bluuebunny/crossref_metadata_2025 huggingface dataset:
A new explicit variable time‐integration self‐starting methodology for computational structural dynamics
Authors: Tamma Kumar K. , D'Costa Joseph F.
Published: August 2005

A new explicit variable time‐integration methodology and architecture which possesses self‐starting attributes, eliminates the need to involve acceleration computations, and which has improved accuracy characteristics in comparison to the traditional central‐difference‐type formulations customarily advocated is described for applicability to computational structural dynamics. To sharpen the focus of the present study, an explicit variable time‐integration architecture which is relatively simple, yet effective, is described. Unlike variable explicit time‐integration formulations adopted in the past, the present self‐starting variable time‐integration architecture and implementation aspects facilitate a simplified representation and a straightforward and effective approach for combining finite element meshes requiring different time steps in a single analysis. Numerical test cases are provided which demonstrate the applicability of the proposed formulations.
Non‐singular boundary integral representation of potential field gradients
Authors: Sladek V. , Sladek J.
Published: August 2005

In this paper we derive the non‐singular boundary integral representation of the field gradients for two‐dimensional problems of classical potential field theory. Numerical implementation of this representation is developed too. The proposed method eliminates the most inaccurate influence coefficients which arise when singular integral representations are used and the internal point approaches the boundary. Since the integrands in this new method are finite at any internal point, accurate numerical results are achieved even in that portion of a solid which is very close to a discretized boundary. Two test problems are analysed in which the numerical results computed by strongly singular, weakly singular and non‐singular integral representations are compared mutually and with exact solutions.
Computing alternative optimal collapse mechanisms
Authors: Tam T. K. H. , Jennings A.
Published: August 2005

Optimal plastic designs for structural frames can be obtained via static or kinematic considerations, each leading to a mathematical model requiring solution by linear programming. In both cases a mechanism can be found which satisfies the Foulkes optimality condition. However, this mechanism generally has many degrees of freedom and is most unlikely to be the actual collapse mode of the frame. A simple algorithm based on the method of redundant forces is presented for the automatic generation of the alternative optimal collapse mechanisms, any of which may be the actual collapse mode.
On the development of explicit robust schemes for implementation of a class of hyperelastic models in large‐strain analysis of rubbers
Authors: Saleeb A. F. , Chang T. Y. P. , Arnold S. M.
Published: August 2005

The issue of developing effective and robust schemes to implement a class of the Ogden‐type hypereiastic constitutive models, for large‐strain analysis of rubber‐like materials, is addressed. To this end, explicit forms for the corresponding material tangent‐stiffness tensors are developed, and these are valid for the entire deformation range; i.e. with both distinct as well as repeated principal‐stretch values. Throughout the analysis the various implications of the underlying property of separability of the strain‐energy functions are exploited, thus leading to compact final forms of the tensor expressions. In particular, this facilitated the treatment of the complex cases of uncoupled volumetric/deviatoric formulations for incompressible materials, which are becoming increasingly popular in recent years. The forms derived are also amenable for use with symbolic‐manipulation packages for systematic code generation.
A study of boundary layers in plates using Mindlin‐Reissner and 3‐D elements
Authors: Rao N. V. R. , Özakça M. , Hinton E.
Published: August 2005

Finite elements based on Mindlin–Reissner theory and three‐dimensional theory are used to study the distribution of shear forces and twisting moments in plates with various simple support conditions. Differences between the results obtained using these two theories are highlighted. A crude adaptive mesh refinement procedure is applied to improve the accuracy of the finite‐element analysis.
Performance of certain iterative methods in solving implicit difference schemes for 2‐D Navier–Stokes equations
Authors: Iliev O. P. , Makarov M. M. , Vassilevski P. S.
Published: August 2005

The performance of three iterative methods, local SOR, preconditioned generalized conjugate gradient methods such as ORTHOMIN(1) and the GCG–LS method with preconditioning matrices derived by incomplete (modified and unmodified) pointwise factorizations of the matrix corresponding to implicit finite difference schemes for the 2‐D Navier–Stokes equations, is compared. The relative merits of these methods in terms of CPU time, average number of iterations with respect to the Reynolds number and discretization parameters are emphasized.
Non‐singular boundary integral representation of stresses
Authors: Sladek V. , Sladek J.
Published: August 2005

This paper presents the derivation of the non‐singular integral representation of stresses in two‐ and three‐dimensional elastostatics. In contrast to the strongly singular and weakly singular integral representations, the numerical computation of the nearly singular integrals is eliminated because all the integrands are made finite in this new formulation even if the internal point approaches the boundary. Thus the method gives accurate numerical results even in that portion of a solid which is very close to a discretized boundary. Three test problems are analysed in which we present a comparison of the accuracies achieved by the numerical computations based on the use of strongly singular, weakly singular and non‐singular integral representations of stresses.
Numerical analysis of elastic contact problems using the boundary integral equation method. Part 1: Theory
Authors: Dandekar B. W. , Conant R. J.
Published: August 2005

A boundary integral equation formulation for the analysis of two‐dimensional elastic contact problems with friction is developed. In this formulation, the contact equations are written explicitly with both tractions and displacements retained as unknowns. These equations are arranged such that a blocked coefficient matrix results. An incremental and iterative procedure is discussed which, in the case of proportional loading, modifies only the equations in the potential contact zone.
Numerical analysis of elastic contact problems using the boundary integral equation method. Part 2: Results
Authors: Dandekar B. W. , Conant R. J.
Published: August 2005

This paper gives solutions to various frictionless and frictional contact problems using the boundary integral formulation developed in Part 1. A range of problems is considered in order to demonstrate the applicability of the approach. In most cases equal size linear elements are found to give best results. In the case of frictional problems the arrangement of strick‐slip zones is affected by the node locations and a relatively large number of elements may be required to produce satisfactory results. In all cases, the boundary integral equation method yields numerical solutions that are in very good agreement with the analytical solutions to which they are compared.
Analytical elements of time domain bem for two‐dimensional scalar wave problems
Authors: Wang Canyun , Takemiya Hirokazu
Published: August 2005

An accurate and efficient time domain BEM for 2‐D scalar wave problems is presented. Emphasis is on developing analytical boundary elements (explicit solutions of the element matrices). The solutions are obtained under the condition of straight line elements and by bringing the problem to a simple and genral form of double convolution equation which is then solved by the Cagniard–De Hoop method. Six kinds of elements for any combination of the spatial interpolation functions of order 0, 1, 2 with the temporal interpolation functions of order 0, 1 are given in a compact form. It is pointed out that if the order of temporal interpolation function is higher than 1, or if the continuity of velocity or acceleration is required, the time‐stepping technique will face difficulty. A method to solve this problem is also presented.

Advantages of using the analytical elements instead of a numerical integral procedure are apparent. Problems with such things as singular integrals, accuracy and stability are solved. Methodology and solutions are demonstrated by a comparative study of two example problems. Numerical solutions reveal that the computation is efficient, accurate and stable.
Elastic postbuckling analysis via finite element and perturbation techniques. Part 1: Formulation
Authors: Flores Fernando G. , Godoy Luis A.
Published: August 2005

The main equations for the equilibrium, stability and critical state analysis of discrete elastic systems are presented following the works of Thompson, but in such a way that the original set of generalized coordinates and loads are preserved in the Total Potential Energy. This introduces differences in the resulting equations in bifurcation analysis but does not introduce any new feature regarding the physics of the problem. The new formulation is approximated by means of a standard finite element approach based on interpolation of displacements, in which the derivatives of the potential energy are approximated. The terms retained are those of moderately large rotation theory. The energy analysis is finally related to the more conventional finite element notation in terms of stiffness matrices, and it is shown how in such a way it can be included in present day codes.

Part 2 of the paper deals with applications to the analysis of shells of revolution using a semi‐analytical approximation. Two cases are presented in detail: bifurcation in axisymmetric and in asymmetric modes, and the results show good correlation with those of other authors. The influence of load and geometric imperfections is evaluated.
Solution of BEM systems of equations via iterative techniques
Authors: Mansur W. J. , Araújo F. C. , Malaghini J. E. B.
Published: August 2005

The present paper is concerned with the application of iterative techniques to solve boundary element method (BEM) systems of equations.

Initially, a brief description of some algorithms which have been employed for symmetric positive‐definite matrices is given (finite element method matrices, for instance). Subsequently, non‐symmetric versions of these algorithms are described and their performance is checked for BEM matrices, through various numerical experiments.

Preconditioned algorithms were found to work quite well.
Application of infinite elements to phase change situations on deforming meshes
Authors: Sullivan John M. , O'Neill Kevin
Published: August 2005

In recent years progress has been made in applying moving and deforming mesh systems to phase change problems. This allows the numerical attention where it is needed, near the migrating phase change zone. In spatially unbounded problems one hopes that numerically finite outer boundaries either escape significant activity or are automatically pushed further away as activity nears. Not infrequently this approach fails. Temperature activity often spreads more rapidly than phase change, thereby reaching far boundaries; stretching of the mesh by movement of far boundaries can challenge mesh control and cause ill‐conditioning. In this paper the advantages of time dependent mesh adaption are enhanced by the joining of a new formulation for infinite elements to far boundaries. This is accomplished through a co‐ordinate transformation within the framework of conventional 2‐D quadratic, biquadratic, and linear–quadratic elements. Standard 2 by 2 Gauss–Legendre quadrature suffices throughout and normal Galerkin finite element features are undisturbed, including strict conservation of energy. The formulation is independent of global co‐ordinates, entails no restrictions on the unknown function and should be applicable to other problem types. All test cases on quadrilateral and triangular grids show very significant improvements with infinite elements relative to comparable solution systems using strictly finite grids.
A solid shell element for the shell structured eyeball with application to radial keratotomy
Authors: Yeh Hsien‐Liang , Huang Tseng , Schachar Ronald A.
Published: August 2005

In order to obtain the curvature changes of the exterior surface of a shell subjected to an internal pressure, it is necessary to evaluate the displacement derivatives up to the second order. To this end, a hexahedronal element is developed with three‐dimensional elastic properties utilized. At a nodal point on the surface of the shell, the first‐order derivatives of the three displacement components are used as degrees of freedom (d.o.f.) in addition to the components themselves. However, at a nodal point not on the surface, only the three displacement components are used. Therefore, an element with aii exterior surface has a total of 48 d.o.f. and other elements have 24 d.o.f.

The stiffness matrix of the 8‐node subparametric hexahedronal high‐order element is derived from the strain energy consideration. The cubic shape functions in the surface co‐ordinates and linear shape functions through the shell thickness are used. The second derivatives of displacement components are continuous at any point on the exterior surface of the element, although they may not be continuous across the nodal line of two adjacent elements.
Optimum design of structures with both natural frequency and frequency response constraints
Authors: Chen Ting‐Yu
Published: August 2005

An efficient method is developed to compute the sensitivities of eigenvalues, eigenvectors and frequency responses in a reduced approximate rnodel. The reanalyses of a modified structure for those dynamic responses are also derived in the approximate model. An optimization process utilizing the efficiently calculated sensitivities and reanalyses of the modified structure is formed. The difficulties of finding eigenvector sensitivities for repeated modes have also been addressed and averted in the approximate model. Two numerical examples show satisfactory outcomes by using this proposed approach.
Large reference displacement analysis of composite plates part I: Finite element formulation
Authors: Kremer J. M. , Shabana A. A. , Widera G. E. O.
Published: August 2005

This investigation concerns itself with the dynamic analysis of thin, laminated composite plates consisting of layers of orthotropic laminae that undergo large arbitrary rigid body displacements and small elastic deformations. A non‐linear finite element formulation is developed which utilizes the assumption that the bonds between the laminae are infinitesimally thin and shear non‐deformable. Using the expressions for the kinetic and strain energies, the lamina mass and stiffness matrices are identified. The non‐linear mass matrix of the lamina is expressed in terms of a set of invariants that depend on the assumed displacement field. By summing the kinetic and strain energies of the laminae of an element, the element mass and stiffness matrix can be defined in terms of the set of element invariants. It is shown that the element invariants can be expressed explicitly in terms of the invariants of its laminae. By assembling the finite elements of the deformable body, the body invariants can be identified and expressed explicitly in terms of the invariants of the laminae of its elements. In the dynamic formulation presented in this paper, the shape functions of the laminae are assumed to have rigid body modes that need to describe only large rigid body translations. The computer implementation and the use of the formulation developed in this investigation in multibody dynamics are discussed in the second part of this paper.
Large reference displacement analysis of composite plates. Part II: Computer implementation
Authors: Kremer J. M. , Shabana A. A. , Widera G. E. O.
Published: August 2005

This investigation concerns itself with the computer implementation of the dynamic formulation of thin laminated composite plates consisting of layers of orthotropic laminae that undergo large arbitrary rigid body displacements and small elastic deformations. A finite element preprocessor computer program is developed to automatically generate the invariants of the laminae, which may have arbitrary orientations. The laminae invariants are then used to obtain the invariants of the elements and the composite laminated plate. The consistent and lumped mass formulations of the invariants of motion of composite plates are compared and it is concluded that the two methods are comparable, if a fine enough finite element mesh is used. The structure of the dynamic equations of motion, based on the formulation presented in Part I of this paper, is examined. Non‐linear centrifugal and Coriolis forces arising as the result of the finite rotations of the laminae are defined, and the solution schemes of the resulting non‐linear differential equations of motion are discussed. Numerical examples illustrating the differences between homogeneous isotropic and laminated composite plates are presented. An RSSR (Revolute‐Spherical‐Spherical‐Revolute) mechanism is used in the numerical examples, with the coupler modelled as a laminated plate flexible body. It is found that the inertia of the plate contributed greatly to the transverse deformation. The effects of laminae orientation is also investigated.
On the numerical integration of interface elements
Authors: Schellekens J. C. J. , De Borst R.
Published: August 2005

Eigenmode analyses of the element stiffness matrices have been used to assess the impact of the applied integration scheme on the stress predictions of two‐ and three‐dimensional plane interface elements. It is demonstrated that large stress gradients over the element and coupling of the individual node‐sets of the interface element may result in an oscillatory type of response. For line elements and linear plane interface elements the performance can be improved by using either a nodal lumping scheme or Newton‐Cotes or Lobatto integration schemes instead of the more traditional Gauss scheme. For quadratic interface elements the same holds true except for a nodal lumping scheme.
A hybrid variational method for multibody dynamics
Authors: Chung Shu , Haug Edward J.
Published: August 2005

This paper presents a hybrid variational method to minimize computational effort in forming and solving the equations of motion for broad classes of rigid multibody mechanical systems. The hybrid method combines the O(n) and O(n3) recursive variational methods for forming the equations of motion in terms of joint relative co‐ordinates. While the O(n3) method is more efficient than the O(n) method for systems with short chains and decoupled loops, the converse is true when the number of bodies in chains is large. The computational complexity of the O(n3) and O(n) methods in forming and solving the equations of motion is analysed as a function of the numbers of bodies, decoupled loops, joints, cut joints, cut‐joint constraint equations and force elements. Based on complexity estimates, the method presented in this paper uses either the O(n) or O(n3) variational method to formulate the equations of motion for each open chain and decoupled loop in the system, to minimize the computational effort.
p‐version least‐squares finite element formulation for convection‐diffusion problems
Authors: Winterscheidt Daniel , Surana Karan S.
Published: August 2005

This paper presents a p‐version least‐squares finite element formulation of the convection‐diffusion equation. The second‐order differential equation describing convection‐diffusion is reduced to a series of equivalent first‐order differential equations for which the least‐squares formulation is constructed using the same order of approximation for each of the dependent variables. The hierarchical approximation functions and the nodal variable operators are established by first constructing the one‐dimensional hierarchical approximation functions of orders pξ and pη and the corresponding nodal variable operators in ξ and η‐direction and then taking their products. Numerical results are presented and compared with analytical and numerical solutions for a two‐dimensional test problem to demonstrate the accuracy and the convergence characteristics of the present formulation.

The Gaussian quadrature rule used to calculate the numerical values of the element matrices, vectors as well as the error functional I(E), is established based on the highest degree of the polynomial in the integrands. It is demonstrated that this quadrature rule with the present p‐version formulation produces excellent results for very low as well as extremely high Peclet numbers (10‐106) and, furthermore, the error functional I (sum of the integrals of E2) is a monotonically decreasing function of the number of degrees of freedom as the p‐levels are increased for a fixed mesh. It is shown that exact integration with the h‐version (linear and parabolic elements) produces inaccurate solutions at high Peclet numbers. Results are also presented using reduced integration. It is shown that the reduced integration with p‐version produces accurate values of the primary variable even for relatively low p‐levels but the error functional I (when calculated using the proper integration rule) has a much higher value (due to errors in the derivatives of the primary variable) and is a non‐monotonic function of the degrees of freedom as p‐levels are increased for a fixed mesh. Similar behaviour of the error functional I is also observed for the h‐models using linear elements when reduced integration is used. Although the h‐models using parabolic elements produce monotonic error functional behaviour as the number of degrees of freedom are increased, the error values are inferior to the p‐version results using exact integration.
Hygrothermomechanical evaluation of porous media under finite deformation: Part II—model validations and field simulations
Authors: Kim C. S. , Lee T. S. , Advani S. H. , Lee J. K.
Published: August 2005

A set of field equations, the associated finite element model formulations and numerical methodology for thermomechanical response evaluations of fluid‐saturated media under finite deformation have been presented in Part I of the companion manuscript.1 In this paper, the formulations and methodologies are initially validated through benchmark model comparisons prior to constitutive model sensitivity analysis and subsequent thermomechanical response determination. The responses for the testbed problems, using the developed solution algorithm, compare favourably with the reported results. The response investigations for complex geomechanical problems illustrate the general applicability of the developed finite element model simulator in predicting the long‐term thermal, pore pressure, displacement and stress responses of fluid‐saturated porous media subjected to thermomechanical loading, as encountered in nuclear waste management scenarios. The presented formulations and numerical procedures can also be used to investigate a wide range of engineering problems involving hygrothermomechanical response prediction.
The effect of non‐linear curvature strains on the buckling of laminated plates and shells
Authors: Dennis S. T. , Palazotto A. N.
Published: August 2005

A versatile geometrically non‐linear curved shell finite element formulation includes exact Green's strain displacement for the inplane strains and linear strain displacement for the transverse shear strains. Additional coupling results for membrane‐bending and membrane‐transverse shear due to non‐linear curvature strain‐displacement relations. Additional non‐linear terms that are a function of the shell's radius of curvature are also present. The approach is applied to the bifurcation buckling of axially compressed flat plates and transversely pressure‐loaded cylindrical shell panels. The method gives a more flexible result for the plates compared to von Karman non‐linearity. Additionally, larger buckling pressures are found for shell panels. The effects of transverse shear flexibility are evident.
On the generalized L2 Galerkin finite element method for linear hyperbolic equations
Authors: Bar‐Yoseph Pinhas , Elata David , Israeli Moshe
Published: August 2005

In this work, a Von Neumann analysis of the generalized L2 Galerkin method is described. The analysis is carried out on a linear scalar hyperbolic equation. The analysis shows both qualitatively and quantitatively the stability, dissipation and dispersion of the standard space‐time discontinuous Galerkin finite element method, and of the space‐time discontinuous streamline upwind Petrov Galerkin (SUPG) method. In addition a new special non‐dissipative non‐dispersive scheme is presented.
Vibration of shear‐deformable rectangular plates using a spline‐function Rayleigh‐Ritz approach
Authors: Wang S. , Dawe D. J.
Published: August 2005

The prediction of the natural frequencies of vibration of rectangular plates or orthotropic laminates is described, through the use of B‐spline functions as trial functions in a Rayleigh‐Ritz approach. Through‐thickness shear deformation effects are included in the analysis and hence assumptions have to be made for the spatial variation over the plate middle surface of each of the lateral deflection and the two rotation components. Two versions of the spline‐function Rayleigh‐Ritz approach are described: in one of these the deflection and rotations are represented by functions of the same polynomial order, whilst in the other a lower‐order representation is used for each rotation component in one of the co‐ordinate directions. It is shown in a number of applications that the former version leads to shear‐locking behaviour whilst the latter version avoids this behaviour and is suitable for the analysis of both thick and thin plates.
Shell elements with drilling degree of freedoms based on micropolar elasticity theory
Authors: Yeh Jyi‐Tyan , Chen Wen‐Hwa
Published: August 2005

Based on the theory of micropolar elasticity, new degenerated shell elements with drilling degree of freedoms are presented. The proper stiffness on the drilling degree of freedom is derived and no spurious modes are encountered in these elements. The implementation of these new shell elements on general structural finite element programs has many advantages, especially for the analysis of a folded shell or the treatment of the twist moment normal to the shell. Several numerical examples are carried out to demonstrate the accuracy and applicability of the present elements. The effects of the coupling factor and the body moment induced in magneto‐solid mechanics are also studied.
A posteriori pointwise upper bound error estimates in the finite element method
Authors: Yang J. D. , Kelly D. W. , Isles J. D.
Published: August 2005

An error estimate for the finite element method is presented in this paper. The error is identified as the response to a set of residual forces, and a complementary analysis provides an upper bound estimate of the global energy of the error. The inequality proposed by Babuška and Miller1 is then employed to bound the error in stress and displacement at a point. The formula is derived for two‐dimensional elasticity, but the procedure is general; and can be applied to three‐dimensional and other problems. Numerical experiments using the procedure are carried out and the results are given for the four‐node bilinear compatible element and plane stress.
Buckling of thick skew plates
Authors: Kitipornchai S. , Xiang Y. , Wang C. M. , Liew K. M.
Published: August 2005

The paper considers the elastic buckling of thick skew plates. Up to now, very little work has been done on this subject and the paper aspires to fill this gap. Based on the principle of stationary total potential energy and the recently developed pb‐2 Rayleigh‐Ritz method as a solution procedure, buckling solutions for skew plates of various aspect ratios, skew angles and boundary conditions are determined. The tabulation of these results, not available thus far, should be useful to designers and researchers who may use them as benchmark values to test the validity and convergence of their numerical techniques and softwares for thick plate analysis.
EAS‐elements for two‐dimensional, three‐dimensional, plate and shell structures and their equivalence to HR‐elements
Authors: Andelfinger U. , Ramm E.
Published: August 2005

The enhanced assumed strain (EAS) method, recently proposed by Simo and Rifai13, is used to develop new four‐node membrane, plate and shell elements and eight‐node solid elements. The equivalence of certain EAS‐elements with Hellinger‐Reissner (HR) elements is discussed. For instance, the seven‐parameter element EAS‐7 with 2 × 2 integration is identical to the HR‐element of Pian and Sumihara2. Eight‐node solid elements which are free of volumetric locking and four‐node shell elements which have an improved membrane and bending behaviour, compared to the Bathe‐Dvorkin shell element7, are introduced. Numerical tests for linear elastic problems show an improved performance of the EAS‐elements.
Further development of a three‐node triangular shell element
Authors: Cook Robert D.
Published: August 2005

A three‐node triangular shell element having six d.o.f. per node can be economically generated as a flat element that combines well‐known formulations for membrane stiffness and plate bending stiffness. Early elements of this type were inaccurate because the membrane response was poor. Researchers improved the membrane response by adding drilling d.o.f. and by underintegrating the membrane stiffness matrix. More recent research has dealt with the addition of membrane‐bending coupling within individual elements and the suppression of mechanisms. The present work intends to continue the improvement by modifying the membrane stiffness, simplifying the membrane‐bending coupling device and suppressing mechanisms without degrading performance or causing the mesh to lock.
Large displacement transient analysis of flexible structures
Authors: Rice D. L. , Ting E. C.
Published: August 2005

A new approach for numerical analysis of flexible space frames subjected to impact forces is presented. The method is particularly effective in the analysis of large‐amplitude vibration and dynamic stability found in extremely flexible structures.

The proposed method of analysis is based on a concept of updated material frame, which allows the algorithm of handling large rotations exceeding 360° and extensions longer than 100 per cent without numerical difficulty and the need for iterations. Thus, an efficient explicit integration finite element algorithm can be adopted. The method is convenient for non‐linear and inelastic material models.

The basic coding procedure is similar to the popular co‐rotational approach. Existing codes can be easily modified to solve transient dynamic problems. The modification steps necessary for the implementation are outlined in the paper.

Several numerical examples are presented. Comparison with the standard co‐rotational approach and large deformation finite element formulations, such as the updated Lagrangian approach, are presented.
An adaptive multigrid technique for three‐dimensional elasticity
Authors: Kočvara Michal
Published: August 2005

A program for finite element analysis of 3D linear elasticity problems is described. The program uses quadratic hexahedral elements. The solution process starts on an initial coarse mesh; here error estimators are determined by the standard Babuška‐Rheinboldt method and local refinement is performed by partitioning of indicated elements, each hexahedron into eight new elements. Then the discrete problem is solved on the second mesh and the refinement process proceeds in the following way‐on the ith mesh only the elements caused by refinement on the (i‐1)th mesh can be refined. The control of refinement is the task of the user because the dimension of the discrete problem grows very rapidly in 3D. The discrete problem is being solved by the frontal solution method on the initial mesh and by a newly developed and very efficient local multigrid method on the refined meshes. The program can be successfully used for solving problems with structural singularities, such as re‐entrant corners and moving boundary conditions. A numerical example shows that such problems are solved with the same efficiency as regular problems.
A normal offsetting technique for automatic mesh generation in three dimensions
Authors: Johnston Bruce P. , Sullivan John M.
Published: August 2005

A technique, based on a normal offsetting procedure, for the fully automatic generation of meshes suitable for finite element analysis in three dimensions is presented. The method is completely automatic, requiring no user intervention in the process and no special modelling procedures. The method is applied to three‐dimensional solid geometries.

The procedure positions nodes in the interior domain of an object by offsetting an initial set of nodes on the object boundary along vectors normal to the boundary to define a layer of new interior point locations. The offset points are processed to ensure good nodal spacing appropriate for generating well‐shaped elements. Following processing, the offset points become a new boundary surrounding the remaining unmeshed region in the interior of the geometric domain. The offsetting procedure is applied again to this new boundary layer to form another offset layer farther into the domain interior. The offset‐process‐offset cycle is repeated until the entire region is filled with nodes. Tetrahedral elements are then formed by triangulation of the nodes.

The boundary‐based technique ensures good quality element shapes for analysis in critical boundary regions and facilitates applications involving integration of mesh generation with design geometry databases. Calculation of nodal locations are based on local parameters avoiding the higher‐order time complexities associated with global calculations.
New strategy for assumed stresses for 4‐node hybrid stress membrane element
Authors: Yuan Kuan‐Ya , Huang Yeong‐Shyang , Pian Theodore H. H.
Published: August 2005

An oblique (skew) co‐ordinate system defined at the origin of the isoparametric co‐ordinates is introduced as the reference co‐ordinate system for assumed stresses in the formulation of a 4‐node hybrid membrane element. The initially uncoupled stresses in these reference co‐ordinates can be constrained to satisfy the equilibrium conditions pointwise by using the procedure of Pian and Wu7, when suitable incompatible displacements are introduced. Such strategy allows the element stiffness to be formulated by using either the Hellinger‐Reissner or the complementary energy functional. Numerical results show that the performances of three elements, constructed by using different sets of incompatible displacements in this paper, are practically identical and are all of slightly higher accuracy than that of the Pian‐Sumihara element6.
Calculation of wave forces on offshore structures using parallel computers
Authors: Hardy N. , Downie M. J. , Bettess P. , Graham J. M. R.
Published: August 2005

Four methods of implementing Morison wave‐force calculations for offshore tubular‐jacket structures on distributed‐memory parallel hardware are presented The Morison equation is given and the method by which it is used to calculate wave forces on members of an offshore structure is briefly described. A brief background to parallel computing and a description of the transputer hardware and software available to the authors is also given. Program structure and methods of achieving parallelism are explained. A number of test runs on an example structure have been timed and the resulting speed‐ups are discussed.
A finite element analysis of rubber coextrusion using a power‐law model
Authors: Buscaglia Gustavo C.
Published: August 2005

A finite element method to simulate coupled thermal viscous coextrusion is presented, with a power‐law viscosity function obtained from viscometric data on rubber composites. It combines, by successive substitution iterations, some well‐known schemes, such as streamline integration for updating interfaces and Lagrange‐Galerkin treatment of the energy equation. Some details of the implementation are discussed. The method is then applied to a comparison of two pre‐forming plates for the dual tuber head extruder of Farrel Corporation. Both the normal stress and the temperature at the interface suggest that the presence of a deflector deteriorates the adherence properties. This prediction is in agreement with operational experience.
Applications of a super element model for non‐linear analysis of stiffened box structures
Authors: Jiang J. , Olson M. D.
Published: August 2005

Numerical investigations are carried out to verify the new super element model developed in Reference 1 for non‐linear analysis of stiffened box structures. The results presented here are obtained from a variety of examples which are chosen to illustrate the accuracy and convergence of the model in various applications. Good agreement is obtained for most of the problems considered and the present formulation is found to be accurate and economical for preliminary engineering design.
The construction of an optimal weakly divergence‐free macroelement
Authors: Ye Xiu , Hall Charles A.
Published: August 2005

The divergence‐free finite element method (DFFEM) is a method to find an approximate solution of the Navier‐Stokes equations in a divergence‐free space. That is, the continuity equation is satisfied a priori. DFFEM eliminates the pressure from the calculations and reduces significantly the dimension of the system to be solved at each time step. For the standard 8‐node velocity and 4‐node pressure DFFEM, an optimal basis for the weakly divergence‐free subspace is constructed such that each basis function has non‐zero support on at most nine contiguous elements. Given this basis, weakly divergence‐free macroelements are constructed.
A six‐noded element for analysing power‐type singularities under thermal loads
Authors: Dutta Bijan K.
Published: August 2005

The shape functions of a 6‐noded triangular element have been derived to model power‐type singularities under thermal loads. A number of case studies have been presented, which involve variable‐order singularities under mechanical and thermal loads. The results show the usefulness of the element.
New basis functions and computational procedures for p‐version finite element analysis
Authors: Carnevali P. , Morris R. B. , Tsuji Y. , Taylor G.
Published: August 2005

New basis functions and solution procedures for p‐version finite element analysis are described. They are used in a highly efficient p‐version finite element solver for linear elastostatics and dynamics, which has been used in an industrial environment for over two years. Using two sample applications it is shown that, using the techniques proposed here, p‐version finite element analysis can have a substantially lower computational cost, for given accuracy, than standard finite element methods. This makes the industrial applicability of p‐version finite element analysis much wider than is commonly believed.
A computational procedure for flexible beams with frictional contact constraints
Authors: Sun S. M. , Natori M. C. , Park K. C.
Published: August 2005

This paper deals with the application of a parametric quadratic programming (PQP) method to the numerical solution of large‐deflection beams involving frictional contact constraints. The flexibility of the structure is modelled by an intrinsic spatial beam theory which is approximated by transverse‐shear deformable linear beam elements. The linear complementary problem (LCP) without the penalty function resulting from PQP is made part of a Newton‐Raphson search. The tool for solving the complementary equations is Lemke's algorithm, in which frictional contact conditions are enforced and new contact surfaces are updated during iteration. Applying the resulting contact element, a more accurate approximation of the contact point can be guaranteed, and the contact force can be directly computed by the adjacent beam elements. Three numerical examples are analysed to show the effectiveness and validity of the method.
Stress computation and consistent tangent operator using non‐linear kinematic hardening models
Authors: Hartmann Stefan , Haupt Peter
Published: August 2005

One possibility of formulating the tinite element method is founded on the principle of virtual displacement, in which we want to include a rate‐independent elastoplastic constitutive model based on the assumption of a yield surface. The constitutive equations result from the assumptions of small deformations, Hooke's law for the elastic domain, the normality rule for the evolution of plastic strains, the von Mises yield condition and a special kind of kinematic hardening due to Armstrong and Frederick,1 in which linear kinematic hardening is generalized with a saturation term. We show that it is not generally recommendable to propose large load steps. To this end, we investigate the influences of the non‐linear kinematic hardening model on the stress computation and the resulting consistent elastoplastic tangent operator. The main topics of this paper are: (1) development of a problem‐optimized backward Euler method with regard to the kinematic hardening model, (2) study of the influence of the saturation term on the numerical accuracy through isoerror maps and (3) computation of the consistent elastoplastic tangent operator.
Discrete micromechanics of elastoplastic crystals
Authors: Borja Ronaldo I. , Wren Jon R.
Published: August 2005

The theoretical prediction of elastoplastic behaviour of single crystals is a basic problem which is central to the prediction of the overall behaviour of the crystal aggregate. It is generally well known that quasi‐static and isothermal plastic deformation in single crystals arises almost solely from slip on specific crystallographic planes, and that this process occurs when the resolved shear stress on a critical slip system reaches a certain maximum value. What is not obvious is how one can identify the specific slip systems activated by a given load increment, since the process usually involves selection from a pool of linearly dependent slip systems. In this paper we use small‐deformation multisurface plasticity theory to phrase properly the problem of crystal slips at infinitesimal increments. We then describe an ‘ultimate’ algorithm for systematically identifying the active slip systems at finite increments. We arrive at the following major conclusions when the ultimate algorithm is applied to f.c.c. crystals: For perfectly plastic crystals the combination of active slip systems may or may not be unique; however, the imposition of the discrete Kuhn‐Tucker conditions is sufficient to determine the (unique) final crystal stresses. For Taylor hardening crystals in which active and latent slip systems harden by the same amount, the discrete Kuhn‐Tucker conditions are also sufficient to make the mathematical problem of crystal stress integration well posed, i.e. the final stresses can be determined uniquely albeit the combination of active slip systems may not be unique. To illustrate the latter point, an accurate return‐mapping algorithm for perfectly plastic and Taylor hardening crystals is described and tested against the ultimate algorithm to demoustrate numerically that it is possible to generate different combinations of active slip systems and yet produce identical final stresses.
Physically correct penalty‐like formulations for accurate pressure calculation in finite element algorithms of the Navier‐Stokes equations
Authors: Dyne B. R. , Heinrich J. C.
Published: August 2005

Finite element algorithms for incompressible fluids, in particular the penalty function method, are re‐examined and re‐formulated based on physically consistent approximations to the mass conservation equation. These approximations lead to methods that satisfy all fluid conditions under the assumption of slightly compressible flow and directly yield approximations to the pressure field that are free from spurious oscillations. Penalty function‐type algorithms are developed for direct steady‐state calculations and for time‐dependent simulations of viscous incompressible flows that are based on the bilinear isoparametric quadrilateral element and circumvent the Ladyszhenskaya, Babuska and Brezzi (LBB) condition. Further‐more, methods that eliminate pressure oscillations in the low Mach number region of high‐speed compressible flows are obtained. These methods are tested in examples that show their superior performance in approximating the pressure field.
Fully implicit integration and consistent tangent modulus in elasto‐plasticity
Authors: Doghri Issam
Published: August 2005

This paper deals with the numerical integration of a class of rate‐independent elasto‐plastic models. The backward Euler scheme is used to integrate the rate constitutive relations. The non‐linear equations obtained are solved by the Newton method. The consistent tangent modulus is obtained by exact linearization of the algorithm. In the case of J2 elasto‐plasticity with non‐linear isotropic hardening and non‐linear kinematic hardening (Chaboche‐Marquis model), explicit formulas are derived, without any approximations.
A parametric study on achieving the same final shape by numerical experimentation using a shape optimization process subject to different initial conditions
Authors: Gates A. A.
Published: August 2005

A finite element based shape optimization program has been developed for three‐dimensional shell structures which allows for multiple edge movement and large shape changes. This program automatically performs shape optimization by linking together adaptive mesh generation, substructuring and optimization algorithms with a commercial finite element analysis program, MSC/NASTRAN. This paper examines the robustness of the shape optimization program by varying the initial shape and design parameters for three examples. This is performed to determine the conditions under which similar optimum shapes will be generated for different initial conditions.
A Streamline‐Upwind‐Full‐Galerkin method for space–time convection dominated ‐transport problems
Authors: Perrochet P.
Published: August 2005

An original space‐time finite element approach for the solution of the diffusion‐convection equation is proposed in this paper. A slight manipulation of the differential equation suggests that transient transport problems may in fact be seen as ‘steady‐state space‐time transport problems’, accurately and easily soluble by the standard Galerkin technique. However, concerning convective transport involving sharp fronts or coarse discretization, it is shown that implementation of dissipation along space‐time trajectories significantly improves the solutions. Classical comparative test problems are run to establish the performances of this method, and to show the limits of the more sophisticated Petrov and Taylor‐Galerkin schemes. Evocation of a possible space‐time anisotropy generated by usual finite difference time‐stepping procedures, as well as comparative analysis of amplification matrices, help to understand the accuracy and the robustness of the proposed approach.
H‐Adaptive finite element methods for dynamic problems, with emphasis on localization
Authors: Belytschko T. , Tabbara M.
Published: August 2005

H‐adaptive procedures for the finite element solution of transient solid mechanics problems are studied, with particular emphasis on problems involving localization due to material instability. Various types of error criteria are examined and it is shown that for problems involving plastic response or localization, an error criterion based on an L2‐projection of strains is the most effective for the constant strain elements considered here. Examples of one‐dimensional and two‐dimensional localization (shear band formation) problems are given.