional code required for adding elements to the finite element library is minimal. The powerful mechanisms provided by object oriented systems facilitate this. These mechanisms enable re‐use of existing code, and allow the programmer to leave certain operations to the computer, which, without object oriented techniques, would not have been possible. In the above model, the finite elements are represented in the form of a hierarchical tree by which it is possible to develop elements by programming only the differences from existing elements. Suitable object oriented designs have been developed for representing mathematical entities like differential operators and shape functions, with a view to automating the process of development of element properties, so that, the element developer needs to specify just the minimum details, leaving most of the operations to the computer. Some of the concepts in object oriented programming are explained in detail, with the examples used in the above model.
SOME STUDIES ON FREE VIBRATION ANALYSIS OF CYCLIC SYMMETRIC STRUCTURES USING SUBSPACE METHOD
Authors: BALASUBRAMANIAN P. , JAGADEESH J.G. , SUHAS H.K. , RAMAMURTI V.
Published: February 2008

The free vibration analysis of cyclic symmetric structures is considered as a Hermitian eigenvalue problem in semi‐complex domain using subspace iteration method is presented. The trial vectors are selected using a modified Ritz vector scheme. A modified convergence criterion which gives true error estimates which is suited for clustered eigenvalue problems is presented. Also the effect of purification of trial vectors on convergence is considered.
A NOTE ON THE ACCURACY OF THE GECKELER APPROXIMATION
Authors: ZINGONI A. , PAVLOVIĆ M.N.
Published: February 2008

A simple estimate of the accuracy of the widely‐used Geckeler approximation for the axisymmetric bending of non‐shallow spherical shells is presented. Based on the edge‐deformation coefficients associated with a pair of arbitrary edge loadings, this estimate is independent of the actual surface‐loading and edge conditions of a practical shell. In this respect, the note complements the findings of an earlier error study, which was based on specific surface loadings and boundary conditions. The complementary nature of the work lies in its use for providing (in the absence of more specialised results) a reasonable assessment of the accuracy of the Geckeler approximation for any loading and/or boundary conditions.
SOME BASIC FINITE ELEMENT ANALYSIS OF MICROVOID NUCLEATION, GROWTH AND COALESCENCE
Authors: BENNANI B. , PICART P. , OUDIN J.
Published: February 2008

Microstructure void volume fraction is taken into account in finite element models developed for large strain elastoplastic problems. Void nucleation rate is related to matrix effective strain rate, void growth to material strain rate and associated elastoplastic potential available for porous material, void coalescence to matrix effective strain rate. The related radial return algorithm is described. Three types of computations are proposed: first, axisymmetric Q4 element traction are given as validation example; second, collar cylinder compression are computed as reference example; third, bulk forming are analysed as large strain specific example. Void volume fraction and hydrostatic stress are mainly discussed according to microvoids nucleation, growth and coalescence. Finally, the main interests of those computations are enhanced.
A COMPARISON BETWEEN THE GENETIC ALGORITHM AND THE FUNCTION SPECIFICATION METHODS FOR AN INVERSE THERMAL FIELD PROBLEM
Authors: WOOD R.L.
Published: February 2008

In principle, it is possible to apply genetic algorithms (GAs) to the solution of inverse problems in the simulation of manufacturing processes. In this context, an inverse problem can be stated as ‘knowing the desired output of a process, what combination of process parameters are required for its achievement?’. Since the simulation of many processes requires the simulation of thermal, solids and/or fluids problems, the application of GAs to inverse process modelling depends on their ability to solve a wide range of inverse field problems. This paper has two major objectives: (a) to demonstrate the application of a GA to a simple inverse thermal field problem, and (b) to compare its performance against a relatively mature technique for the solution of such problems. The results of this study indicate that, despite the relatively large computational cost of GAs, their accuracy and robustness warrants further investigation of their performance in more demanding applications.