bluuebunny/crossref_metadata_2025_split huggingface dataset:
p‐version hierarchical three dimensional curved shell element for elastostatics
Authors: Surana Karan S. , Sorem Robert M. 
Published: August 2005

AbstractThis paper presents a hierarchical three dimensional curved shell finite element formulation based on the p‐approximation concept. The element displacement approximation can be of arbitrary and different polynomial orders in the plane of the shell (ξ, η) and the transverse direction (ξ). The curved shell element approximation functions and the corresponding nodal variables are derived by first constructing the approximation functions of orders pξ, pη and pξ and the corresponding nodal variable operators for each of the three directions ξ, η and ξ and then taking their products (sometimes also known as tensor product). This procedure gives the approximation functions and the corresponding nodal variables corresponding to the polynomial orders pξ, pη and pξ. Both the element displacement functions and the nodal variables are hierarchical; therefore, the resulting element matrices and the equivalent nodal load vectors are hierarchical also, i.e. the element properties corresponding to the polynomial orders pξ, pη and pξ are a subset of those corresponding to the orders (pξ + 1), (pη +1) and (pξ +1). The formulation guarantees C° continuity or smoothness of the displacement field across the interelement boundaries.The geometry of the element is described by the co‐ordinates of the nodes on its middle surface (ξ = 0) and the nodal vectors describing its bottom (ξ = −1) and top (ξ = +1) surfaces. The element properties are derived using the principle of virtual work and the hierarchical element approximation. The formulation is equally effective for very thin as well as very thick plates and curved shells. In fact, in many three dimensional applications the element can be used to replace the hierarchical three dimensional solid element without loss of accuracy but significant gain in modelling convenience. Numerical examples are presented to demonstrate the accuracy, efficiency and overall superiority of the present formulation. The results obtained from the present formulation are compared with those available in the literature as well as analytical solutions.
Potential of earthing grid in heterogeneous soil
Authors: Kurtovic Mate , Vujevic Slavko 
Published: August 2005

AbstractCalculation of the scalar electric potential of an earthing grid in heterogeneous soil is obtained by the finite element technique combining differential and integral formulations of the problem. Such a combined formulation made it possible to generate easily the mesh of finite elements and to divide the problem domain into a sufficiently small number of large finite elements. The unbounded domain of calculation is solved by using mapped infinite elements. The contribution of singular sources is represented by the analytical expression, and included in the approximation function of the potential. A sufficiently satisfactory approximation is realized with a small number of singular source images, obtained by local imaging of sources within a finite element on its boundary surfaces. The calculation accuracy is tested on examples solvable by an average potential method which is based on an integral formulation of the problem.
A frequency dependent rectangular plate finite dynamic element for high precision transverse vibration analysis of simply supported plates
Authors: Downs B. 
Published: August 2005

AbstractThe need for adding to the many existing rectangular plate elements is justified and the inclusion of the twist parameter, in the degrees of freedom selected, is shown to be essential. Using a rational choice of parameters to form the deflection functions for a simply supported plate element, a constant term, sixteen degrees of freedom rectangular element is developed which is shown to predict exactly the first mode frequency and mode shape when used in whole plate modelling. The properties of this ‘dynamic’ element are combined with the properties of an existing ‘static’ element to obtain the frequency dependent properties of a ‘blended’ element. It is demonstrated that in order to obtain high accuracy in eigenvalue determination it is necessary to use three separate modellings of the plate using a square element and two rectangular elements which are oriented orthogonally. From 3 × 3 and 2 × 5 modelling, it is shown that the frequencies of the first 20 modes of a simply supported square plate, resulting from matrix eigenvalue determinations are obtainable within one per cent of the exact values. Modes 11 and 18 are determined exactly. Mode shape distortions associated with frequency errors are examined and shown to be minimal for the first 20 modes.
Transient scattering of elastic waves by three dimensional non‐axisymmetric dipping layers
Authors: Eshraghi Hossein , Dravinski Marijan 
Published: August 2005

AbstractScattering of elastic plane waves by three dimensional non‐axisymmetric multiple dipping layers embedded in an elastic half‐space is investigated by using a boundary method. The dipping layer is subjected to incident Rayleigh waves and oblique incident SH, SV and P waves. For the steady state problem, spherical wave functions are used to express the unkown scattered field. These functions satisfy the equation of motion and radiation conditions at infinity but they do not satisfy the stress free boundary conditions on the surface of the half‐space. The boundary and continuity conditions are imposed locally in the least‐square sense at points on the layer interfaces and on the surface of the half‐space. The transient response is constructed from the steady state solution by using Fourier synthesis.Numerical results are presented for both steady state and transient problems. Steady state problems include solutions for two non‐axisymmetric dipping layers in the form of a prolate. Transient responses are presented for one and two dipping layer models subjected to incident wave signals in the shape of a Ricker wavelet. It is shown that change in azimuthal orientation of the incident wave may significantly change the surface response of the dipping layer. For the transient problem, response comparison of one and two dipping layers indicates that the addition of an extra layer may also completely change the response characteristics of the alluvium. In particular, the delay in arrival of much larger amplitude surface waves by two dipping layers in comparison with other geometrically compatible models demonstrates the importance of the detailed three dimensional modelling of layered irregularities.
A Petrov–Galerkin formulation for the incompressible Navier–Stokes equations using equal order interpolation for velocity and pressure
Authors: De Sampaio P. A. B. 
Published: August 2005

AbstractA new Petrov‐Galerkin method for the incompressible Navier‐Stokes equations is presented. The use of the so‐called ‘optimal upwind’ parameter in multidimensions is justified by a time‐scale analysis of the relevant physical processes. The resulting procedure circumvents the Babuška‐Brezzi condition and allows equal order interpolation for velocity and pressure to be used.
A monomial‐based method for solving systems of non‐linear algebraic equations
Authors: Burns S. A. , Locascio A. 
Published: August 2005

AbstractA monomial‐based method for solving systems of algebraic non‐linear equations is presented. The method uses the arithmetic‐geometric mean inequality to construct a system of monomial equations that approximates the system of non‐linear equations. A change of variables transforms the monomial system into a system of linear equations, which is readily solved. Special properties of the monomial method are identified and their significance is discussed. Invariance properties of the monomial method produce a built‐in, self‐adjusting scaling of the variables and equilibration of the equations of the linear system. Other special properties can lead to useful bounds on, and invariances of, the conditioning of the linear system. An invariance to uniform scaling is responsible for extremely rapid convergence to the equation surfaces in the initial iterations. An invariance to multiplication of the algebraic equations by a certain class of functions leads to a useful insensitivity to form of the algebraic system. Insensitivity of the monomial method to solutions with negative components avoids meaningless solutiuons of the algebraic system that appear as undesirable by‐products of the formulation. A practical engineering design problem is solved to demonstrate the special properties of the monomial method.
Thick shell and solid finite elements with independent rotation fields
Authors: Ibrahimbegovic Adnan , Wilson Edward L. 
Published: August 2005

AbstractThick shell and solid elements presented in this work are derived from variational principles employing independent rotation fields. Both elements are built on a special hierarchical interpolation and both possess six degrees of freedom per node. Performance of the elements is evaluated on a set of problems in elastostatics. However, the formulation presented herein is also suitable for transient and non‐linear problems.
Three‐dimensional full Navier–Stokes solvers for incompressible flows past arbitrary geometries
Authors: Deng G. B. , Piquet J. , Queutey P. , Visonneau M. 
Published: August 2005

AbstractThe computation of the three‐dimensional viscous flow past several geometries is investigated. An iterative technique resting on the fully elliptic mode is applied to the Reynolds‐Averaged Navier‐Stokes Equations written in a non‐orthogonal curvilinear body‐fitted co‐ordinate system. Results of the computation are compared with available experiments.
A time‐dependent incompressible viscous BEM for moderate Reynolds numbers
Authors: Dargush G. F. , Banerjee P. K. 
Published: August 2005

AbstractThe boundary element method is applied to transient viscous incompressible flow. The time‐domain formulation allows a boundary‐only solution for linear Stokes flow. For higher speed flows in which the non‐linear convective effects cannot be ignored, a volume integral must be retained. However, the introduction of reference velocities often limits the non‐linear region to the vicinity of obstacles or bounding surfaces. Additionally, the volume terms are rewritten to eliminate the need for the calculation of velocity gradients. A general purpose numerical implementation of this new formulation then produces a very attractive tool for engineering analysis. This implementation includes a Newton‐Raphson algorithm, permitting accurate solutions up to the moderate Reynolds number range. Several numerical examples are provided to validate the present approach.
An adjoint variable method for sensitivity analysis of non‐linear elastic systems
Authors: Phelan David G. , Vidal Creto , Haber Robert B. 
Published: August 2005

AbstractAn adjoint variable method for design sensitivity analysis of non‐linear elastic systems is presented. The method uses domain parameterization and a mutual form of the Hu‐Washizu energy principle, and extends results reported in a recent work for linear elastic systems to non‐linear elasticity. Non‐linearities due to finite deformations and non‐linear, hyperelastic constitutive models are considered. In contrast to other methods for non‐linear sensitivity analysis, the present formulation can be applied with force, displacement or mixed approximate solution methods.The mutual energy expression used in the adjoint sensitivity derivation is developed from a non‐linear extension of the Hu‐Washizu energy functional and yields a linear governing equation for the adjoint system. This has important ramifications for the computational cost of a sensitivity analyses of non‐linear systems: excluding the cost of determining the response of the system, the cost of a sensitivity analysis for a non‐linear system is essentially the same as that for a linear system. Finite element implementation of the resulting sensitivity expressions is discussed, and two numerical examples are presented. The first example involves large deformations of a Mooney‐Rivlin body, while the second involves design sensitivity analysis for mixed solution methods.
Numerical stability and constitution analysis of λ‐type incompatible elements
Authors: Wu Changchun , Cheung Y. K. 
Published: August 2005

AbstractThe weak connection conditions and an independence principle for internal displacements which can guarantee the numerical stability of the incompatible element solution are presented in this paper. A number of problems such as the uncoupling of the two types of displacement functions in the λ‐type element, zero energy modes, etc., have been investigated. Some simple and practical guidelines for establishing trial functions of non‐compatible elements are given.
An assumed‐stress hybrid 4‐node shell element with drilling degrees of freedom
Authors: Aminpour M. A. 
Published: August 2005

AbstractAn assumed‐stress hybrid/mixed 4‐node quadrilateral shell element is introduced that alleviates most of the deficiencies associated with such elements. The formulation of the element is based on the assumed‐stress hybrid/mixed method using the Hellinger‐Reissner variational principle. The membrane part of the element has 12 degrees of freedom including rotational or ‘drilling’ degrees of freedom at the nodes. 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 contributions. The element formulation is derived from an 8‐node isoparametric element by expressing the midside displacement degrees of freedom in terms of displacement and rotational degrees of freedom at corner nodes. The element passes the patch test, is nearly insensitive to mesh distortion, does not ‘lock’, possesses the desirable invariance properties, has no hidden spurious modes, and for the majority of test cases used in this paper produces more accurate results than the other elements employed herein for comparison.
A family of integration algorithms for constitutive equations in finite deformation elasto‐viscoplasticity
Authors: Zabaras Nicholas , Arif Abul Fazal Muhammad 
Published: August 2005

AbstractA two parameter family of incrementally objective integration schemes is proposed for the analysis of a broad range of unified rate‐dependent viscoplastic constitutive models in large deformation problems. A similar scheme can be applied to rate‐independent solids as well. These algorithms are a generalization of the mid‐point integration rule. Full linearization of the principle of virtual work is performed in an updated Lagrangian framework together with a calculation of the consistent linearized moduli. Some details of the finite element implementation are given for plane strain and axisymmetric problems. The method is compared with other objective integration schemes and is tested with several examples where large strains and rotations occur.
Solution and sensitivity analysis of a complex transcendental eigenproblem with pairs of real eigenvalues
Authors: Murthy Durbha V. 
Published: August 2005

AbstractThis paper considers complex transcendental eigenvalue problems where one is interested in pairs of eigenvalues that are restricted to take real values only. Such eigenvalue problems arise in dynamic stability analysis of non‐conservative physical systems–flutter analysis of aeroelastic systems, to name one example. Some available solution methods are discussed and a new method is presented. Two computational approaches are described for analytical evaluation of the sensitivities of these eigenvalues when they are dependent on other parameters. The algorithms presented are illustrated through examples.
An application of the arc length method involving concrete cracking
Authors: Foster Stephen 
Published: August 2005

AbstractTo overcome numerical difficulties in highly non‐linear materials Crisfield6 proposed a solution procedure involving the use of a constant arc length solution scheme with line searches and accelerations. This paper uses the arc length method with line searches to increase the stability and substantially reduce the cpu time required for convergence in the finite element modelling of reinforced concrete. The arc length method is compared with the modified Newton–Raphson solution scheme and it was found that substantial savings in computer resources are obtained by using the arc length method. On difficult iterations the use of line searches is shown to lead to substantial improvement, with the best results occurring when using a slack tolerance of ψ = 0.8.
A general methodology for deriving shear constrained Reissner‐Mindlin plate elements
Authors: Oñate E. , Zienkiewicz O. C. , Suarez B. , Taylor R. L. 
Published: August 2005

AbstractIn this paper the necessary requirements for the good behaviour of shear constrained Reissner–Mindlin plate elements for thick and thin plate situations are re‐interpreted and a simple explicit form of the substitute shear strain matrix is obtained. This extends the previous work of the authors presented in References 18 and 31. The general methodology is applied to the re‐formulation of some well known quadrilateral plate elements and some new triangular and quadrilateral plate elements which show promising features. Some examples of the good behaviour of these elements are given.
A new acoustic interface element for fluid‐structure interaction problems
Authors: Rajakumar C. , Ali Ashraf , Yunus Shah M. 
Published: August 2005

AbstractA new comprehensive acoustic 2‐D interface element capable of coupling the boundary element (BE) and finite element (FE) discretizations has been formulated for fluid–structure interaction problems. The Helmholtz equation governing the acoustic pressure in a fluid is discretized using the BE method and coupled to the FE discretization of a vibrating structure that is in contact with the fluid. Since the BE method naturally maps the infinite fluid domain into finite node points on the fluid–structure interface, the formulation is especially useful for problems where the fluid domain extends to infinity. Details of the BE matrix computation process adapted to FE code architecture are included for easy incorporation of the interface element in FE codes. The interface element has been used to solve a few simple fluid–structure problems to demonstrate the validity of the formulation. Also, the vibration response of a submerged cylindrical shell has been computed and compared with the results from an entirely finite element formulation.
Fully automatic two dimensional mesh generation using normal offsetting
Authors: Johnston Bruce P. , Sullivan John M. 
Published: August 2005

AbstractA technique, based on a normal offsetting procedure, for the fully automatic generation of two dimensional meshes suitable for finite element analysis is presented. The method positions nodes by first meshing the geometric entities that compose the object boundary, then offsetting those nodal locations along vectors normal to the boundary geometry. The offset row of nodes is processed to ensure a good nodal spacing appropriate for generating well shaped elements. Following processing, the new row is offset again and the cycle is repeated until the entire area is filled with 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. Nodal locations are calculated based on local parameters avoiding the higher order time complexities associated with global calculations.A technique for controlling mesh density by overlaying an independent mesh density function on the geometry is also presented as part of the method. This approach allows mesh density to be automatically controlled by a variety of factors, such as previous analysis results, that are external to the actual mesh generation process. The independent nature of the function method allows different sources of density information to be used interchangeably without modification to the mesh generation procedure.
Effective modelling of spatial buckling of beam assemblages, accounting for warping constraints and rotation‐dependency of moments
Authors: Saleeb A. F. , Chang T. Y. P. , Gendy A. S. 
Published: August 2005

AbstractA simple, two‐noded, finite element model for the three‐dimensional buckling analysis of beam assemblages is developed. The underlying generalized‐beam theory employed accounts for all coupled significant modes of deformations, including stretching, bending, shear and torsion, as well as warping. Its mixed formulation is of the two‐field type, utilizing linear and constant interpolants for displacements and strain fields. Due considerations are given to the effect off inite rotations in space on the non‐linear kinematic descriptions as well as the configuration‐dependent behaviour of externally applied moment vectors of the conservative and non‐conservative types. The performance of the model, and particularly the accuracy of its geometric and load‐correction stiffnesses, is assessed in a fairly complete set of numerical simulations.
A general finite element approach for contact stress analysis
Authors: Mottershead J. E. , Pascoe S. K. , English R. G. 
Published: August 2005

AbstractThis paper presents a general finite element approach for the treatment of contact stress problems. Stanctard shape function routines are used for the detection of contact between previously separate meshes and for the application of displacement constraints where contact has been identified. The mesh contact routines are installed in an incremental approach whereby the contact constraints are imposed by using either penalty functions or Lagrange multipliers.
On consistent stress rates in solid mechanics: Computational implications
Authors: Perić Djordje 
Published: August 2005

AbstractIn the context of general isothermal elastic processes, issues related to work conjugacy and its effect on the choice of a stress rate are discussed for processes involving large strains. It is shown that a unique stress rate consistent with hyperelasticity can be defined for every conjugate pair chosen through the rate form of the associated hyperelastic constitutive equation. That results in non‐constant and generally anisotropic spatial elasticity tensors even for a linear isotropic material. The anisotropic spatial elasticity tensor connected with the Green–Naghdi rate of Kirchhoff stress is evaluated, which provides a basis for the spatial formulation of processes governed by the Hencky's strain energy function.48,49 Notions of equivalent and irreducible form of stress rate are introduced using a ‘workless’ component of the deformation rate. The hyperelastic constitutive models for the conjugate pairs {S, E(2)} and {T, In U}, which are of significance for computation, are stated in their explicit form. Exact rate forms are derived and the order of approximation of currently employed computational algorithms discussed. Finally, computational implications of the work presented are reviewed.