bluuebunny/crossref_metadata_2025 huggingface dataset:
On a generalized conjugate gradient orthogonal residual method
Authors: Axelsson Owe , Makarov M.
Published: October 2005

To solve a linear system of equations with a generally nonsymmetric matrix, a generalized conjugate gradientorthogonal residual method is presented. The method uses all previous search directions (or a truncated set of them) at each step but, contrary to standard implementations of similar methods, it requires storage of only one set with a linearly growing number of vectors (or the number in the truncated set). Furthermore, there is only one vector (the residual), which must be updated using all the vectors in this set, at each step. In this respect it is similar to the popular GMRES method but it has the additional advantage that it can stop at any stage when the norm of the residual is sufficiently small and no extra computation is needed to compute this norm. Furthermore, the new method can be truncated.

The rate of convergence of the method is also discussed.
An improved finite difference method for plate vibration
Authors: Chang Anthony T.
Published: October 2005

An improved finite difference method is presented. This is exemplified by computing the natural frequency of vibrating plates. A new formulation of the problem showing computational advantages is derived. A procedure for efficient implementation of the improved method is given. Numerical examples are calculated showing results comparable to other methods but employing far fewer unknowns.
Stability and convergence of streamline curvature flow analysis procedures
Authors: Bindon Jeffery P.
Published: October 2005

A convergence technique for use with the streamline curvature method of cascade and channel flow is presented which produces stable and rapid convergence for subsonic, transonic and supersonic flow and also in the downstream region where the Kutta–Joukowski condition is applied to a cascade flow. The convergence method is fully two‐dimensional in nature, the iterative changes being determined via a model which takes into account the actual streamwise error distribution and the real normal changes in the grid.
Accelerating the convergence of elastic‐plastic stress analysis
Authors: Boyle E. F. , Jennings A.
Published: October 2005

Some results are given in which a modified Aitken acceleration is applied to elastic‐plastic stress analysis.
Normal gradient boundary condition in finite difference calculations
Authors: Parker R. , Ma C. Y.
Published: October 2005

An outline is given of a method for dealing with curved boundaries in finite difference calculations (relaxation or other similar techniques) where the gradient normal to the boundary is specified. Fluid flow calculations using the velocity potential are typical of such problems and the flow round a circular cylinder is computed as an example. The method makes no approximation which is not made in the usual finite difference techniques, therefore accuracy at the boundary is as good as in the remainder of the field.
Acoustic vibration of a liquid filled distorted circular cylindrical shell
Authors: Firth D.
Published: October 2005

A theory is developed whereby acoustic and structural modes are coupled by means of geometrical distortions in a circular cylindrical shell filled with liqued.

The prediction is that a circularly symmetric discrete frequency acoustic wave in the liquid will excite in the shell not only a circular symmetric ‘breathing mode’ (which would be the only one present in an undistorted shell) but also short wavelength flexural waves at the excitation frequency. It is possible, even for quite small distortions, for the displacement amplitude of some of these flexural waves to exceed that of the ‘breathing mode’.

The results of calculations for a particular shell are shown to be consistent with experimental results.
Seismic response analysis of offshore pipelines in contact with the sea‐bed
Authors: Nath B. , Soh C. H.
Published: October 2005

The seismic behaviour of an offshore pipeline, which may be totally or partially in contact with the sea‐bed, is characterized by the confluence of structural dynamics, hydrodynamics and soil mechanics and also the possible dynamic interactions between these aspects. This paper contains a study dealing with the seismic response analysis of such a pipeline including pressure drag effects. A numerical analysis basesd on the assumption that the pipe behaves linearly elastically and that pipe deffection is elastoplastically related, without loss, to sea‐bed resistance shows that pipe response in significantly attenuated by contact, as aspected, the amount of attenuation depending upon contact length and the parameters defining idealized sea‐bed behaviour.
A finite element procedure for the stress analysis of tubular joint connections
Authors: Panagiotopoulos George D.
Published: October 2005

Ahmad's superparametric thick shell element with reduced integration, a transition element type having variable degrees‐of‐freedom per node and a three‐dimensional incompatible element have been used to calculate the stress distribution at the intersection region of T‐ and Y‐joint connections. To minimize the numerical effort, a transfinite blending function interpolation approach has been applied for the automatic mesh generation and the resulting system of linear equations has been solved using the front width method. Comparison of the computed solutions with some very carefully conducted experimental results has shown very good agreement.
Structural optimization: A new dual method using mixed variables
Authors: Fleury Claude , Braibant Vincent
Published: October 2005

A new and powerful mathematical programming method is described, which is capable of solving a broad class of structural optimization problems. The method employs mixed direct/reciprocal design variables in order to get conservative, first‐order approximations to the objective function and to the constraints. By this approach the primary optimization problem is replaced with a sequence of explicit subproblems. Each subproblem being convex and separable, it can be efficiently solved by using a dual formulation. An attractive feature of the new method lies in its inherent tendency to generate a sequence of steadily improving feasible designs. Examples of application to real‐life aerospace structures are offered to demonstrate the power and generality of the approach presented.
An orthogonal decomposition approach to modal synthesis
Authors: Flashner H.
Published: October 2005

Modal synthesis is a method of formulating the equations of motion for complex vibratory systems. This approach has many advantages in modelling systems that consist of an assembly of linear dynamic elements whose modal characteristics are given. Presented in the paper is a procedure for synthesizing linear dynamic models into one dynamic description in a numerically stable way. This task is achieved by an orthogonal co‐ordinate transformation replacing the matrix inversions required when other procedures are used. The modal synthesis approach is formulated as a problem of finding the equations of motion for a linear system subject to a set of linear constraints. The numerical procedure to generate the equations of motion in terms of independent co‐ordinates is presented. The paper concludes with several examples that demonstrate the properties of the proposed method and its application to the modelling of vibratory systems.
An improved finite element for connecting adjacent laminae of two‐dimensional elements
Authors: Pack Steven C. , Mandel James A.
Published: October 2005

A connector element for linking planes of two‐dimensional elements to enable approximate multiplane solutions to a class of three‐dimensional problems is developed. This connector element embodies the same displacement fields as assumed by the connected two‐dimensional isoparametric elements. A reduction from the general multiplane formulation to a dual plane model is shown to be appropriate for analysing bodies with uniformly spaced inclusions. Sample solutions are given, including cases with different continuity conditions in each plane.
Dynamic Lagrangian computations for solids, with variable nodal connectivity for severe distortions
Authors: Johnson Gordon R. , Stryk Robert A. , Dodd Jack G.
Published: October 2005

This paper presents an algorithm for dynamic Lagrangian computations for solids, in plane strain geometry, with variable nodal connectivity to allow for severe distortions. The nodes are somewhat analogous to flexible circular disks. When they move closer together than their equilibrium distance they generate compressive, repulsive forces. Conversely, when they move apart, they generate tensile, attractive forces. Material strength effects are also included. Because a node can only be affected by its ‘neighbour’ nodes, the approach has been designated the ‘NABOR’ approach. The key to this approach is that it is possible to have variable nodal connectivity—a node can acquire new neighbours, thus allowing all forms of distortion. The NABOR algorithm has been incorporated as an option into the explicit finite element code, EPIC‐2. By using both the NABOR grid and the EPIC‐2 finite element grid together, it is possible to perform Lagrangian computations for a wide range of problems.
Higher order Chebyshev basis functions for two‐point boundary value problems
Authors: Bamigbola O. M. , Ibiejugba M. A. , Onumanyi P.
Published: October 2005

Cubic basis functions in one dimension for the solution of two‐point boundary value problems are constructed based on the zeros of Chebyshev polynomials of the first kind. A general formula is derived for the construction of polynomial basis functions of degree r, where 1 ≤r < ∞. A Galerkin finite element method using the constructed basis functions for the cases r = 1, 2 and 3 is successfully applied to three different types of problem including a singular perturbation problem.
Hybrid finite element‐Monte Carlo method for coupled conduction and gas radiation enclosure heat transport
Authors: Kraus H. G.
Published: October 2005

A hybrid two‐dimensional finite element‐Monte Carlo numerical solution method has been developed for solving complex transient non‐linear gas radiation enclosure problems. Solid conducting media are coupled to conducting gaseous or particulate participating media and both may be internally energy generating. Bilinear isoparametric elements are used, allowing geometrically complex enclosures with internal objects to be present. Radiative energy transport within the gaseous enclosures is accounted for using a Monte Carlo method which permits a broad range of complexities. Included here are: diffuse‐grey and specularly reflecting walls with temperature and spectrally dependent, and non‐homogeneous emissivities or absorptivities; absorbing/emitting gases with temperature and spectrally dependent, and non‐homogeneous emissivities or absorptivities; and isotropic or anisotropic scattering gases or particles. This method was verified by solving several standard steady state problems and comparing the solutions to those found using the conventional finite element, the P–N and the exchange factor methods. Solution times are comparable to those of the finite element method. A more complex transient problem solution is then given to demonstrate the versatility and power of the method.
Spline collocation in the flow of non‐Newtonian fluids
Authors: Doctor H. D. , Kalthia N. L.
Published: October 2005

Natural convection flow of a non‐Newtonian fluid between two vertical infinite parallel flat plates forms the case study of the present work. Velocity profiles for the Prandtl–Eyring and Powell–Eyring fluid models are obtained through the method of spline collocation.

The applicability and reliability of the techniques employed here are discussed in detail with a suggested error estimate and analysis. Accuracy in the successive iterations in the results is of the fourth order. To maintain this accuracy the help of a computer is not required for carrying out the calculation of velocity profiles. Thus the simplicity of the spline collocation technique is demonstrated in its application to flow problems.
Multilevel dynamic substructures
Authors: Leung A. Y. T.
Published: October 2005

The dynamic substructure method is extended to multilevel (recursive) substructures. The obvious distinction of the two approaches is that the stiffness and mass matrices before condensation are no longer frequency independent. The dynamic stiffness matrix at any substructure level is proved to be a function of the vibrating frequency in terms of some constant matrices which are derivable from the dynamic stiffness matrix at one lower substructure level. The method can accurately predict more modes than the number of degrees of freedom retained. The computational procedure, the generalized inverse iteration, the stationary principle of the system natural frequency and the generalized Rayleigh's quotient are derived for the frequency dependent matrices. Numerical examples are given to illustrate some engineering applications. A transcendental dynamic stiffness matrix can be transformed to a more convenient algebraic form by the present method.
Finite element/Newton method for the analysis of Czochralski crystal growth with diffuse‐grey radiative heat transfer
Authors: Bornside D. E. , Kinney T. A. , Brown R. A. , Kim George
Published: October 2005

A quasi‐steady‐state, integrated system model describing high temperature heat transfer, solidification and the action of capillarity in the Czochralski crystal growth process is solved by a finite element/Newton method. The numerical analysis couples the calculation of the temperature field in all phases and the determination of the melt/crystal and melt/gas interfaces and the crystal radius free boundaries. The analysis includes conductive heat transfer in the melt, crystal, crucible, pedestal, heater and the surrounding insulation and diffuse‐grey radiation, which couples the heat transfer between surfaces, the crystal radius and the melt/gas free boundary through the view factors. Finite element approximations are used to reduce the entire problem to a coupled set of non‐linear algebraic equations. These are solved simultaneously by Newton's method with the Jacobian matrix computed by a combination of closed form expressions and finite difference approximations. Quadratic convergence of the Newton iteration is demonstrated along with a factor of four increase in computational efficiency over a successive iteration procedure that decouples the calculation of radiation from the rest of the heat transfer model.
Biharmonic analysis of rectilinear plates by the boundary element method
Authors: Camp C. V. , Gipson G. S.
Published: October 2005

An improved boundary element formulation (BEM) for two‐dimensional non‐homogeneous biharmonic analysis of rectilinear plates is presented. A boundary element formulation is developed from a coupled set of Poisson‐type boundary integral equations derived from the governing non‐homogeneous biharmonic equation. Emphasis is given to the development of exact expressions for the piecewise rectilinear boundary integration of the fundamental solution and its derivatives over several types of isoparametric elements. Incorporation of the explicit form of the integrations into the boundary element formulation improves the computational accuracy of the solution by substantially eliminating the error introduced by numerical quadrature, particularly those errors encountered near singularities. In addition, the single iterative nature of the exact calculations reduces the time necessary to compile the boundary system matrices and also provides a more rapid evaluation of internal point values than do formulations using regular numerical quadrature techniques. The evaluation of the domain integrations associated with biharmonic forms of the non‐homogeneous terms of the governing equation are transformed to an equivalent set of boundary integrals. Transformations of this type are introduced to avoid the difficulties of domain integration. The resulting set of boundary integrals describing the domain contribution is generally evaluated numerically; however, some exact expressions for several commonly encountered non‐homogeneous terms are used. Several numerical solutions of the deflection of rectilinear plates using the boundary element method (BEM) are presented and compared to existing numerical or exact solutions.
A finite element simulation of metal flow in moulds
Authors: Dhatt G. , Gao D. M. , Cheikh A. Ben
Published: October 2005

Numerical tools for simulating the casting process are employed in an increasing manner by foundry engineers in order to understand and improve casting techniques. The correct simulation of metal flow and temperature profiles during filling is an important part of an overall numerical simulation kit which includes solidification and residual stress evaluations.

In this study, we develop a two‐dimensional finite element model for studying metal flow and temperature fields during filling of mould cavities. A proper choice of turbulent/laminar model, correct tracking of metal free surface and evaluation of temperature to include metal‐air‐sand interaction are some of the essential features of the model.
Radiative ignition of fabrics and assemblies: Experiments and modelling
Authors: Durbetaki Pandeli , Tran Phuoc X.
Published: October 2005

Radiative ignition studies wre carried out on vertical 2.54 cm circular fabric pairs, and single fabrics of 2.54 cm diameter and 15.2 × 15.2 cm. These fabrics were exposed to a time invariant radiative heat flux using the Large Ignition test Apparatus (LITA) and the Radiative Ignition Time Apparatus (RITA). A model has been developed which uses a quasi‐steady‐steady‐state approximation for the gas pahse. The transient effects and the thermal interaction between the plne‐parallel fabrics are accounted for through the variation of the fabric temperature with time. Ignition is considered to occur when the gas phase pyrolysate reaction rate is equal to the rate of pyrolysis. The predicted ignition times are compared with measured values and they show excellent agreement. Ignition times were found to depend strongly on heat flux, fabric size, interface spacing and oxygen concentration. IN the presence of a back fabric, the ignition time of the front fabrics decreases and this reduction is more pronounced at lower radiative heating intensities. Strong thermal interaction between the fabrics was also observed and it is expected that such interactions are responsible for the reduction of ignition time of the front fabric. No evidence of chemical interaciton has been observed.
Fixed grid techniques for phase change problems: A review
Authors: Voller V. R. , Swaminathan C. R. , Thomas B. G.
Published: October 2005

The aim of this paper is to categorize the major fixed grid formulations and solution methods for conduction controlled phase change problems. Using a two phase model of a solid/liquid phase change, the basic enthalpy equation is derived. Starting from this equation, a number of alternative formulations are obtained. All the formulations are reduced to a standard form. From this standard form, finite element and finite volume discretizations are developed. These discretizations are used as the basis for a number of fixed grid numerical solution techniques for solidification phase change systems. In particular, various apparent capacity and source based enthalpy methods are explored.
Application of the Trefftz method in plane elasticity problems
Authors: Jin W. G. , Cheung Y. K. , Zienkiewicz O. C.
Published: October 2005

Direct and indirect approximations using sets of non‐singular, complete Trefftz functions, i.e. the complete systems of solutions, have been successfully applied to harmonic problems.1 In this paper, the procedure is applied to a more complex situation—plane elasticity problems.

The examples show that the present method can avoid the difficulties relating to singular integration and has good accuracy compared with traditional boundary elements.
Viscous flow and transport with moving free and reactive surfaces
Authors: Murray Paul , Carey G. F.
Published: October 2005

Transport of a chemical species through a viscous fluid with reaction at an interface is modelled by a quasi‐static process in which the transient behaviour is dominated by motion of the reactive surface. The reaction is accompanied by a molar volume change which leads to motion of the free surface. A decoupled stream function‐vorticity formulation is introduced in conjunction with a moving finite element method. This also permits convenient treatment of the free and reactive surface boundary conditions. The model is applied to the growth of oxide films on silicon surfaces and reveals the effect of surface curvature on film growth.
A numerical model for immiscible two‐phase fluid flow in a porous medium and its time domain solution
Authors: Li Xikui , Zienkiewicz O. C. , Xie Y. M.
Published: October 2005

The governing equations for the interaction of two immiscible fluids within a deforming porous medium are formulated on the basis of generalized Biot theory. The displacement of the solid skeleton, the pressure and saturation of wetting fluid are taken as primary unknowns of the model. The finite element method is applied to discretize the governing eqations in space. The time domain numerical solution to the coupled problem is achieved by using an unconditionally stable direct integration procedure. Examples are presented to illustrate the performance and capability of the approach.
Minimax multiobjective optimization in structural design
Authors: Tseng C. H. , Lu T. W.
Published: October 2005

The use of multiobjective optimization techniques, which may be regarded as a systematic sensitivity analysis, for the selection and modification of system parameters is presented. A minimax multiobjective optimization model for structural optimization is proposed. Three typical multiobjective optimization techniques—goal programming, compromise programming and the surrogate worth trade‐off method—are used to solve such a problem. The application of multiobjective optimization techniques to the selection of system parameters and large scale structural design optimization problems is the main purpose of this paper.
A study of heat transfer during flat rolling
Authors: Pietrzyk M. , Lenard J. G.
Published: October 2005

Two finite element thermal models of the flat rolling process are presented. The first gives a steady‐state convective‐diffusion solution in the centre plane and the other a non‐steady‐state solution in the plane perpendicular to the strip axis. To account for mechanical events the models use a rigid‐plastic finite element approach. The predictions of both models are compared with temperature measurements carried out in laboratory conditions during hot rolling of low carbon steel and cold rolling of aluminium. The models are also tested against temperature measurements in the seventh stand of a production type continuous hot strip mill. Conclusions are drawn regarding the adequacy of both two‐dimensional models for various kinds of flat rolling processes.
Adaptive FEM computation of forming processes—Application to porous and non‐porous materials
Authors: Zienkiewicz O. C. , Huang G. C. , Liu Y. C.
Published: October 2005

This paper presents the ‘flow formulation’ approach applicable to both compressible and incompressible forming analysis. Appropriate error estimates and adaptive remeshing schemes are described for updated co‐ordinate analysis. Several numerical examples are given. These are backward‐forward extrusion and thermally coupled extrusion of pore‐free materials, followed by cylinder upsetting, and tapered die extrusion of porous materials. The simulation of the deformation is shown as well as the distribution of effective strain and density at different time stages. The procedures are automatic and are incorporated in a general purpose code FEMMETA.
Finite element analysis of sheet metal forming problems using a selective viscous bending/membrane formulation
Authors: Oñate E. , de Saracibar C. Agelet
Published: October 2005

In this paper the possibilities of the viscous voided shell approach for deriving bending/membrane finite elements for sheet metal forming problems are presented. These elements can be selectively used for membrane or full bending analysis of some parts of the sheet according to the nature of the deformation. Numerical aspects of this approach are discussed and some examples of application are also given.
A numerical analysis of wrinkle formation tendencies in sheet metals
Authors: Neale K. W. , Tuǧcu P.
Published: October 2005

A numerical analysis for the assessment of wrinkle formation tendencies in sheet metals is presented. A doubly‐curved thin shell element under biaxial plane stress states is considered, and the critical stress values for wrinkling are determined. The analysis is based on plastic bifurcation theory for the buckling of thin shells in short‐wavelength shallow modes. The effects of the various material and geometric parameters on wrinkling are investigated.
A new approach to the development of automatic quadrilateral mesh generation
Authors: Zhu J. Z. , Zienkiewicz O. C. , Hinton E. , Wu J.
Published: October 2005

A methodology for the automatic mesh generation of quadrilateral elements is proposed. The methodology is based on the facts that (i) a region can always be subdivided entirely into quadrilaterals if the polygon which forms the boundary of the region has an even number of sides, (ii) a quadrilateral can be formed by two triangles which share a common side. By taking advantage of the techniques developed in an existing automatic triangular mesh generator, quadrilateral meshes can be generated according to the distribution of user specified element size over the domain of interest. In particular, an automatic quadrilateral mesh generator based on the advancing front technique for triangular mesh generation1 is described. Techniques to improve the quality of the generated quadrilateral meshes are introduced. The robustness and versatility of the mesh generator are demonstrated by a variety of examples.
Source field superposition analysis of two‐dimensional potential problems
Authors: Fenner R. T.
Published: October 2005

The source field superposition method for problems governed by Laplace's equation involves representing the potential field in a given solution domain as a superposition of fields generated by a number of sources. These sources are located outside the solution domain, and in the case of two‐dimensional singly‐connected finite domain problems can be uniformly distributed around the perimeter of a circle enclosing the physical domain. Some test problems are used to make detailed comparisons with the boundary element method. The results show that remarkable accuracy can be achieved, often to five or six significant figures, with very little computational effort relative to other numerical methods. In contrast to the boundary element method, however, geometric corners require no special treatment, and high aspect ratio of the solution domain is not a significant limitation.
An algorithm for three‐dimensional convection and diffusion with very different horizontal and vertical length scales
Authors: Lardner R. W. , Song Y.
Published: October 2005

An algorithm is developed and tested for the numerical solution of the three‐dimensional convection—diffusion equation appropriate for the marine environment, in which the horizontal and vertical scales differ by one or two orders of magnitude. The algorithm splits the horizontal and vertical parts of the process, treating the horizontal convection and diffusion explicitly and the vertical convection and diffusion by an implicit finite element method that is unconditionally stable. The overall stability conditions on the algorithm are discussed and its accuracy is verified through a number of test problems whose exact solutions are known.
A penalty finite element analysis for nonlinear mechanics of biphasic hydrated soft tissue under large deformation
Authors: Suh J.‐K. , Spilker R. L. , Holmes M. H.
Published: October 2005

The non‐linear response of soft hydrated tissues under physiologically relevant levels of mechanical loading can be represented by a two‐phase continuum model based on the theory of mixtures. The governing equations for a biphasic soft tissue, consisting of an incompressible solid and an incompressible, inviscid fluid, under finite deformation are presented and a finite element formulation of this highly non‐linear problem is developed. The solid phase is assumed to be hyperelastic, and the stress‐strain relations for the solid phase are defined in terms of the free energy function. A finite element model is formulated via the Galerkin weighted residual method coupled with a penalty treatment of the continuity equation for the mixture. Using a total Lagrangian formulation, the non‐linear weighted residual statement, expressed with respect to the reference configuration, leads to a coupled non‐linear system of first order differential equations. The non‐linear constitutive equation for the solid phase elasticity is incrementally linearized in terms of the second Piola‐Kirchhoff stress and the corresponding Lagrangian strain. A tangent stiffness matrix is defined in terms of the free energy function; this matrix definition can be applied to any free energy function, and will yield a symmetric matrix when the free energy function is convex. An unconditionally stable implicit predictor‐corrector algorithm is used to obtain the temporal response histories. The confined compression mechanical test of soft tissue in stress relaxation is used as an example problem. Results are presented for moderate and rapid rates of loading, as well as small and large applied strains. Comparison of the finite element solution with an independent finite difference solution demonstrates the accuracy of the formulation.
A modular multibody analysis capability for high‐precision, active control and real‐time applications
Authors: Park K. C. , Downer J. D. , Chiou J. C. , Farhat C.
Published: October 2005

A computationally oriented formulation and its solution procedures for the analysis of rigid‐flexible multibody dynamics systems are presented. The present formulation adopts a set of dual co‐ordinate systems, an inertially fixed one for the measure of translational motions and a body‐based one for rotational motions. The origins of these co‐ordinate systems are located at the centres of rigid bodies and at the nodal points of flexible bodies for implementation ease. The flexibility is modelled by an intrinsic spatial beam theory which is approximated by transverse‐shear deformable linear beam elements. The solution of the resulting equations of motion including system constraints is obtained by a partitioned procedure, which solves first for the constraint force vector, then the generalized co‐ordinates for the rigid and flexible components, and finally interaction quantities such as active control forces, manoeuvring space ranges and corrections due to state measurements, with each solution stage being processed by the corresponding separate module. A central feature of the present capability is its high accuracy of the analysis results by demanding the energy conservation throughout the various stages of response analyses. Several examples are included to demonstrate the capabilities of the present analysis software both on sequential and parallel machines.
Constrained motion of deformable bodies
Authors: Shabana A. A.
Published: October 2005

In this paper, issues related to the dynamic modelling of constrained deformable bodies that undergo large rigid body displacements are discussed. Particular attention is focused on finite element formulations. It is shown that the use of nodal co‐ordinates and shape functions to describe the finite rotation of some of the commonly used finite elements leads to a linearization of the kinematics and dynamic relationships. The structure of the non‐linear dynamic equations that govern the motion of deformable bodies that undergo large displacements is examined. Comments on the finite element formulation of the invariants of motion, the definition of the generalized forces and moments in flexible body dynamics and the computational strategy used for the automatic generation of the equations of motion are made. The computer formulation of the joint constraints between deformable bodies as well as the numerical algorithms currently used in many of the general purpose computer programs that are based on the augmented formulation are discussed. A decoupled joint‐elastic acceleration recursive formulation is also presented. This formulation leads to a small system of acceleration equations whose dimensions are independent of the number of the elastic degrees of freedom of the system. In this paper, the coupling between the displacements of the deformable bodies is classified as kinematic, inertia and elastic. In view of this classification, comments on the validity of using the updated finite element Lagrangian formulation and the 4 × 4 transformation matrix in the dynamic analysis of flexible multibody systems are made. The coupling between the finite rotation and the wave motion in constrained deformable bodies is also discussed.
Representation of geometric stiffening in multibody system simulation
Authors: Wallrapp Oskar , Schwertassek Richard
Published: October 2005

Geometric, rotational or dynamic stiffening is a well and long known phenomenon in the analysis of flexible bodies. In multibody dynamics the effect has attracted attention only recently. The objective of this paper is to contribute to the understanding of the modelling of geometric stiffening in multibody system simulation. Today's methods for modelling the effect assume that the (applied) stresses in a flexible system body are zero in its reference configuration, in which it performs large overall motions. The corresponding inertial loads are shown to be balanced by constraint stresses. This can be seen easily when formulating the system equations of motion for non‐zero reference stresses. As a result one obtains an efficient alternative to compute the geometric stiffening terms. The method increases the generality of flexible body models for multibody system simulation.
Strain localization in multipotential elastoplasticity
Authors: Aubry Denis , Modaressi Arezou
Published: October 2005

Conditions of strain localization in multipotential elastoplasticity are studied in this paper for a strain discontinuity mode. The formulation is specialized to the case of a general anisotropic Mohr‐Coulomb model, where plastic shear deformations are envisaged as the contribution of microstrains in several planes. Some finite element simulations with strain projection show the relationship between the predicted direction of localization and the post bifurcation modes.
Structural analysis and optimization modelling including fracture conditions
Authors: Eschenauer H. A. , Kobelev V. V.
Published: October 2005

This paper introduces a model of a woven monolayer composed of two orthogonal fibres and describes an optimization technique including a fracture condition. The first fracture behaviour of the material containing a local break is analysed. The description of the stress‐state in the local break vicinity is reduced to the determination of a special form of the Green function for simultaneous finite‐difference equations. The problem allows the analytical solution for unknown functions in terms of Fourier series. The solution of the problem shows that the fracture behaviour of the material depends on the presence of stabilizing tension of fibres parallel to the crack direction. The model is used for establishing an optimization model and for applying an optimization procedure including strength conditions.
Fracture mechanics and optimal design
Authors: Pitukhin A. V.
Published: October 2005

The purpose of this paper is to present a mechanical fracture method for the optimal design of machine components. A single criterion design is used. Mean annual cost expenses are the objective function. They depend on the survival function. Statistical fracture mechanics methods are able to estimate machine components reliability dependence on crack‐like defect length. A numerical example is given to demonstrate the application of this method. It is recommended to evaluate the reliability of spiral cylindrical springs too.
Supporting design decisions by Prolog database
Authors: Borkowski Adam , Danicka Stanislaw Jóźwiak Małgorzata
Published: October 2005

The paper presents an effort to develop an ‘intelligent drawing desk’: a computer program that incorporates CAD, structural analysis and optimization, database query and automatic choice of the initial design. The advantages of such an integrated software are demonstrated on the testbed of plane steel trusses.

After a brief presentation of the conventional part of the package, its expert module is discussed more thoroughly. Implemented in ‘Prolog’, that module aids the user in choosing the initial layout of the truss. It checks and supplements, if necessary, the values of the structural attributes given by the designer. After a complete set of attributes has been established, the module searches for similar solutions in the database. The latter represents the experience, i.e. all solutions accepted by the user in the past. An initial design is obtained without strength analysis by matching the current values of the attributes against those stored in the database. Provided the latter is exhaustive enough, one obtains in this way quite reasonable initial values of the design variables. The final design can be found then by using conventional analysis, optimization and sizing procedures that belong to the procedural part of the package.
Automated adaptive analysis of the biphasic equations for soft tissue mechanics using a posteriori error indicators
Authors: Donzelli P. S. , Spilker R. L. , Baehmann P. L. , Niu Q. , Shephard M. S.
Published: October 2005

Hydrated soft tissues of the human musculoskeletal system, such as articular cartilage in diarthrodial joints or the annulus fibrosis of the inter vertebral disk, are accurately represented by a biphasic continuum model consisting of an incompressible solid phase (collagen and proteoglycan) and incompressible, inviscid fluid (interstitial fluid) and derive from the continuum theory of mixtures. These tissues exhibit a viscoelastic‐type response which is caused by the diffusive drag of the fluid phase as it flows past the solid phase. In this study an automated, adaptive, finite element solution of the governing biphasic equations is presented. The finite element formulation is based on a mixed‐penalty approach in which the penalty form of the continuity equation for the mixture is included in the weak form. Pressure, solid and fluid velocities are interpolated independently, and the coefficients of the C−1 pressure field are eliminated at the element level. The resulting matrix form is a system of first order differential equations which is solved via standard finite difference methods. Mesh generation and updating, including both refinement and coarsening, for the two‐dimensional examples examined in this study are performed using Finite Quadtree. The adaptive analysis is based on an error indicator which is the L2 norm of the difference between the finite element solution and a projected finite element solution. Total stress, calculated as the sum of the solid and fluid phase stresses, is used in the error indicator. Rezoning is accomplished by transferring the finite element solution for the primary variables onto the locally updated mesh using a projected field. These projected values allow the finite difference algorithm to proceed in time using the updated mesh. The accuracy and effectiveness of this adaptive finite element analysis is demonstrated using two‐dimensional axisymmetric problems corresponding to the uncomined compression of a cylindrical disk of soft tissue and the indentation of a thin sheet of soft tissue. The method is shown to effectively capture the steep gradients in both problems and to produce solutions in good agreement with independent, converged, numerical solutions.
Characteristic, local grid refinement techniques for reservoir flow problems
Authors: Dahle Helge K. , Espedal Magne S. , Sævareid Ove
Published: October 2005

Using a sequential time‐marching approach, we describe and implement effective solution strategies for the equations governing immiscible displacement in a porous medium. By combining adaptive grid refinement with an operator‐splitting technique based on the modified method of characteristics, the saturation equation is treated in a consistent and accurate way. For the pressure equation we construct accurate piecewise linear velocity components from a piecewise linear pressure approximation.
Accelerated bisection techniques for tri‐ and quindiagonal matrices
Authors: Baker Graham
Published: October 2005

This paper considers accelerated bisection methods for calculating the eigenvalues of symmetric tridiagonal and quindiagonal matrices using cubic polynomial interpolation, as well as first and second order Newton iteration. Recursive relations based on the Sturm sequences are presented for the Newton type methods. The relations use a convenient scaling which retains the relative magnitudes in the iterative schemes but which avoids numerical overflow. Numerical examples show a significant increase in convergence rate.
A multicorner variable order singularity triangle to model neighbouring singularities
Authors: Maiti S. K.
Published: October 2005

A six noded triangular finite element has been proposed to model variable order singularities in the first derivatives of field variables occurring at multiple locations (up to three) lying in close proximity. The element satisfies the convergence requirements fully. The element will be very useful in the analysis of neighbouring cracks, zig‐zag cracks, kinked cracks, etc., involving mechanical and/or thermal loadings. The first degenerate form, which is a two point variable order singularity element, can be used, for example, to cover the distance between two adjacent crack tips. The second degenerate form, which is a one point variable order singularity element, can be used around a crack tip like any other crack tip elements. Six case studies have been reported, three involving mechanical loadings and the other three thermal loadings. These have helped to check the performance of the element and its two degenerate forms. The accuracy of the results in all the examples is good.
A finite element approach for modelling metal flow and pressurised solidification in the squeeze casting process
Authors: Gethin D. T. , Lewis R. W. , Tadayon M. R.
Published: October 2005

A finite element numerical modelling procedure for simulating combined flow and heat transfer in a squeeze casting process is developed where the flow model is based on simple mass conservation. The coincident node method is used to model the thermal interface with metal advancement over the relatively colder die surface. The effect of pressure on the solidus and liquidus temperatures is built in based on the Clausius‐Clapeyron equation and the thermophysical properties of enthalpy and thermal conductivity are affected by this pressure. For the casting material concerned, the effect of pressure on thermophysical properties was found to be small, having only a marginal effect on the part solidification.
Direct formulation of a hybrid 4‐node shell element with drilling degrees of freedom
Authors: Aminpour M. A.
Published: October 2005

A simple 4‐node assumed‐stress hybrid quadrilateral shell element with rotational or 'drilling' degrees of freedom is formulated. The element formulation is based directly on a 4‐node element. This direct formulation requires fewer computations than a similar element that is derived from an 'internal' 8‐node isoparametric element in which the midside degrees of freedom are eliminated by expressing them in terms of displacements and rotations at corner nodes. The formulation is based on the principle of minimum complementary energy. The membrane part of the element has 12 degrees of freedom, including the drilling degrees of freedom. The bending part of the element also has 12 degrees of freedom. The bending part of the element uses the Reissner‐Mindlin plate theory which takes into account the transverse shear effects. Quadratic variations for both in‐plane and out‐of‐plane displacement fields and linear variations for both in‐plane and out‐of‐plane rotation fields are assumed along the edges of the element. The element Cartesian‐co‐ordinate system is selected such as to make the stress field invariant with respect to node numbering. The membrane part of the stress field is based on a 9‐parameter equilibrating stress field, while the bending part is based on a 13‐parameter equilibrating stress field. The element passes the patch test, is nearly insensitive to mesh distortion, alleviates the 'locking' phenomenon, is invariant with respect to node numbering, has no hidden spurious modes, and produces accurate and reliable results.
A stabilization procedure by line‐search computation for first order approximation strategies in structural optimization
Authors: Mahnken R. , Stein E. , Bischoff D.
Published: October 2005

The paper is concerned with first order approximation methods to solve non‐linear optimization problems as they arise in structural optimization. A modification of the original Method of Moving Asymptotes (MMA) is presented to prevent oscillation or divergence by incorporating a line‐search into the global iteration algorithm. In this line‐search a merit‐function of augmented Lagrangian type is decreased by using a backtracking strategy. A proof is presented to show the descent property of the proposed merit‐function for MMA. Numerical examples demonstrate how the new technique stabilizes the iteration process.
A finite element method for domains with corners
Authors: Givoli Dan , Rivkin Leonid , Keller Joseph B.
Published: October 2005

A new finite element method is devised for the numerical solution of elliptic boundary value problems with geometrical singularities. In it, the singularity is eliminated form the computational domain in an exact fashion. This is in contrast to other common methods, such as those which use a refined mesh in the singularity region, or those which use special singular finite elements. In them, the singularity is treated as a part of the numerical scheme. The new method is illustrated on an elliptic differential equation in a domain containing a re‐entrant corner. Numerical experiments show that the new method yields result which are generally much more accurate than those obtained by using the standard finite element method with mesh refinement in the singularity region. Both methods require about the same computing time.
Polynomial particular solutions based boundary element analysis of acoustic eigenfrequency problems
Authors: Raveendra S. T. , Banerjee P. K.
Published: October 2005

The boundary element formulation for acoustic eigenfrequency analysis based on treating the forcing function, in the governing differential equation, as an initially unknown distributed source within the domain is presented. The volume integral due to this distributed source is eliminated by approximating the internal source by global interpolation and polynomial function representations and finding particular solutions for the governing, inhomogeneous equations. The resulting non‐symmetric system matrix is solved by using Arnoldi's algorithm, modified to take advantage of the special structure of the substructured boundary element method. The techniques described here are embedded in a computer program GPBEST, and the numerical results are obtained by using this computer code.