bluuebunny/crossref_metadata_2025_split huggingface dataset:
Computation of isotropic tensor functions
Authors: Miehe C. 
Published: August 2005

AbstractAn explicit formulation and a procedure for the computation of isotropic tensor‐valued tensor functions is discussed. The formulation is based on a spectral decomposition in terms of second‐order eigenvalue bases, which avoids the costly computation of eigenvectors. As an important result a compact structure of the fourth‐order derivatives of general second‐order isotropic tensor functions is presented.
Use of load‐dependent vectors for dynamic analysis of large space structures
Authors: Ricles J. M. , Léger P. 
Published: August 2005

AbstractStructural models of large space structures have a substantial number of degrees of freedom (DOF) and possess semi‐positive‐definite stiffness matrices. The paper presents an efficient co‐ordinate reduction procedure for structural dynamic analysis of large space structures. The method is based on the superposition of load‐dependent Ritz vectors, which are computed in block form using a shifted stiffness matrix. Comparative transient dynamic analyses are performed on a 2803 DOF model of the space station Freedom using the load‐dependent method (LDM) and the mode‐displacement method (MDM) based on the superposition of eigenvectors. It is shown that the LDM is able to provide convergence of displacements with a small number of vectors. The acceleration response is found to be more sensitive to vector truncation than the displacement response. Error norms based on the representation of the dynamic load by the vector basis are developed to provide an indication of the effect of vector truncation on the structural response.
Mapping of finite elements around corner singularities of the quasi‐harmonic equation
Authors: Aalto Jukka 
Published: August 2005

AbstractThe paper deals with the solution of the quasi‐harmonic equation by the finite element method in a domain with corners on its boundary. A mapping technique, which can be used for locating the nodes of standard isoparametric elements in a subgrid (patch) of finite elements in the vicinity of a corner singularity point, is presented. The equations of the mapping are based on the analytical singular solution of the problem. Some analytical and numerical results to show the efficiency of the technique are presented.
New assumed natural strain formulation of the shallow shell element
Authors: Muhanna Rafi L. 
Published: August 2005

AbstractA new efficient formulation of the 36 degree‐of‐freedom conforming shallow shell element of an arbitrary triangular shape is presented. This formulation is based on natural co‐ordinates and independently assumed natural strain fields, and applied to shallow shell analysis. The 3‐node element incorporates the normal displacement and its first and second derivatives plus the tangential displacements and their first derivatives at each vertex. A closed form of the element stiffness matrix is achieved. The form of the stiffness matrix derived in this formulation explicitly reveals the essence of the shallow shell theory.The presented approach results in avoiding definite integrals and matrix inversions, and permits operation with lower‐order numerical matrices, which are the same for all elements. The example applications presented demonstrate that accurate predictions of stresses as well as displacements are obtained with only a few elements.
Compound difference schemes for time‐dependent equations on non‐uniform nets
Authors: Charakhch'Yan A. A. 
Published: August 2005

AbstractA new approach to constructing monotonous second‐order‐accurate schemes for time‐dependent Navier‐Stokes equations in the compressible case is suggested. Flows with shock waves and thin viscous boundary layers are considered. The approach joins two different schemes while each of them is appropriate for its own type of flow. The resulting scheme is constructed as a splitting one, and the approach is applied at the stage governed by the Euler equations in Lagrangian variables. The approach turns out to be fruitful also for parabolic equations with ‘viscous’ terms. The method is illustrated by the problem on compression of deuterium in a conical solid‐body target with viscous heating of deuterium.
Accuracy and efficiency of multivariant finite elements for three‐dimensional simulation of viscous incompressible flows
Authors: Gupta Mahesh , Kwon Tai H. 
Published: August 2005

AbstractThe performance of the univariant finite element Q1P0 and the multivariant finite elements QP0 and RP0 are compared for simulation of three‐dimensional incompressible viscous flows. Incompressible flow vortices for the RP0 element are presented. For the two flows simulated, the RP0 element is found to be not only the most accurate but also computationally the most efficient of the three types of finite element used. For one of the two flows simulated, the pressure distribution obtained by using the Q1P0 element is found to be afflicted with the checker‐board spurious pressure mode. For the uniform finite‐element mesh used, the checker‐board pressure mode is eliminated by taking a weighted average of the pressure over the neighbouring Q1P0 elements.
A 3D element for non‐linear analysis of solids
Authors: Radovitzky Raúl A. , Dvorkin Eduardo N. 
Published: August 2005

AbstractAn 8‐node element (HMITC) for 3D non‐linear analysis of solids is presented. The new element is based on an element developed by Wilson and Ibrahimbegovic, that incorporates incompatible modes, and on the method of mixed interpolation of tonsorial components. The HMITC element does not contain spurious zero energy modes and satisfies Irons' Patch Test. The numerical experimentation indicates that the HMITC has good performance even with distorted meshes.
Neural‐network‐based approximations for solving partial differential equations
Authors: Dissanayake M. W. M. G. , Phan‐Thien N. 
Published: August 2005

AbstractA numerical method, based on neural‐network‐based functions, for solving partial differential equations is reported in the paper. Using a ‘universal approximator’ based on a neural network and point collocation, the numerical problem of solving the partial differential equation is transformed to an unconstrained minimization problem. The method is extremely easy to implement and is suitable for obtaining an approximate solution in a short period of time. The technique is illustrated with the aid of two numerical examples.
Superconvergent patch recovery of finite‐element solution and a posteriori L2 norm error estimate
Authors: Wiberg N.‐E. , Li X. D. 
Published: August 2005

AbstractIn the paper we present a superconvergent patch recovery technique for obtaining higher‐order‐accurate finite‐element solutions and thus a postprocessed type of L2 norm error estimate. Two modifications make our procedure different from the one proposed by Zienkiewicz and Zhu (1992), in which higher‐order‐accurate derivatives of the finite‐element solution at nodes are determined. Firstly, the recovery process is made for element, not for nodes. An ‘element patch’, which represents the union of an element under consideration and the surrounding elements, is introduced. Secondly, the local error estimate is calculated directly from the improved solution for this element. Numerical tests on both 1D and 2D model problems show that this method can provide an asymptotically exact a posteriori L2 norm error estimate if the used element possesses superconvergent points for the solutions.
Universal matrices with new infinite elements for quasiharmonic equation
Authors: Raghavarao C. V. , Sanyasiraju Yvss 
Published: August 2005

AbstractA new approach to developing serendipity quadrilateral infinite elements is presented. Using these elements universal matrices for quasiharmonic equation are developed. For a particular member of the family these matrices are independent of the size and shape of the element. Using these matrices the element stiffness matrix can be generated in a simpler manner by taking into account the size and shape of the element.
Improvement on dual reciprocity boundary element method for equations with convective terms
Authors: Zhu Songping , Zhang Yinglong 
Published: August 2005

AbstractThe dual reciprocity boundary element method, first proposed by Nardini and Brebbia (1982, 1985), is a powerful technique for solving elliptic partial differential equations. Adopting this approach, a singular volume integral, which needs to be evaluated with a traditional boundary element method, can be converted into a boundary integral. However, when the governing equation is of a certain type, this conversion fails due to the singularities being introduced inside the physical domain and on the boundary arising by differentiating distance functions. We avoid these artificially created singularities by constructing a transformation which leads to improved numerical results.
Method to generate complex computational meshes efficiently
Authors: Landertshamer F. , Steffan H. 
Published: August 2005

AbstractThe paper demonstrates an approach to generate three‐dimensional boundary‐fitted computational meshes efficiently. One basic idea underlying the present study is that often similar geometries have to be meshed, and therefore an efficient mesh‐adaption method, which allows adaptation of the topological mesh to the specific geometry, would be more efficient than generating all new meshes. On the other hand the mesh generation for Cartesian topologies has been shown to be a very simple task. It can be executed by connecting and removing brick elements to a basic cube. In connection with a so‐called ‘Macro Command Language’, a high degree of automation can be reached when adapting topologically defined meshes to a surface. Furthermore, a high mesh quality has proved to be the key to good simulation results. During the mesh generation it is important to provide the possibility of modifiying the mesh quality and also the mesh density at any time of the meshing process. Using this generation method the meshing time is reduced—e.g. a computational mesh for a two‐valve cylinder head can be generated within a few hours.
Optimal uniform finite difference schemes of order two for stiff initial value problems
Authors: Selvakumar K. 
Published: August 2005

AbstractThe paper presents finite difference schemes of order two for stiff initial‐value problems, with a small parameter ε multiplying the first derivative. The schemes are a modified form of the classical trapezoidal rule. They are both optimal and uniform with respect to the small parameter ε, that is, the solution of the difference schemes satisfies error estimates of the form

Where C is independent of i, h and ε. Here h is the mesh size and ti in any mesh point. The schemes presented in this paper are different from the scheme of order two avaiable in the literature. Finally, numerical experiments are presented.
An alternative approach for large deflection analysis of axisymmetric plates on elastic foundation
Authors: Ye Jianqiao 
Published: August 2005

AbstractThe geometric non‐linear behaviour of thin axisymmetric circular plates on an elastic foundation is studied in the paper by using a boundary integral equation approach. A plate analogue procedure is suggested to simplify the solution. With such simplification, the foundation reaction can be arbitrary functions of plate deflection, rotation and curvatures. The boundary integral equation of thin plates and the fundamental solution of a biharmonic equation are employed for both bending and plane stress analysis. A number of numerical examples are given in the paper to show the effectiveness of the proposed method.
Conjugate gradient based projection: A new explicit computational methodology for frictional contact problems
Authors: Tamma Kumar K. , Li Maocheng , Sha Desong 
Published: August 2005

AbstractWith special attention towards the applicability to parallel computation or vectorization, a new and effective explicit computational approach for linear complementary formulations involving a conjugate gradient based projection methodology is proposed in this study for contact problems with Coulomb friction. The overall objectives are focused towards providing an explicit methodology of computation for the complete contact problem with friction. In this regard, the primary idea for solving the linear complementary formulations stems from an established search direction which is projected to a feasible region determined by the non‐negative constraint condition; this direction is then applied to the Fletcher‐Reeves conjugate gradient method resulting in a powerful explicit methodology which possesses high accuracy, excellent convergence characteristics, fast computational speed and is relatively simple to implement for contact problems involving Coulomb friction. Numerical test cases are also included to demonstrate the proposed methodology for contact problems with friction.
A time‐splitting finite difference method for two‐dimensional diffusion with an integral condition
Authors: Noye B. J. , Dehghan M. 
Published: August 2005

AbstractA new fourth‐order locally one‐dimensional (LOD) finite difference scheme based upon the Noye‐Hayman method for one‐dimensional diffusion is used to solve a two‐dimensional time‐dependent diffusion equation with an integral condition replacing one boundary condition. Numerical testing shows this gives better results than a locally one‐dimensional scheme based on the classical forward‐time centred‐space (FTCS) method for one‐dimensional diffusion except when the diffusion number is 1/6 and the methods are identical. Results from some numerical experiments are presented.
A fourth‐order difference scheme for quasilinear poisson equation in polar co‐ordinates
Authors: Jain M. K. , Jain R. K. , Krishna Meera 
Published: August 2005

AbstractWe present in this paper a nine‐point, fourth‐order difference scheme for the numerical solution of the quasilinear Poisson equation in polar co‐ordinates,

with appropriate boundary conditions. A separate difference scheme of order four valid at r = 0 has also been obtained. The method is based on five evaluations of the function f. The numerical results of two problems obtained using this scheme are listed. The numerical results demonstrate the fourth‐order accuracy of the scheme.
Integral transform solution of eigenvalue problems
Authors: Mikhailov M. D. , Cotta R. M. 
Published: August 2005

AbstractThe generalized integral transform technique is used to reduce eigenvalue problems described by partial differential equations to algebraic ones, that can be solved by existing codes for matrix eigensystem analysis. The method is illustrated for the operators that correspond to heat and mass diffusion, but can be employed in different fields. Three examples demonstrate the potential of the method.
An adaptive time‐stepping algorithm for quasistatic processes
Authors: van den Boogaard A. H. , De Borst R. , van den Bogert P. A. J. 
Published: August 2005

AbstractA scheme is presented that automatically determines the magnitude of the time step in quasistatic boundary value problems discretized via some customary method (finite elements, finite differences). The basic idea stems from the path‐following techniques widely employed in purely static analyses in the sense that the incremental displacements, measured in some suitable norm, are constrained to a prefixed value. Examples of trusses composed of a viscoelastic material are included to demonstrate the effectiveness of the method.
A new algorithm for finding a pseudoperipheral vertex or the endpoints of a pseudodiameter in a graph
Authors: Paulino Glaucio H. , Menezes Ivan F. M. , Gattass Marcelo , Mukherjee Subrata 
Published: August 2005

AbstractBased on the concept of the Laplacian matrix of a graph, this paper presents the SGPD (spectral graph pseudoperipheral and pseudodiameter) algorithm for finding a pseudoperipheral vertex or the end‐points of a pseudodiameter in a graph. This algorithm is compared with the ones by Grimes et al. (1990), George and Liu (1979), and Gibbs et al. (1976). Numerical results from a collection of benchmark test problems show the effectiveness of the proposed algorithm. Moreover, it is shown that this algorithm can be efficiently used in conjunction with heuristic algorithms for ordering sparse matrix equations. Such heuristic algorithms, of course, must be the ones which use the pseudoperipheral vertex or pseudodiameter concepts.
Local‐global analysis on localized non‐linear shells of revolution
Authors: Harintho H. , Gould P. L. 
Published: August 2005

AbstractA finite element program is developed as a tool to analyse shells of revolution with local non‐linearities. In reality, shells of revolution often exhibit local deviations, like a cut‐out, a junction and/or an imperfection. The stress concentration around a local deviation may produce plasticity and/or geometric non‐linearities in the surrounding region. The analytical model consists of three different types of elements: rotational, transitional and general. The rotational shell elements are used in the region where the shell is axisymmetrical and linear, while the two‐dimensional general shell elements are deployed in the deviation region where non‐linearities may occur. Transitional shell elements connect the two distinctively different types of elements to achieve displacement field continuities. The solution using the local‐global system with appropriate condensation and a predicted stress incremental procedure is suggested. It is shown that the technique is a very attractive alternative to the entirely general element style analysis for axisymetric shell structures with local deviations.
Coupled discrete‐layer finite elements for laminated piezoelectric platess
Authors: Heyliger Paul , Ramirez Guillermo , Saravanos Dimitris 
Published: August 2005

AbstractFinite element models based on discrete‐layer theories are presented for the coupled‐field analysis of laminated plates containing piezoelectric layers. The three displacements and the electrostatic potential are treated as unknowns in this formulation, which allows for piece‐wise approximations of the variables through the thickness of each layer. Two specific models are demonstrated in which the transverse displacement is either variable or constant, and the in‐plane displacements and potential take piece‐wise linear approximations through the thickness. The models are applied to example problems with applied surface tractions and specified surface potentials. Good agreement is found with exact solutions.
Comparison of explicit and implicit finite element methods in the quasistatic simulation of uniaxial tension
Authors: Hu Xiaoyu , Wagoner Robert H. , Daehn Glenn S. , Ghosh Somnath 
Published: August 2005

AbstractOn the basis of simple one‐dimensional finite element analyses, comparison in simulations of uniaxial tension using explicit dynamic and implicit static tonnulations has been made. Results show that for materials having a Hollomon‐type constitutive law with power‐law strain rate sensitivity, the explicit dynamic method can be employed for the quasistatic simulations of tensile tests only below the critical test velocities or critical normalized material densities. These critical values are determined numerically as a function of material parameters.
Boundary characteristic orthogonal polynomials in numerical approximation
Authors: Singh Bani , Chakraverty S. 
Published: August 2005

AbstractThe paper describes a procedure to generate boundary characteristic orthogonal polynomials (BCOPs) over a domain in Rn. The method is based upon the Gram‐Schmidt process of orthogonalization. The orthogonal polynomial sequence (OPS) is generated from a set of linearly independent functions which satisfy the given boundary conditions. The procedure is illustrated by taking several examples in R2, the most important case from the application point of view. Extensive numerical work has been carried out for simple domains like the circle, square and isosceles right‐angled triangle. The following cases have been considered: (a) when the BCOPs vanish on the boundary; (b) when they and their normal derivatives vanish on the boundary; (c) when no conditions have been imposed on the boundary. The results for other geometries such as an ellipse, a parallelogram and an arbitrary triangle follow by some simple transformations. The procedure is also applicable to one‐dimensional problems and can be easily extended to R3.
Investigation of equilibrium states of viscoelastic circular plates by the deformation map technique
Authors: Drawshi Muhamad , Cederbaum Gabriel 
Published: August 2005

AbstractThe geometrically non‐linear response of a circular plate is investigated by means of a ‘deformation map’. The plate is subjected to static radial forces and bending moments, both uniformly distributed along the supported edges, in addition to a transverse load. The deformation map gives the complete picture for the investigated structure. The classical formulation of large deformation for the above‐mentioned problem goes back to Timoshenko (1940). To create a deformation map, it is necessary to convert the boundary value problem into an initial value problem (Cauchy's problem). The Runge‐Kutta (RK) method can then be used to solve numerically the equilibrium equations for the above‐mentioned circular plate. In the paper several kinds of transverse loading are considered and their influence on the plate response is examined. It is shown that in some cases the plate's behaviour is chaotic‐like (unpredictable), in the sense that various equilibrium states are possible for a certain given set of loads. Yet, it is shown that the viscoelasticity reduces the range of the possible equilibrium states, and thus stabilizes the system.
2D or 3D frictional contact algorithms and applications in a large deformation context
Authors: Feng Zhi‐Qiang 
Published: August 2005

AbstractThe paper is devoted to the analysis of two‐ or three‐dimensional contact problems with Coulomb friction and large deformation. The classical approach is based on two minimum principles or two variational inequalities: the first for unilateral contact and the second for friction. A coupled approach using only one principle or one inequality is presented. This new approach allows us to extend the notion of normality law to dissipative behaviours with a non‐associated flow rule, such as surface friction. Non‐differentiable contact potentials are regularized by means of the augmented Lagrangian method. Using the C++ language, an object‐oriented finite element database is created, which allows us to implement the contact and friction in an existing code in a very simple and neat way. Numerical examples are carried out in many difficult cases such as shock absorber and three‐dimensional contact. The numerical results prove that this approach is robust and efficient concerning numerical stability.
A robust implementation of Zienkiewicz and Zhu's local patch recovery method
Authors: Labbé P. , Garon A 
Published: August 2005

AbstractWhile implementing Zienkiewicz and Zhu's superconvergent patch recovery method in our finite element solver, we came across two difficulties: rank deficiency of the local system to be solved, and ill‐conditioning. The first problem was solved by increasing the number of sampling points and the second by using LU decomposition with partial pivoting.