bluuebunny/crossref_metadata_2025_split huggingface dataset:
Time finite element methods for structural dynamics
Authors: Hulbert Gregory M. 
Published: August 2005

AbstractTime finite element methods are developed for the equations of structural dynamics. The approach employs the time‐discontinuous Galerkin method and incorporates stabilizing terms having least‐squares form. These enable a general convergence theorem to be proved in a norm stronger than the energy norm. Results are presented from finite difference analyses of the time‐discontinuous Galerkin and least‐squares methods with various temporal interpolations and commonly used finite difference methods for structural dynamics. These results show that, for particular interpolations, the time finite element method exhibits improved accuracy and stability.
Static and vibration analysis of laminated composite beams with an interlaminar shear stress continuity theory
Authors: Lee Chun‐Ying , Liu Dahsin , Lu Xianqiang 
Published: August 2005

AbstractA finite element method for stress and vibration analysis of laminated composite beams was investigated. The analysis was based on a multilayered theory presented by Lu and Liu. This theory accounts for the continuity of interlaminar shear stress. The principle of minimum potential energy was used in the finite element formulation. The interlaminar shear stress was obtained directly from the constitutive equations. It was verified that the present technique was able to give excellent results for displacements, stresses and vibration frequencies for both thin and thick composite beams. The effects of the number of layers and the number of elements on the convergence were also discussed.
Plane strain finite element simulation of shear band formation during metal forming
Authors: Heinstein Martin W , Yang Henry T. Y. 
Published: August 2005

AbstractA plane strain finite element formulation and solution procedure for shear band failure during the plane strain metal forming process are developed and presented. The large strain elastic‐plastic formulation includes a 5‐node 10‐degree‐of‐freedom (d.o.f.) ‘crossed‐triangle’ element, a 4‐node 8‐d.o.f. element with selective reduced integration, an 8‐node 16‐d.o.f. element and a 4‐node 8‐d.o.f. element with an embedded shear band. The formulation includes an elastic‐plastic material model with a modified Gurson yield function and combined isotropic‐kinematic hardening. The solution procedure is based on a Newton–Raphson incremental‐iterative method with an orthogonal projection of zero or negative eigen‐modes when required. Two different examples of plane strain tension test are studied with results compared with available numerical solutions to evaluate the present formulation and solution procedure of the four different elements. The results demonstrate that both types of the 4‐node quadrilaterals are comparable to the 5‐node crossed‐triangle element as well as the 8‐jiode element. To further validate and to demonstrate the predictive capability and practical applicability of the present development, two plane strain metal forming examples are investigated. The first application is a numerical simulation of a sheet‐stretching test with results compared with experimental data for a commercially pure aluminium–magnesium 5182‐O sheet. The load vs. extension history and the through‐thickness strain are compared. The good agreement suggests that it is possible to numerically determine the parameters needed for the modified Gurson yield function. The second application is a numerical simulation of the formation of dead metal zones in the extrusion process. A plane strain extrusion of a short aluminium billet through straight‐sided dies is presented and characteristic features of the formation of dead metal zone are observed.
On the multi‐grid technique for solving three‐dimensional boundary value engineering problems
Authors: Bulgakov V. E. , Belyi M. V. 
Published: August 2005

AbstractThe paper proposes an iterative technique with a similar multi‐grid operator for solving complex spatial bounctary value problems. The description of the method and efficient vectorial algorithms based on a simple ctata structure applicable to solving three‐dimensional engineering problems are presented. The discussion of the method's convergence includes theoretical grounds and practical aspects. We give a general proof of convergence and consider the model cases to estimate the rate of convergence. We also address the histories of convergence derived from the numerical tests and consider two examples of practical problems.
Assessment of discretized errors and adaptive refinement with quadrilateral finite elements
Authors: Liu Y. C. , Elmaraghy H. A. 
Published: August 2005

AbstractThis paper studies discretized errors, and their estimation in conjunction with quadrilateral finite element meshes which are generated by the intelligent mesh generator XFORMQ.1 The exact energy error is used to evaluate the distortion effect of the quadrilateral mesh. The Zienkiewicz–Zhu2 error estimate and actaptive procedure are applied to the short cantilever and the square plate problems using the quadrilateral mesh generator XFORMQ. It is shown that the multistage quadrilateral element refinement produces results superior to the triangular element refinement in the test cases.
On the coupled thermomechanical treatment of necking problems via finite element methods
Authors: Wriggers P. , Miehe C. , Kleiber M. , Simo J. C. 
Published: August 2005

AbstractThe necking process of a bar in an uniaxial tension test is influenced by the heat production due to inelastic deformations. Thus, for an analysis of this problem the thermomechanical coupling has to be considered. A finite element model and an associated algorithm are developed for this purpose. This computational tool allows the study of adiabatic processes as well as processes with heat flux. The analysis of the necking process of a perfectly cylindrical specimen shows that, in contrast to isothermal and adiabatic cases, no bifurcation occurs in the case where heat flux is considered.
A three‐dimensional BEM solution for plasticity using regression interpolation within the plastic field
Authors: Gupta Anil , Delgado Hugo E. , Sullivan John M. 
Published: August 2005

AbstractThis paper presents an improved solution of three‐dimensional plasticity problems using the boundary element method (BEM). The BEM formulation for plasticity requires volume as well as boundary discretizations. An initial stress formulation is used to satisfy the material non‐linearity. Conventionally, the plastic field in the volume element (or cell) is interpolated based on the value of plastic stress at the nodes of the cell. In this paper, the distribution of the plastic field in the cell is based on a number of points interior to the cell. The plastic field is described using regression interpolation polynomials through these interior points. The constitutive relation is satisfied at each interior point. The number of points can be varied in each cell, thus allowing for adaptive volume cells. The plastic stresses are computed at the interior points only, therefore, the need for surface stress computation (which uses numerical derivatives at the surface) is completely eliminated. Three‐dimensional applications are used to compare the present regression interpolation procedure with the conventional method for elasto‐plasticity problems. In all variations of the applications studied regression interpolation based on interior points provided superior results to those determined via the conventional nodal interpolation method.
An inverse method for determining elastic material properties and a material interface
Authors: Schnur D. S. , Zabaras Nicholas 
Published: August 2005

AbstractA numerical procedure which integrates optimization, finite element analysis and automatic finite element mesh generation is developed for solving a two‐dimensional inverse/parameter estimation problem in solid mechanics. The problem consists of determining the location and size of a circular inclusion in a finite matrix and the elastic material properties of the inclusion and the matrix. Traction and displacement boundary conditions sufficient for solving a direct problem are applied to the boundary of the domain. In addition, displacements are measured at discrete points on the part of the boundary where the tractions are prescribed. The inverse problem is solved using a modified Levenberg‐Marquardt method to match the measured displacements to a finite element model solution which depends on the unknown parameters. Numerical experiments are presented to show how different factors in the problem and the solution procedure influence the accuracy of the estimated parameters.
Adaptive solution strategy for solving large systems of p‐type finite element equations
Authors: Morris R. B. , Tsuji Y. , Carnevali P. 
Published: August 2005

AbstractA solution strategy is proposed and implemented for taking advantage of the hierarchical structure of linear equation sets arising from the p‐type finite element method using a hierarchical basis function set. The algorithm dynamically branches to either direct or iterative solution methods. In. the iterative solution branch, the substructure of the finite element equation set is used to generate a lower order preconditioner for a preconditioned conjugate gradient (PCG) method. The convergence rate of the PCG algorithm is monitored to improve the heuristics used in the choice of the preconditioner. The robustness and efficiency of the method are demonstrated on a variety of three dimensional examples utilizing both hexahedral and tetrahedral mesh discretizations. This strategy has been implemented in a p‐version finite element code which has been used in an industrial environment for over two years to solve mechanical design problems.
Axisymmetric thermoelastic shape sensitivity analysis and its application to turbine disc design
Authors: Lee Boo Youn , Kwak Byung Man 
Published: August 2005

AbstractA general method for shape design sensiti vityi analysis (SDSA) as applied to an axisymmetric thermoelasticity problem is presented using the material derivative concept and the adjoint variable method. The sensitivity of a general functional composed of thermal and mechanical quantities is considered. The method for deriving the sensitivity formula is based on standard direct thermal and elastic boundary integral equation formulation. It is then applied to obtain explicit formulas for a representative displacement and stress constraint imposed on a sector of the boundary. Results of numerical implementation are presented for weight minimization of a turbine disc under thermomechanical loading. The sensitivities of the displacement and stress constraint calculated by the formulas are compared with those by finite differences. Optimum shape obtained under the thermomechanical loading is discussed with that under the mechanical loading only, clearly showing the practical importance of the SDSA of thermoelastic systems.
Postbuckling analysis of layered composites using p‐ version finite strips
Authors: Kasagi Akihito , Sridharan Srinivasan 
Published: August 2005

AbstractThis paper presents the results of a study on the buckling and postbuckling analyses of layered shear‐deformable composite plates using p‐version finite strips. The plates are considered to be sufficiently long so that the effect of boundary conditions along the shorter edges is of little significance; this makes it possible to use the ‘exact’ trigonometric functions in the longitudinal direction. The displacement field in the transverse direction is discretized by p‐version finite strips and convergence is studied by p‐extension, i.e. keeping the number of strips relatively small whilst increasing the polynomial order till convergence of the buckling load or the postbuckling stiffness is achieved.Detailed convergence studies are presented and comparison with results of earlier investigations are shown wherever appropriate. The results demonstrate the superior convergence characteristics of the p‐version approach.
Least squares element method for boundary eigenvalue problems
Authors: Rothe Kai 
Published: August 2005

AbstractLinear and non‐linear boundary eigenvalue problems are discretized by a new finite element like method. The reason for the new construction principle is the non‐linear dependence of the dynamic stiffness element matrix on an eigenparameter. The dynamic stiffness element matrix is evaluated for a fixed number of parameters and is then elementwise replaced by a polynomial in the eigenparameter by solving least squares problems. A fast solver is introduced for the resulting non‐linear matrix eigenvalue problem. It consists of a combination of bisection method and inverse iteration. The superiority of the newconstructionprinciple in comparison with the finite or dynamic element method is demonstrated finally for some numerical examples.
A structural mapping technique for geometric parametrization in the optimization of magnetic devices
Authors: Weeber Konrad , Ratnajeevan S. , Hoole H. 
Published: August 2005

AbstractThe continuity and differentiability of object functions is a basic prerequisite for the application of gradient methods in optimization. However, for parameters defining the shape of an electromagnetic device, the finite element discretization in the field analysis introduces discontinuities into the object function which slow down the convergence rate. Additionally, depending on the geometric parametrizaiion employed, the optimization frequently yields shape contours that are impracticable for manufacturing purposes. This paper investigates the problems inherent in geometric parametrization and shows that the discontinuities in the object function are caused by changes in mesh topology as the geometric parameters vary; these changes inevitably follow from the use of free meshing algorithms. As a solution to these shortcomings a structural mapping technique is outlined that maps surface displacements onto the parameters of the finite element mesh and obtains the parameter dependent geometric variations without a change in mesh topology. This resulting geometric parametrization yields continuous object functions without artificial local minima and results in smooth surface contours of the optimized device. Using this new parametrization technique, design sensitivity analysis, is shown to be a reliable and essential part in the efficient application of gradient methods for shape optimization.
An application of preconditioned conjugate gradients to relative placement in chip design
Authors: Kredler Christian , Zillober Christian , Johannes Frank , Sigl Georg 
Published: August 2005

AbstractIn distance geometry problems and many other applications, we are faced with the optimization of high‐dimensional quadratic functions subject to linear equality constraints. A new approach is presented that projects the constraints, preserving sparsity properties of the original quadratic form such that well‐known preconditioning techniques for the conjugate gradient method remain applicable. Very‐large‐scale cell placement problems in chip design have been solved successfully with diagonal and incomplete Cholesky preconditioning. Numerical results produced by a FORTRAN 77 program illustrate the good behaviour of the algorithm.
Interpolation of curved shell geometries by low order finite elements—errors and modifications
Authors: Gebhardt H. , Schweizerhof Karl 
Published: August 2005

AbstractLow order finite elements are of vital interest for practical applications in linear and non‐linear structural analysis. The possible discretization errors, when Reissner‐Mindlin shell elements with bilinear shape functions are used, and modifications to prevent these errors are presented. On some numerical examples the influence of these errors and of various modifications on the results is shown. Finally, the case of membrane locking with low order Reissner‐Mindlin elements for particular assumptions concerning the base vectors and methods to prevent this locking are discussed.
Elastic postbuckling analysis via finite element and perturbation techniques part II: Application to shells of revolution
Authors: Flores Fernando G. , Godoy Luis A. 
Published: August 2005

AbstractThe general theory developed in Part 1 of this paper for the finite element stability analysis of structural systems, using perturbation expansions in the vicinity of a critical point, is applied here to the analysis of shells of revolution. The discretization of the shell is performed by means of a semianalytical approximation, and the matrices required for the evaluation of critical points and postcritical equilibrium paths are obtained. Two cases are presented: bifurcation in axisymmetric and in asymmetric buckling modes. The derivatives required for an imperfection analysis are also obtained. A technique of switching between two paths using continuation methods is also discussed, in which the switch is performed using derivatives of the perturbation expansion. Results are presented for bifurcation in axisymmetric and in non‐axisymmetric modes, and compared with known solutions or with results from changing the path using continuation methods; good correlation is shown. For structures displaying unstable bifurcation, the influence of load and geometric imperfections is evaluated.
The effect of ordering on preconditioned GMRES algorithm, for solving the compressible Navier‐Stokes equations
Authors: Dutto Laura C. 
Published: August 2005

AbstractWe investigate the effect of the ordering of the blocks of unknowns on the rate of convergence of a preconditioned non‐linear GMRES algorithm, for solving the Navier‐Stokes equations for compressible flows, using finite element methods on unstructured grids. The GMRES algorithm is preconditioned by an incomplete LDU block factorization of the Jacobian matrix associated with the non‐linear problem to solve. We examine a wide range of ordering methods including minimum degree, (reverse) Cuthill‐McKee and snake, and consider preconditionings without fill‐in. We show empirically that there can be a significant difference in the number of iterations required by the preconditioned non‐linear GMRES method and suggest a criterion for choosing a good ordering algorithm, according to the problem to solve.We also consider the effect of orderings when an incomplete factorization which allows some fill‐in is performed. We consider the effect of automatically controlling the sparsity of the incomplete factorization through the level of fill‐in.Finally, following the principal ideas of non‐linear GMRES algorithm, we suggest other inexact Newton methods.
An algorithm for adaptive refinement of triangular element meshes
Authors: Nambiar R. V. , Valera R. S. , Lawrence K. L. , Morgan Robert B. , Amil David 
Published: August 2005

AbstractA simple algorithm is developed for adaptive and automatic h refinement of two‐dimensional triangular finite element meshes. The algorithm is based on an element refinement ratio that can be calculated from an a posteriori error indicator. The element subdivision algorithm is robust and recursive. Smooth transition between large and small elements is achieved without significant degradation of the aspect ratio of the elements in the mesh. Several example problems are presented to illustrate the utility of the approach.
Boundary element solution of heat conduction problems in multizone bodies of non‐linear material
Authors: Bialecki Ryszard , Kuhn Günther 
Published: August 2005

AbstractA novel algorithm for handling material non‐linearities in bodies consisting of subregions having different, temperature dependent heat conductivities is developed. The technique is based on Kirchhoff's transformation. The material non‐linearity is reduced to a solution dependent function of unified form added to unknown nodal Kirchhoff's transforms. Assembling of element contributions brings the non‐linearity to the right hand sides of the global set of equations. The first step of the solution of this set is the Gaussian pre‐elimination (condensation) of linear degrees of freedom. At this stage efficient block solvers can be used. Then, a set of non‐linear equations is extracted from the condensed one and solved employing the Newton‐Raphson technique. The iteratively solved set consists of the least possible number of equations and its Jacobian matrix is calculated efficiently by taking advantage of the specific form of the equations.
Superconvergent extraction techniques for finite element analysis
Authors: Niu Qingxiang , Shephard Mark S. 
Published: August 2005

AbstractA class of extraction techniques is developed to recover stresses as well as displacements from finite element solutions. Particular emphasis is placed on the extraction of boundary stresses along slope continuous portions of the boundary. The techniques are superconvergent in that the convergence of the recovered quantities is equal to that of the strain energy. Numerical examples are used to demonstrate that the techniques are efficient and reliable, and can be easily implemented in the finite element analysis environment.
Explicit time‐domain transmitting boundary for dam‐reservoir interaction analysis
Authors: Yang R. , Tsai C. S. , Lee G. C. 
Published: August 2005

AbstractAn explicit time‐domain transmitting boundary for the analysis of dam‐reservoir interactions is presented. This transmitting boundary is a semi‐analytical solution of the governing wave equation of the far field of the reservoir. By using this transmitting boundary, the radiation condition and water compressibility can readily be incorporated in the time‐domain analysis of dam‐reservoir systems. Therefore, the finite element method can be used to accurately analyse a dam‐reservoir system including the semi‐infinite reservoir while maintaining its efficiency in time‐domain analysis. Numerical results have excellent agreement with the available analytical solution. Results also show that the proposed explicit transmitting boundary is more efficient computationally than the implicit transmitting boundary presented by Tsai and Lee.
A numerical treatment to the solution of quasiparabolic partial differential equations
Authors: Chocholaty Pavol 
Published: August 2005

AbstractThis paper presents results obtained by the implementation of a hybrid Laplace transform finite element method to the solution of quasiparabolic problem. The present method removes the time derivatives from the quasiparabolic partial differential equation using the Laplace transform and then solves the associated equation with the finite element method. The numerical inverse of the Laplace transform is realized by solving linear overdetermined systems and a polynomial equation of the kth order. Test examples are used to show that the numerical solution is comparable to the exact solution of the initial‐boundary value problem at the given grid points.
A new discrete Kirchhoff‐Mindlin element based on Mindlin‐Reissner plate theory and assumed shear strain fields—part I: An extended DKT element for thick‐plate bending analysis
Authors: Katili Irwan 
Published: August 2005

AbstractThis is the first of a two‐part paper on plate bending elements with shear effects included. This paper presents a new three‐node, nine‐d.o.f. triangular plate bending element valid for the analysis of thick to thin plates. The element, called DKMT, has a proper rank (contains no spurious zero‐energy modes), passes the patch test for thin and thick plates in an arbitrary mesh and is free of shear locking. Very good results have been obtained for thin and thick plates' by the element. An extended DKQ element for thick‐plate bending analysis is evaluated in Part II.24