bluuebunny/crossref_metadata_2025_split huggingface dataset:
Accuracy of a class of concurrent algorithms for transient finite element analysis
Authors: Ortiz Michael , Nour‐Omid Bahram , Sotelino Elisa D. 
Published: November 2005

AbstractThe accuracy of a new class of concurrent, procedures for transient finite element analysis is examined. A phase error analysis is carried out which shows that wave retardation leading to unacceptable loss of accuracy may occur if a Courant condition based on the dimensions of the subdomains is violated. Numerical tests suggest that this Courant condition is conservative for typical structural applications and may lead to a marked increase in accuracy as the number of subdomains is increased. Theoretical speed‐up ratios are derived which suggest that the algorithms under consideration can be expected to exhibit a performance superior to that of globally implicit methods when implemented on parallel machines.
Sensitivity analysis and shape optimization of axisymmetric structures
Authors: Cheu Tsu‐Chien 
Published: November 2005

AbstractAn efficient method is developed for sensitivity analysis in shape optimization of axisymmetric structures. The technique of isoparametric mapping is used to generate the finite element mesh from a small set of master elements and master nodes. Co‐ordinates of selected master nodes are used as design variables. Shape function values of master elements at derived finite element nodes obtained during the isoparametric mapping process are utilized to calculate the gradients of weight and response of the structures with respect to the design variables. Analytic formulations of the gradients are developed for sensitivity analysis of axisymmetric structures. An optimization procedure using a sequential linear programming method is applied to effectively utilize the calculated gradients. Numerical examples of optimum design of disks subject to thermo‐mechanical loadings are presented.
Frictionless geometrically non‐linear contact using quadratic programming
Authors: Johnson A. R. , Quigley C. J. 
Published: November 2005

AbstractThe successive quadratic programming (SQP) method is used with the finite element method (FEM) to solve frictionless geometrically non‐linear contact problems involving large deformations of the elastica in the presence of flat rigid walls. To formulate the SQP problems, the potential energy (PE) is expanded in a Taylor series of second order in displacement increments about a configuration near a contact solution. The SQP problems consist of minimizing the Taylor expansion of the PE subject to the inequality constraints which represent contact. The quadratic programming (QP) method is made part of a Newton–Raphson (NR) search in which the QP corrections are made when a NR step does not satisfy the constraints. A revised simplex method developed by Rusin is used to solve the QP problems. The elastica is modelled with a total Lagrangian FEM developed by Fried. Solutions are obtained for the end loaded buckled elastica in point contact with a rigid wall and for a uniformly loaded elastica in regional contact with a rigid wall. The problems are also solved using a penalty method. The results obtained for the point contact problem are compared to an analytical solution. Calculations were made to obtain numerical information on maximum load step size and the number of inverse operations required for each load step. Cases in which the elastica stiffened substantially as a result of the initiation of contact are also discussed.
The FDM in arbitrary curvilinear co‐ordinates—formulation, numerical approach and applications
Authors: Tworzydlo Wlodzimierz W. 
Published: November 2005

AbstractThe basic concept, formulation and numerical application of a fully automatic version of the finite difference method (FDM) on a two‐dimensional manifold embedded in three‐dimensional Euclidean space are presented. This version of the FDM was developed in order to enable automatic solution of problems formulated in arbitrary curvilinear co‐ordinate systems in terms of covariant derivatives (e.g. shell equations).In the classical version of the FDM all operations in the curvilinear co‐ordinates (the derivation of base vectors, curvature tensors and so on) have to be performed manually. The goal of the present work was to transfer this job to a computer, in order to minimize the user's effort during the numerical formulation of the physical problem. The relevant version of the fully automatized program FIDAMF, based on the FDM on arbitrary irregular grids,1,2 has been worked out. This code performs automatically all stages of the numerical analysis, starting from the mesh generation and approximation of the shape of the manifold, through computation of necessary objects on this manifold, to the solution of linear or non‐linear problems formulated in terms of covariant derivatives.The method has been extended to the analysis of problems in which the co‐ordinate system changes during the computation (e.g. the analysis of large deformations in the convectional description). This version of the curvilinear FDM was applied to the analysis of large deformations of hyperelastic membrane shells.The approach and the numerical routines, although used here with the FDM, can be combined with any other approximation method, in particular the finite element method.
Approximate direct‐search minimax circuit optimization
Authors: Sussman‐Fort Stephen E. 
Published: November 2005

AbstractA direct‐search optimization strategy, involving pattern‐searches, pattern‐moves and a simplex algorithm, has been applied to a number of frequency‐domain circuit problems. We show that an approximate minimax result can be obtained with our simple approach, which includes using a modified minimax error function. In the examples attempted, the method comes quite close to the accuracy, if not the efficiency, of true minimax optimizers, and yields an accuracy as good as or better than a least‐pth (p = 10) gradient optimizer. The method is broadly appropriate wherever it is difficult or inconvenient to calculate the gradients required for conventional minimax optimization.
Application of differential quadrature to static analysis of structural components
Authors: Jang Sung K. , Bert Charles W. , Striz Alfred G. 
Published: November 2005

AbstractThe numerical technique of differential quadrature for the solution of linear and non‐linear partial differential equations, first introduced by Bellman and his associates, is applied to the equations governing the deflection and buckling behaviour of one‐ and two‐dimensional structural components. Separate transformations are used for higher‐order derivatives, as suggested by Mingle, thus extending the method to treat fourth‐order equations and to include multiple, boundary conditions in the respective co‐ordinate directions. Results are obtained for various boundary and loading conditions and are compared with existing exact and numerical solutions by other methods. The application of differential quadrature to this class of problems is seen to lead to accurate results with relatively small computational effort.
An optimality criterion method for dynamic optimization of structures
Authors: Sadek Edward A. 
Published: November 2005

AbstractThis paper presents an optimality criterion method for the determination of the least weight design of a structural system which satisfies a specific frequency requirement plus upper and lower bounds on the design variables. The design algorithm is an iterative solution of the Kuhn–Tucker optimality criterion based on choosing a single value of the Lagrange multiplier which minimizes the sum of the squares of residuals.The method has been applied to a variety of structures. Results assert that the method is capable of locating the optimal design in a small number of redesign cycles. The method avoids the scaling of design variables. It can treat non‐structural masses and is applicable to. structural elements with a wide variety of size‐stiffness. The procedure has been completely automated in a computer program on an IBM‐PC microcomputer.
Efficient optimization of integrated aerodynamic–structural design
Authors: Haftka R. T. , Grossman B. , Eppard W. M. , Kao P. J. , Polen D. M. 
Published: November 2005

AbstractThe introduction of composite materials is having a profound effect on the design process. Because these materials permit the designer to tailor material properties to improve structural, aerodynamic and acoustic performance, they require a more integrated multidisciplinary design process. Because of the complexity of the design process numerical optimization methods are required.The present paper is focused on a major difficulty associated with the multidisciplinary design optimization process—its enormous computational cost. We consider two approaches for reducing this computational burden: (i)development of efficient methods for cross‐sensitivity calculation using perturbation methods; and (ii) the use of approximate numerical optimization procedures. Our efforts are concentrated upon combined aerodynamic‐structural optimization. Results are presented for the integrated design of a sailplane wing. The impact of our computational procedures on the computational costs of integrated designs is discussed.
Iterated θ‐method for hyperbolic equations
Authors: van der Houwen P. J. , Sommeijer B. P. 
Published: November 2005

AbstractThe iterated θ‐methods employing residue smoothing for finding both steady state and time‐accurate solutions of semidiscrete hyperbolic differential equations are analysed. By the technique of residue smoothing the stability condition is considerably relaxed, so that larger time steps are allowed which improves the efficiency of the method. The additional computational effort involved by the explicit smoothing technique used here is rather low when compared with its stabilizing effect. However, in the case where time‐accurate solutions are desired, the overall accuracy may be decreased. This paper investigates the effect of residue smoothing on both the stability and accuracy, and presents a number of explicitly given methods based on the iterated implicit midpoint rule (θ = 1/2). Numerical examples confirm the theoretical results.
A finite element spectral method with application to the thermoelastic analysis of space structures
Authors: Rand Omri , Givoli Dan 
Published: November 2005

AbstractA combined spectral finite element method is devised for use in finding the thermal and thermoelastic dynamic response of truss structures to time‐periodic loading. The thermal problem is strongly non‐linear due to the presence of heat radiation. The problems considered are typical in the analysis of space structures. In the method proposed, the spatial domain is first discretized using a consistent finite element formulation. Then the resulting semi‐discrete equations in time are solved analytically by using a spectral method that is symbolically coded. Some numerical examples are presented which demonstrate the performance of the method and its ability to identify some key characteristics in space structure problems.
A Petrov–Galerkin/modified operator formulation for convection–diffusion problems
Authors: de Sampaio P. A. B. 
Published: November 2005

AbstractA new Petrov–Galerkin method to deal with convection–diffusion problems is presented. The formulation is derived from the concept of using a modifying function to make the differential operator self‐adjoint. The so‐called ‘optimal upwind’ parameter (α) arises naturally from the process of approximating the modifying function. Transient and steady‐state examples on uniform and non‐uniform meshes are shown.
Thermo‐mechanical finite element model of casting systems
Authors: Song R. , Dhatt G. , Cheikh A. Ben 
Published: November 2005

AbstractA coupled finite element model is developed to simulate the metal casting process. We present a new method for capturing the solidification zone and obtaining the corresponding rate of phase change. The latent energy release is predicted by the heat conduction rate and introduced by following the enthalpy‐temperature curve. The influence of mould‐metal contact is considered in calculating the heat flux through the mould‐metal interface. A viscoplastic model is employed to predict the gap opening and evolution of plastification.Four examples are presented to demonstrate certain numerical aspects and the capability of the model for industrial applications.
The numerical simulation of heat conduction in irregularly‐shaped materials of thermally‐dependent properties
Authors: Schreiber W. C. 
Published: November 2005

AbstractThe numerical simulation of conduction heat transfer in arbitrarily‐shaped regions is relevant to many engineering applications including the casting of plastics and metals, cold region problems and latent heat storage. This class of problem offers its particular challenges. The accurate computational simulation of conduction with thermally‐dependent properties requires a solution technique with good conservation properties. The boundary‐fitted co‐ordinates of an arbitrary solution domain typically yield grids which are non‐orthogonal and which, consequently, make energy conservation difficult to model.In the current article, a technique is described to simulate accurately the conduction heat transfer in materials of thermally‐dependent properties in irregular domains. The method combines boundary‐fitted co‐ordinates with the finite volume method, FVM, to produce a numerical technique which will accurately solve this non‐linear conduction problem using a grid which may be highly skewed. This capability is achieved through a unique treatment of the cross‐derivative terms that arise when the heat conduction equation is transformed to a non‐orthogonal grid. The cross‐derivative terms represent the non‐normal components of the heat fluxes into the skewed control volume. The tangent components of the heat fluxes are interpreted in a special way to produce finite difference expressions which accurately model the cross‐derivative partial.The numerical procedure is validated by comparing it against a purely analytical mathematical method. Although the numerical results have been obtained using a highly skewed grid, they exhibit close agreement with the analytically‐derived solution.
A conservative algorithm for multidimensional conduction phase change
Authors: Comini G. , Giudice S. Del , Saro O. 
Published: November 2005

AbstractIn this paper, a generally applicable version of an algorithm, for multidimensional phase change conduction, is presented which bridges the gap between ‘full enthalpy’ and ‘equivalent heat capacity’ methods. In the text the problem is formulated first with reference to the three‐time‐level method for the FE analysis of non‐linear heat conduction. Then the suggested algorithm is utilized as a ‘corrector’ which can be activated for the analysis of isothermal phase change problems. In the corrector step the enthalpy balance is recovered from the standard formulation, and temperatures are post‐calculated by means of the inverse temperature vs. enthalpy function. The algorithm is verified in one‐dimensional situations by comparing the results obtained with available analytical and numerical solutions for boundary conditions of the first kind (temperature) and of the third kind (convection). Finally, as a 2‐D test problem, a solution is presented for inward solidification in a cylinder, using Cartesian co‐ordinates to demonstrate robustness with respect to space deformation of the mesh.
Computer simulation of salami drying
Authors: Imre L. , Környey T. 
Published: November 2005

AbstractSalami sorts are made of special meat pastes filled in hygroscopic casing and preserved by drying.The characteristic features and the time of drying are greatly affected by the operational conditions. Factories are interested in reducing the time of the drying treatment. To determine a reliable and economic drying schedule a physical‐mathematical model has been elaborated and used. The system of equations has been solved numerically by using the FDM technique for the determination of the temperature, concentration and stress fields as a function of the time. Computed results have been verified by experiments.By the numerical analysis it has been proved that the maximum rate of drying to be permitted is limited by the danger of possible deformations and inner fissures caused by tensile stresses occurring if shrinkage is prevented.On the basis of the proper drying schedule an algorithm and a strategy of the microprocessing operational control has been elaborated.
Recent advances, trends and new perspectives via enthalpy‐based finite element formulations for applications to solidification problems
Authors: Tamma Kumar K. , Namburu Raju R. 
Published: November 2005

AbstractThe present paper describes recent advances and trends in finite element developments and applications for solidification problems. In particular, in comparison to traditional methods of approach, new enthalpy‐based architectures based on a generalized trapezoidal family of representations are presented which provide different perspectives, physical interpretation and solution architectures for effective numerical simulation of phase change processes encountered in solidification problems. Various numerical test models are presented and the results support the proposition for employing such formulations for general phase change applications.
Approximate predictions of ice accretion along conductors of finite torsional stiffness and control of rotation using counterweights
Authors: Skelton P. L. I. , Poots G. 
Published: November 2005

AbstractA mathematical/computational model for the approximate prediction of ice accretion on a conductor of finite torsional stiffness is constructed. The model, which is adapted to allow for the attachment of counterweights along the span, is three‐dimensional and time‐dependent. In the absence of counterweights, axial growth is predicted near the anchors, and cylindrical‐sleeve growth at the centre of the conductor span. The latter is caused by eccentric ice loading on the windward side of the conductor which then induces the conductor to rotate.The ‘icing‐clock’ model, based on the use of the large relaxation time approximation for particle impaction, yields an upper bound to the mass of ice accreted. At the end of each deposit time the torque density along the conductor span due to ice loading is calculated. On solving the non‐linear torsion equation for the conductor the rotation of the conductor and location of the evolving ice surface as a function of the distance from the tower and the accretion time are then deduced.Numerical results are given for conductor with varying mechanical properties, which are represented in terms of a single dimensionless torque parameter, with and without the attachment of counterweights. For a specific case illustrative results are given for the mass of ice accreted and conductor rotation when one, two, three and four counterweights are attached per span.
Computational enhancement of an unsymmetric block Lanczos algorithm
Authors: Kim Hyoung M. , Craig Roy R. 
Published: November 2005

AbstractAn unsymmetric block Lanczos algorithm has been employed for the dynamic analysis of a large system which has arbitrary damping and/or repeated (or closely spaced) eigenvalues. In the algorithm development, the right and left Lanczos vectors are all theoretically biorthogonal to each other. However, these vectors may lose the biorthogonality owing to cancellation and roundoff errors. For the unsymmetric case there can be a breakdown, even without numerical errors. This paper describes computational techniques which have led to a robust unsymmetric block Lanczos algorithm.
New hybrid Laplace transform/finite element method for three‐dimensional transient heat conduction problem
Authors: Chen Cha'o‐Kuang , Chen Tzer‐Ming 
Published: November 2005

AbstractThe paper presents results obtained by the implementation of a new hybrid Laplace transform/finite element method developed by the authors. The present method removes the time derivatives from the governing differential equation using the Laplace transform and then solves the associated equation with the finite element method. Previously reported hybrid Laplace transform/finite element methods1 have been confined to one nodal solution at a time. When applied to many nodes it takes an excessive amount of computer time. By using a similarity transform method on the matrix of the complex number coefficients this restriction is removed and the reported new method provides a more useful tool for the solution of linear transient problems. Test examples are used to show that the basic accuracy is comparable to that obtainable by analytical, finite difference and finite element methods.
Lagrange constraints for transient finite element surface contact
Authors: Carpenter Nicholas J. , Taylor Robert L. , Katona Michael G. 
Published: November 2005

AbstractA new approach to enforce surface contact conditions in transient non‐linear finite element problems is developed in this paper. The method is based on the Lagrange multiplier concept and is compatible with explicit time integration operators. Compatibility with explicit operators is established by referencing Lagrange multipliers one time increment ahead of associated surface contact displacement constraints. However, the method is not purely explicit because a coupled system of equations must be solved to obtain the Lagrange multipliers. An important development herein is the formulation of a highly efficient method to solve the Lagrange multiplier equations. The equation solving strategy is a modified Gauss‐Seidel method in which non‐linear surface contact force conditions are enforced during iteration. The new surface contact method presented has two significant advantages over the widely accepted penalty function method: surface contact conditions are satisfied more precisely, and the method does not adversely affect the numerical stability of explicit integration. Transient finite element analysis results are presented for problems involving impact and sliding with friction. A brief review of the classical Lagrange multiplier method with implicit integration is also included.
An efficient hybrid quadrilateral Kirchhoff plate bending element
Authors: Sze K. Y. , Chow C. L. 
Published: November 2005

AbstractThis paper discusses the formulation of a hybrid stress quadrilateral Kirchhoff plate bending element based on an extended complementary energy functional first proposed by Tong. With the inclusion of a Lagrange multiplier in the functional to enforce a constraint on the assumed moment space, the construction of the C1 deflection profile inside the element is no longer necessary. The continuity requirement on the deflection across the element interfaces is fulfilled by interpolating the generalized nodal displacements over the element boundary in the usual way. Special attention is paid to the selection of assumed moment space such that the element stability, convergency, invariance and nodal point numbering insensitivity are secured while the implementational cost of the element is kept low. Quadratic serendipity interpolation of the transverse deflection is adopted to discretize the distributed transverse loading. Numerical examples are presented and the accuracy achieved is found to be satisfactory.