bluuebunny/crossref_metadata_2025_split huggingface dataset:
An h‐p‐ multigrid method for finite element analysis
Authors: Field David A. , Pressburger Yoram 
Published: August 2005

AbstractThe finite element method generates solutions to partial differential equations by minimizing a strain energy based functional. Strain energy based techniques for adaptive mesh refinements are not always effective, however. The adaptive refinement technique proposed in this paper uses strain energy but also incorporates advantages from the h‐ and p‐ finite element methods, the multigrid method and a Delaunay based mesh generation method. The refinement technique converged rapidly and was numerically efficient when applied to determining stress concentrations around the circular hole of a thick plate under tension.
Work‐increment‐control method for non‐linear analysis
Authors: Chen Hong , Blandford George E. 
Published: August 2005

AbstractTo perform non‐linear structural analysis including large displacements and rotations requires evaluation of the non‐linear equilibrium equations. A quadratically converging, fixed‐point iteration scheme, referred to as the work‐increment‐control solution method, is presented to iteratively evaluate the non‐linear algebraic equations. The work‐increment‐control method is superior, in many respects, to other published solution strategies.
Singularity in structural optimization
Authors: Patnaik S. N. , Guptill J. D. , Berke L. 
Published: August 2005

AbstractSingularity conditions that arise during structural optimization can seriously degrade the performance of the optimizer. The singularities are intrinsic to the formulation of the structural optimization problem and are not associated with the method of analysis. Certain conditions that give rise to singularities in linear elastic structures have been identified in earlier papers, along with a proposition to alleviate the consequences of their presence.1‐3 These singularities were global in nature, encompassing the entire structure. Further examination revealed more complex sets of conditions in which singularities occur. Some of these singularities are local in nature, being associated with only a segment of the structure. Moreover, the likelihood that one of these local singularities may arise during an optimization procedure can be much greater than that of the global singularity identified earlier. This paper provides examples of these additional forms of singularities. It gives a framework in which these singularities can be recognized. In particular, the singularities can be identified by examination of the stress‐displacement relations along with the compatibility conditions and/or the displacement‐stress relations derived in the integrated force method of structural analysis. Methods for the elimination of the effects of these singularities are suggested and numerical illustrations are given.
A natural partitioning scheme for parallel simulation of multibody systems
Authors: Chiou J. C. , Park K. C. , Farhat C. 
Published: August 2005

AbstractA parallel partitioning scheme based on physical‐co‐ordinate variables is presented to systematically eliminate system constraint forces and yield the equations of motion of multibody dynamics systems in terms of their independent co‐ordinates. Key features of the present scheme include an explicit determination of the independent co‐ordinates, a parallel construction of the null space matrix of the constraint Jacobian matrix, an easy incorporation of the previously developed two‐stage staggered solution procedure and a Schur complement based parallel preconditioned conjugate gradient numerical algorithm.
A variational boundary integral equation method for an elastodynamic antiplane crack
Authors: Becache E. 
Published: August 2005

AbstractThis paper investigates the transient wave scattering by a crack by means of the Boundary Integral Equation Method (BIEM). The author has developed a new formulation to solve the BIE for the Crack Opening Displacement (COD). The resolution is done directly in the time domain. The solution is represented by means of a retarded double layer potential, and the resulting BIE, with the COD as unknown, has a hypersingular kernel. The corresponding difficulty is overcome by using a variational method. We present the application of this method to an antiplane crack, describe the approximate problem and finally give some numerical results.
A discrete momentum‐conserving explicit algorithm for rigid body dynamics analysis
Authors: Park K. C. , Chiou J. C. 
Published: August 2005

AbstractA discrete momentum‐conserving, explicit time integration is presented. The accurate feature and simplicity of the present algorithm are realized by a mid‐point implicit formula for integrating the Euler parameters and a second‐order discrete momentum‐conserving form of the central difference algorithm, respectively. The accuracy and robustness of the algorithm is demonstrated by example problems which exhibit large overall rigid motions under holonomic constraints.
An asymptotic‐numerical method to compute the postbuckling behaviour of elastic plates and shells
Authors: Azrar L. , Cochelin B. , Damil N. , Potier‐Ferry M. 
Published: August 2005

AbstractIn this paper, we apply an asymptotic‐numerical method for computing the postbuckling behaviour of plate and shell structures. The bifurcating branch is sought in the form of polynomial expansions, and it is determined by solving numerically (FEM) several linear problems with a single stiffness matrix. A large number of terms of the series can easily be computed by using recurrent formulas. In comparison with a more classical step‐by‐step procedure, the method is rapid and automatic. However, the polynomial expansions have a radius of convergence which limits the validity of the solution to a neighbourhood of the bifurcation point. In the present form, the method should be viewed as a cheap and automatic way of completing a linear buckling analysis. It is illustrated in two examples: a square plate under in‐plane compression and a cylindrical shell under pressure.
Stability analysis of the forward Euler scheme for the convection‐diffusion equation using the SUPG formulation in space
Authors: Codina Ramon 
Published: August 2005

AbstractThe stability and accuracy of the forward Euler scheme for the semidiscrete problem arising from the space discretization of the convection‐diffusion equation using the SUPG formulation are analysed. Both linear and quadratic finite elements are considered. The stability limits are derived for the one‐dimensional problem and a heuristic criterion is proposed for the multidimensional equation. Some numerical experiments are conducted in order to assess the performance of different finite elements.
Experimental and finite element predictions of residual stresses due to orthogonal metal cutting
Authors: Shih Albert J. , Yang Henry T. Y. 
Published: August 2005

AbstractThe development and implementation of a finite element method for the simulation of plane‐strain orthogonal metal cutting processes with continuous chip formation are presented. Experimental procedures for orthogonal metal cutting and measurement of distributions of residual stresses using the X‐ray diffraction method are also presented. A four‐node, eight degree‐of‐freedom, quadrilateral plane‐strain finite element is formulated. The effects of elasticity, viscoplasticity, temperature, friction, strain‐rate and large strain are included in this formulation. Some special techniques for the finite element simulation of metal cutting processes, such as element separation and mesh rezoning, are used to enhance the computational accuracy and efficiency. The orthogonal metal cutting experiment is set‐up on a shaper, and the distributions of residual stresses of the annealed 1020 carbon steel sample are measured using the X‐ray diffraction method. Under nominally the same cutting conditions as the experiment, the cutting processes are also simulated using the finite element method. Comparisons of the experimental and finite element results for the distributions of residual stresses indicate a fairly reasonable level of agreement. The versatility of the present finite element simulation method allows for displaying detailed results and knowledge generated by orthogonal metal cutting processes, such as the distribution of temperature, yield stress, effective stress, plastic strain, plastic strain‐rate, hydrostatic stress, deformed configuration, etc. Such knowledge is useful to provide physical insights into the process as well as to better design the process for machining parts with improved performance.
A general boundary‐integral formulation for zoned three‐dimensional media
Authors: Rezayat Mohsen 
Published: August 2005

AbstractA new boundary‐integral formulation is proposed to analyse the heat transfer in zoned three‐dimensional geometries. The proposed formulation couples the boundary formula, the gradient of the boundary formula and the exterior formula. An advantage of this method over the traditional methods is that any linear condition at the interface between subdomains may be incorporated into the formulation at the outset. In addition, the new method provides a sparse and well‐conditioned matrix of coefficients with a minimum number of equations.
The ‘fractal assumption’ in cracks: Bilateral calculation methods
Authors: Theocaris P. S. , Panagiotopoulos P. D. 
Published: August 2005

AbstractThe paper considers the fractal nature of cracks by assuming the fractal as the fixed point of a given transformation. This concept enables the study of a sequence of classical‐geometry crack problems whose limit gives the solution of the fractal‐geometry crack problem. The method is illustrated by a numerical example. It was shown that the fractal nature of the cracks influences the value of the stress intensity factors.
Frictional contact finite elements based on mixed variational principles
Authors: Cescotto S. , Charlier R. 
Published: August 2005

AbstractThis paper presents an original approach to the numerical modelling of unilateral contact by the finite element method. The main point is the development of mixed contact finite elements in which the displacement field and the contact stress field (pressure and friction shear) are discretized independently. The theory, based on variational principles, is first presented in the framework of infinitesimal deformations and, subsequently, is extended to large inelastic strains.
A multiple‐node method to resolve the difficulties in the boundary integral equation method caused by corners and discontinuous boundary conditions
Authors: Mitra Ambar K. , Ingber Marc S. 
Published: August 2005

AbstractIn the boundary integral equation method (BIEM), use of Lagrangian shape functions together with conforming boundary elements requires continuity of functions at the interelement boundary. When the flux or the traction is discontinuous due to the presence of corners or discontinuous boundary conditions, conforming elements can be a source of error. In this paper, we detail a multiple‐node method in which this error can either be eliminated or substantially reduced. The paper is limited to the Laplace problem and the problem of elastostatics in two dimensions. However, the method can be easily extended to problems of other types and to higher dimensions.
A boundary element formulation for the inverse elastostatics problem (iesp) of flaw detection
Authors: Bezerra Luciano M. , Saigal Sunil 
Published: August 2005

AbstractA boundary integral formulation is presented for the detection of flaws in planar structural members from the displacement measurements given at some boundary locations and the applied loading. Such inverse problems usually start with an initial guess for the flaw location and size and proceed towards the final configuration in a sequence of iterative steps. A finite element formulation will require a remeshing of the object corresponding to the revised flaw configuration in each iteration making the procedure computationally expensive and cumbersome. No such remeshing is required for the boundary element approach. The inverse problem is written as an optimization problem with the objective function being the sum of the squares of the differences between the measured displacements and the computed displacements for the assumed flaw configuration. The geometric condition that the flaw lies within the domain of the object is imposed using the internal penalty function approach in which the objective function is augmented by the constraint using a penalty parameter. A first‐order regularization procedure is also implemented to modify the objective function in order to minimize the numerical fluctuations that may be caused in the numerical procedure due to errors in the experimental measurements for displacements. The flaw configuration is defined in terms of geometric parameters and the sensitivities with respect to these parameters are obtained in the boundary element framework using the implicit differentiation approach. A series of numerical examples involving the detection of circular and elliptical flaws of various sizes and orientations are solved using the present approach. Good predictions of the flaw shape and location are obtained.
A super element model for non‐linear analysis of stiffened box structures
Authors: Jiang J. , Olson M. D. 
Published: August 2005

AbstractA numerical model for non‐linear static and dynamic analysis of stiffened box structures is presented. The model is based on a new super element formulation which provides complete C1 continuity for both plate and beam elements. Geometric and material non‐linearities are included and the temporal equations are solved by the implicit Newmark‐β method with Newton‐Raphson subiteration. The new formulation has been applied to the static, vibration and transient analysis of various structures such as flat plates, folded plates and rectangular boxes. Both isotropic and beam stiffened structures are considered and the results obtained are compared with other available solutions. It is observed that the new super element formulation can provide reasonable solutions to both linear and non‐linear problems of stiffened box structures. The mathematical formulation of the model is presented in this paper, while the numerical verifications are given in the companion paper.1
A three‐dimensional multilayer composite finite element for stress analysis of composite laminates
Authors: Han Jianhua , Hoa S. V. 
Published: August 2005

AbstractA three‐dimensional multilayer composite finite element method has been developed based on a composite variational functional which takes three in‐plane strains εx, εx, εxy and three transverse stresses σz, σyz, σxz as the basic variables. The continuity of the transverse stresses σz, σyz, σxz across the laminate thickness is assured a priori by introducing a partial stress field parameter α which is associated with the lower and upper surfaces of a lamina in a laminate. A method has been developed to form the partial stress field based on the assumed displacement field. With this method, a three dimensional (3‐D) multilayer composite finite element is formulated for stress analysis of composite laminates. A numerical example is given, which shows some advantages of this composite element.
An efficient method for solving the eigenvalue problem for matrices having a skew‐symmetric (or skew‐Hermitian) component of low rank
Authors: Garvey S. D. 
Published: August 2005

AbstractIn the numerical modelling of mechanical systems, eigenvalue problems occur in connection with the evaluation of resonance frequencies, buckling modes and other more esoteric calculations. The matrices whose eigenvalues are sought sometimes have a skew‐symmetric component and the presence of this component adds significantly to the computational effort required. In many cases where there is a skew‐symmetric component, this component has a much lower rank than the symmetric component which generally has rank equal to its dimension. Examples of such cases abound in the area of rotor dynamics where the stiffness and damping matrices associated with journal bearings have significant skew‐symmetric components. The solution of the eigenvalue problem for an unsymmetric matrix takes more than twice the number of operations required for the solution of the eigenvalue problem for a symmetric matrix of the same dimension. This paper puts forward a new method for the solution of the eigenvalue problem for matrices having a skew‐symmetric component of low rank and shows that it is faster than established methods of comparable accuracy for the general unsymmetric NxN matrix if the rank of the skew‐symmetric component is less than N/7.3.
A finite element formulation for rod/continuum interactions: The one‐dimensional slideline
Authors: Maker B. N. , Laursen T. A. 
Published: August 2005

AbstractA finite element formulation is presented for treatment of the mechanical interaction between a rod‐like object and a continuous medium, as occurs, for example, between reinforcing steel and surrounding concrete. An impenetrability constraint restricts the rod's lateral motion relative to the continuum, while an accompanying constraint allows axial slip subject to a release criterion. Satisfaction of these constraints is enforced via application of penalty and augmented Lagrangian regularizations. The proposed implementation is suitable for both static and dynamic implicit equation solving schemes, making it useful for a wide range of problems.
A basic flat facet finite element for the analysis of general shells
Authors: Allman D. J. 
Published: August 2005

AbstractA triangular flat facet finite element for the analysis of general thin shells is presented. It is constructed from simple cubic polynomial displacement fields using a complete set of six degrees of freedom at the element vertices, thereby easily meeting the requirements of standard commercial computer programs. The theoretical development is based on a variational principle which allows a direct formulation of the element stiffness matrix, without inversion, and which permits considerable simplification of the mathematical formulation. The new flat facet element generally produces more accurate numerical results than those obtained in earlier related work. It also offers a possible basis for constructing an improved curved approximation to a shell surface and for further developments in connection with applications involving geometric non‐linearity.
Tangent operators, sensitivity expressions, and optimal design of non‐linear elastica in contact with applications to beams
Authors: Spivey C. O. , Tortorelli D. A. 
Published: August 2005

AbstractThe tangent operator and design sensitivity expressions for non‐linear elastica subject to frictionless unilateral contact are derived and computed via the finite element method. The sensitivity computations are then combined with a numerical programming package to create an optimal design environment. To exemplify the optimal design environment, a beam's contact surface is contoured to minimize bending stress. This work combines the research on the sensitivity analysis of non‐linear elastic bodies subject to constraints, finite strain non‐linear elastic beam analysis and contact analyses. The analysis is valid for any smooth contact surface; and specialized for the case in which the surface is represented by a cubic spline. The direct differentiation method is utilized to perform the sensitivity analysis. In an example problem, the sensitivity analysis is verified by finite difference computations and then combined with a numerical optimization program to design the stop profile of a valve.
A consistent finite element formulation for non‐linear dynamic analysis of planar beam
Authors: Hsiao Kuo Mo , Yang Rong Tser , Lee An Chen 
Published: August 2005

AbstractA co‐rotational finite element formulation for the dynamic analysis of planar Euler beam is presented. Both the internal nodal forces due to deformation and the inertia nodal forces are systematically derived by consistent linearization of the fully geometrically non‐linear beam theory using the d'Alembert principle and the virtual work principle. Due to the consideration of the exact kinematics of Euler beam, some velocity coupling terms are obtained in the inertia nodal forces. An incremental‐iterative method based on the Newmark direct integration method and the Newton–Raphson method is employed here for the solution of the non‐linear dynamic equilibrium equations. Numerical examples are presented to investigate the effect of the velocity coupling terms on the dynamic response of the beam structures.
The position code algorithm for contact searching
Authors: Oldenburg Mats , Nilsson Larsgunnar 
Published: August 2005

AbstractA new global search method for general contact systems is developed and implemented in the DYNA3D program, along with a recent contact interface algorithm. The concept of ‘position codes’ for efficient global contact searching is presented. With the position code algorithm, the problem of sorting and searching in three dimensions is transformed to a process of sorting and searching within a one‐dimensional array. The cost of contact searching is of the order of N log2 N, where N is the number of nodes in the system. The proposed algorithms are uncomplicated and the implementation into any finite element code is straightforward. Numerical experiments are presented in order to examine the behaviour of the algorithms in different aspects.
Stability of collapsed 8‐node 2‐D and 20‐node 3‐D isoparametric finite elements
Authors: Dhondt Guido 
Published: August 2005

AbstractThe collapse of ordinary finite elements to generate the desired strain singularity at the crack tip for fracture mechanics applications can lead to unwanted additional singularities in that area. Although neither the quarter‐point nor the half‐point 8‐node two‐dimensional (2‐D) and 20‐node three‐dimensional (3‐D) elements exhibit this behaviour, the present article proves that arbitrarily small deviations from the quarter‐point element can be constructed which do have additional singularities. Since the general behaviour of the half‐point element is not affected by small modifications, this element is better suited to match complex body geometries.
Superconvergent patch recovery with equilibrium and conjoint interpolant enhancements
Authors: Blacker Ted , Belytschko Ted 
Published: August 2005

AbstractThe superconvergent patch derivative recovery method of Zienkiewicz and Zhu is enhanced by adding the squares of the residuals of the equilibrium equation and natural boundary conditions. In addition, a new conjoint polynomial for interpolating the local patch stresses over the element which significantly improves the local projection scheme is presented. Results show that in the 4‐node quadrilateral, the equilibrium and boundary condition residuals usually improve accuracy but not the rate of convergence, whereas in the 9‐node quadrilateral, results are mixed. The conjoint polynomial always improves the accuracy of the derivative field within the element as compared to the standard nodal interpolation, particularly in 4‐node quadrilaterals.