bluuebunny/crossref_metadata_2025_split huggingface dataset:
Non‐singular boundary integral representation of potential field gradients
Authors: Sladek V. , Sladek J. 
Published: August 2005

AbstractIn 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

AbstractOptimal 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

AbstractThe 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

AbstractFinite 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

AbstractThe 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

AbstractThis 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

AbstractA 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

AbstractThis 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

AbstractAn 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

AbstractThe 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

AbstractThe 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

AbstractIn 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

AbstractIn 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

AbstractAn 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

AbstractThis 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

AbstractThis 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

AbstractEigenmode 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

AbstractThis 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

AbstractThis 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

AbstractA 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

AbstractA 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

AbstractIn 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.