bluuebunny/crossref_metadata_2025_split huggingface dataset:
Transmitting boundaries for time‐harmonic elastodynamics on infinite domains
Authors: Murakami H. , Shioya S. , Yamada R. , Luco J. Enrique 
Published: August 2005

AbstractA finite element method with transmitting boundary is developed for time‐harmonic elastodynamics on infinite domains. Only a finite inner domain needs to be discretized into conventional finite elements, while the effect of the exterior domain is simulated by introducing the transmitting boundary stiffness matrix on the degrees‐of‐freedom of the transmitting boundary nodes. In order to incorporate the Sommerfeld radiation condition, the reciprocity relation, on the transmitting boundary for the radiating elastodynamic state under consideration and the one which is induced by a finite number of point source is used to calculate the transmitting boundary stiffness matrix. The effectiveness of the transmitting boundary technique has been demonstrated by solving the stress concentration problems of a homogeneous isotropic full space with a circular cylindrical cavity and of the one with a spherical cavity, which are subjected to plane incident waves, and the results are compared with the ones of the conventional FEM and the exact data.
A preprocessor for the finite element program SAP IV
Authors: Haugeneder E. , Prochazka W. , Tavolato P. 
Published: August 2005

AbstractThe following work proposes the use of a special description‐language for producing input data of finite element programs. The programs now used require a detailed description of the structure to be analysed, and they require it in a form which is unfavourable to the user and which promotes errors. Therefore, a language was designed which allows a short and compact description of the structure. This description is then automatically transformed into the input data. In this paper, the design process and the characteristics of the language are presented. Some comments on its implementation, that is on the development of a special preprocessor, are made. As target system, the finite element program SAP IV has been chosen. Finally, we want to present an example of the improvements achieved by the use of this language and the SAP IV preprocessor, respectively.
A finite element formulation based on Nadai's deformation theory for elasto‐plastic analysis
Authors: Kim Hong Ou 
Published: August 2005

AbstractA numerical method of the Newton‐Raphson type is presented for elasto‐plastic analysis using the finite element method. The method is developed from Nadai's deformation theory and Hooke's law. Numerical examples are used to show that the method provides very rapid solution convergence.
Loubignac's iterative method in finite element elastostatics
Authors: Cook Robert D. 
Published: August 2005

AbstractFinite element models provide only approximate results under most loadings. A beam modelled by constant‐strain triangles and loaded by pure moment is a case in point. Yet if the iterative method advanced by Loubignac et al.1 is applied to this model, the exact stress field will be generated. The iterative method derives from a parent formulation that can be solved without iteration.2 As shown in this paper, the parent formulation contains the sum of two stiffness matrices. One is produced by the customary finite element shape functions. The other is produced by finite difference expressions for strain gradients that are not contained in the shape functions.Loubignac's method produces a stress field that is continous across interelement boundaries. Other methods that seek to impose interelement continuity are noted in the concluding section.
Investigation of highly accurate integration formulae for transient heat conduction analysis using the conjugate gradient method
Authors: Trujillo D. M. , Busby H. R. 
Published: August 2005

AbstractTwo highly accurate implicit Padé approximations to the transient heat conduction equation are investigated using the conjugate gradient method to solve, for the temperatures. The accuracy and stability of the approximations are discussed and numerical examples are presented showing the relative performance. Comparisons with the Crank‐Nicolson method are also presented.
An efficient algorithm for analysis of nonlinear heat transfer with phase changes
Authors: Rolph W. Donald , Bathe Klaus‐JÜRgen 
Published: August 2005

AbstractA new, simple and effective finite element procedure is presented for the practical solution of heat transfer conditions with phase changes. In this method, a fixed finite element mesh is employed, and a relatively coarse finite element mesh and large time step can be used in the incremental solution. The results of various numerical studies using the algorithm are presented that demonstrate the effectiveness of the procedure.
A finite element model for nonlinear shells of revolution
Authors: Cook W. A. 
Published: August 2005

AbstractA finite element model for symmetrically loaded shells of revolution is described. The nonlinear geometric effects are accounted for by incrementing loads and iterating for equilibrium. The iteration process also allows for nonlinear materials. The shell model accounts for large strains, large rotations and shear deformation. Three example problems demonstrate the ability of this model to solve linear problems. Also, three example problems demonstrate the versatility and accuracy of this model for nonlinear problems. These nonlinear example problems are an axially loaded cylinder and an internally pressurized spherical shell that have large membrane strains, and a cylinder that deforms into a spherical shape, having large rotations.
Reduced integration and the shear‐flexible beam element
Authors: Prathap G. , Bhashyam G. R. 
Published: August 2005

AbstractA clearer insight into the ‘shear locking’ phenomenon, which appears in the development of C0 continuous element using shear‐flexible or penalty type formulations, is obtained by a careful study of the Timoshenko beam element. When a penalty type argument is used to degenerate thick elements to thin elements, the various approximations of the shear related energy terms act as different types of constraints and, depending on the formulation, two types of constraints which are classified as true or spurious may emerge. The spurious constraints, where they exist, are responsible for the ‘shear locking’ phenomenon, and its manifestation and elimination is demonstrated in a very simple example. The source of difficulty is shown to be the mathematical operations involved in the various shape function definitions and subsequent integration of functionals. It is seen that formulations that ensure only true constraints in the extreme penalty limit cases display far superior performance in the thick element situation as well, and thus guidelines for the development of efficient elements are drawn. A similar type of behaviour is observed in a shallow curved beam element and here ‘inplane locking’ can be eliminated by selective integration to obtain an improved curved beam element. However, ‘inplane locking’ does not cause a spurious constraint as the error quickly vanishes with the reduction of element size for a reasonable radius of curvature conforming with shallow shell theory.
Automatic mesh generation with tetrahedron elements
Authors: Nguyen‐Van‐Phai  
Published: August 2005

AbstractTo reduce the manual work involved in the application of the FEM in practice, preprocessors can be applied for the construction of network structures, which are complicated in generation strategy and do not form any optimum discrete structure. The time necessary for generation can be minimized even more by the application of only one element type within the whole network structure. A technique for the automatic generation of 3D‐network structures with tetrahedron elements is presented in this paper. In this proposed technique, the nodal points of the network structure must be defined manually before the generation procedure, since a random positioning of points is usually undesirable for FEM calculation. The nodal points are connected by a program to a network structure consisting of tetrahedron elements which have optimum form for the numerical computation of the element matrices. After the generation, the element sides forming any part of the boundary surface of the network structure can be automatically identified. If necessary, the network structure can be automatically refined.
Approximate structural reanalysis for optimization along a line
Authors: Kirsch Uri 
Published: August 2005

AbstractThe need for multiple repeated analyses, which usually involve much computational effort, is one of the main difficulties in the optimization of large structures. This study deals with approximate structural reanalysis along a line in the design space, a problem common to many optimal design procedures. The problem is first stated in terms of a single independent variable. Explicit polynomial approximations for the nodal displacements are then presented. It is shown that Taylor series expansion of the displacements and a series based on a simple iteration procedure are equivalent. Furthermore, the series coefficients can readily be computed, providing efficient and high‐degree polynomial approximations.To improve the quality of the approximations, two nonpolynomial series are proposed. The relationship between the various methods is discussed and simple numerical examples demonstrate applications. All the proposed procedures require only a single exact analysis to obtain the explicit expressions for any given line.The results obtained are very close to the exact solution and indicate that the proposed methods provide efficient and high‐quality approximations for the nodal displacements.
Three‐dimensional shape optimization
Authors: Imam M. Hasan 
Published: August 2005

AbstractOptimal structural desingn generally deals with frame or shell structures where the optimization is limited to resizing of structural members to obtain optimum cross‐sections or thicknesses. Shape optimization solves another class of problems involving continuous structural components where the optimum shape (the shape of the boundaries and the surfaces of the components) is determined. This report describes shape optimization of three‐dimensional structural components. The finite element method of analysis is used employing the 20‐noded isoparametric element. The objective function, mass, is minimized by the direct use of nonlinear mathematical programming, specifically the feasible direction method. Numerical shape representation and the selection of design variables are the most important aspects of the problem. The problem is addressed from a practical standpoint and techniques are presented to minimize the number of desingn variables. Isoparametric representation of the surfaces and the numerical superposition of shapes are discussed. These techniques are compared and demonstrated on simple cantilever beams and their minimum mass designs are obtained. In one example, the optimum shape of a non‐uniform cross‐sectinal beam is obtained under stress constraint. The final design has a crosssectional shape varying over the length of the beam which could not be predicted using the bending theory of beams. One major difficulty encountered in some problems was that the shape changes during the optimization process may require a change in the finite element mesh because the initial configuration of the finite element mesh may result in very distorted elements for the new shape. The analyis with a mesh containing distorted elements may not be possible at all or the results of the analysis may be inaccurate.
Finite element methods for constrained problems in elasticity
Authors: Oden J. T. , Kikuchi N. 
Published: August 2005

AbstractSeveral different variational formulations of boundary‐value problems with constraints are discussed, with particular reference to constrained problems in elasticity. Special attention is given to exterior penalty methods. A discussion of the conditions necessary for penalty methods to provide a basis for stable and convergent finite element methods is given. In particular, the use of reduced integration is discussed and criteria on the order of reduced integration rules sufficient to produce stable and convergent schemes are described. Applications of reduced integration‐penalty methods to incompressible elasticity problems and contact problems are described.
Some problems of a plate bending hybrid model with shear effect
Authors: Wu Chang‐Chun 
Published: August 2005

AbstractA triangular plate bending hybrid element is constructed according to Reissner's principle. It has 9 degrees‐of‐freedom and the shear effect is included. The C0 formulation of thick plate is directly developed to solve the thin plate by imposing the discrete Kirchhoff constraints. The matching problem for bending and shear in the hybrid model of thick plate is effectively treated by use of the principle of the energy regulation such that the unified analysis of thick and thin plates is realized. Finally, numerical examples are presented.
A receptance formula for general second‐degree square lambda matrices
Authors: Palazzolo Alan B. , Wang Bo Ping , Pilkey Walter D. 
Published: August 2005

AbstractA computational algorithm utilizing the free vibration modes of a structure is presented for calculating receptances. The usual eigensystem computed for large structural models is incomplete; hence the receptances are approximate. The formulae developed here increased receptance accuracy compared to classical spectral representations. Receptances are used extensively in eigensolution reanalysis, design and synthesis and also for forced harmonic response studies. In these areas receptance approaches offer a popular alternative to Rayleigh–Ritz subspace type methods. Structural models represented by nonsymmetric mass, damping and stiffness matrices, which occur frequently in rotating structures, may be treated using the receptance formulae presented. The receptance matrix derived is applicable to general, second‐degree, square lambda matrices. This generalizes the receptance matrix commonly associated with matrix pencils.
A new penalty function element for thin shell analysis
Authors: Haugeneder E. 
Published: August 2005

AbstractIn this paper a triangular thin shell element is presented where C1 continuity is introduced by means of the penalty function technique. The displacement field has complete cubic polynomials for each component. The introduced constraint condition is the continuity of normal slopes of the transverse displacements along interelement boundaries. Classical thin shell theory for small deformations is applied. Several analyses of thin plates and shells are performed, including a large problem of practical interest, to study the effect of an increasing penalty factor. The accuracy of the results is estimated and compared to the actually occurred error. In the conclusions a recommended value for the penalty factor is given.
A direct vector combination procedure for finite element stiffness matrix formulation
Authors: Mau S. T. 
Published: August 2005

AbstractA direct vector combination procedure is developed for the formulation of finite element stiffness matrices. Only the homogeneous solution modes to governing equations of a problem and a uniquely defined interpolation displacement function along the element boundary are used to generate pairs of nodal displacement and nodal force vectors. The stiffness matrix is obtained by a simple multiplication of the nodal displacement and nodal force vectors. The element formed passes all the higher order patch tests for the order of solution modes included in the formulation. However, the stiffness matrix may become unsymmetrical. Restoring symmetry leads to compromising some of the higher order patch test performances. The present procedure is shown to have direct relations to those of the displacement model and the hybrid stress model. The present procedure presents new possibilities for the improvement of element performance. The procedure itself can also be used to study the limitations of element behaviour.
Line node and transitional shell element for rotational shells
Authors: Han Kye J. , Gould Phillip L. 
Published: August 2005

AbstractA transitional shell finite element which is useful for the analysis of shells of revolution with local deviations is developed. For the analysis of such a structure, rotational shell elements may be used in the axisymmetric portion of the shell, while general shell elements are needed in the region where deviations create a local non‐axisymmetry. The transitional shell element connects these two different types of elements. To facilitate the transition, a line node, which can accommodate any type of shape function, is developed. Numerical examples are presented to demonstrate the accuracy of the new element.
Application of point least squares method with B‐splines in solid mechanics problems
Authors: Mizusawa T. , Kajita T. 
Published: August 2005

AbstractA discrete approach using the B‐spline functions and the concept of the point least square is presented. The general procedure, in which trial functions satisfy neither governing differential equations nor boundary conditions, is used in solving solid mechanics problems. No numerical integration is required in the formulation and the resulting matrix has the advantage of always being symmetrical.To demonstrate the accuracy and versatility of the present method, vibration of beams, skew plate problems, thick plates and a non‐self‐adjoint problem are analysed. A good accuracy is obtained with increase in the number of fitting points and of knots of B‐spline functions.
Some ‘special’ interpolation formulae for triangular and quadrilateral elements
Authors: Ying Lung‐An 
Published: August 2005

AbstractPresented herein are methods to generate special interpolation formulae of the following type: (i) C0 continuous interpolation over triangular elements which induces a given type of singularity for the first derivatives at one of the vertices, and yet preserves ‘rigid and constant strain’ motions, (ii) C1 continuous interpolation over triangular elements which induces a given type of singularity for second derivatives at one of the vertices.
A block equation solver for large unsymmetric matrices arising in the boundary integral equation method
Authors: Crotty J. M. 
Published: August 2005

AbstractAn equation solver for the large unsymmetric systems of linear equations arising in the application of the boundary integral equation method to problems of linear elasticity in homogeneous or piecewise homogeneous solids is presented. The solver uses Gaussian elimination. The advantages of the solver over many existing eliminational or iterational methods are that it ignores many of the large groups of zeros that occur in piecewise homogeneous work, and also restrains growth of the number of non‐zero matrix entries. Memory requirements and computation times therefore are reduced for many piecewise homogeneous problems.
Higher order accuracy finite‐difference schemes for hyperbolic conservation laws
Authors: Reddy A. Sivasankara 
Published: August 2005

AbstractAn explicit algorithm which gives stable finite‐difference schemes, of order of accuracy greater than two, for solving a quasi‐linear hyperbolic system of partial differential equations in several space dimensions is presented. Third and fourth order accuracy schemes are derived using this algorithm. The fourth order scheme needs fewer flux evaluations than the scheme given by Abarbanel and Gottlieb.1 Numerical results obtained show that these schemes have the expected accuracy and stability.
Finite element analysis of non‐stationary one‐dimensional random diffusion problems
Authors: Tasaka Seiichi , Matsuoka Osamu 
Published: August 2005

AbstractA finite element analysis of a class of non‐stationary random diffusion problems is considered. By using the one‐dimensional heat equation with random initial condition and random external excitation, the statistical numerical formulation is presented. Two typical numerical examples are given for somewhat simplified problems by which the validity of the finite element scheme is discussed. The results obtained by the finite difference scheme are also shown.
Universal finite element matrices for tetrahedra
Authors: Silvester Peter P. 
Published: August 2005

AbstractMethods are described for forming element matrices for a wide variety of operators on tetrahedral finite elements, in a manner similar to that previously employed for line segments and triangles. This technique models the differentiation and product‐embedding operators as rectangular matrices, and produces finite element matrices by replacing all required analytic operations by their finite matrix analogues. The method is illustrated by deriving the conventional matrix representation for Laplace's equation. Computer programs are available, which generate universal finite element matrices for use in various applications.
Invariant 8‐node hybrid‐stress elements for thin and moderately thick plates
Authors: Spilker R. L. 
Published: August 2005

AbstractEight‐node hybrid‐stress elements are developed for the analysis of plates ranging from arbitrarily thin to moderately thick. The displacement behaviour is characterized by a transverse displacement and independent cross‐section rotations, which are interpolated using the 8‐node Serendipity shape functions. All components of stress are included; alternative elements are developed which differe in the form of the inplane distribution of the stresses. Elements are sought for whic the stiffiness is invariant and of correct rank, and whic show on signs of deterioration in the thin‐plate limit. A discussion of the prospects for developing a 4‐node element with these characteristics is also presented. Example problems are used to compare the performance of the 8‐node elements including convergence behaviour, intraelement stress distributions and optimal sampling locations, and range of applicability in terms of plate thickness ratio.
A qualitative accuracy consideration on arch elements
Authors: Yamamoto Yoshiyuki , Ohtsubo Hideomi 
Published: August 2005

AbstractIn the present paper, discretization errors in the finite element analysis of arches are investigated quantitatively. So far they have been estimated as an order, such as a power of the element size by means of functional analysis; however, it is insufficient for practical applications, because they depend to a great extent upon the constant of proportionality, which is investigated herein. As a result, it is shown that the constant is affected largely by the arch's stiffness. Errors for displacements are also evaluated with the aid of the energy principle. A formula for a posteriori estimating errors is proposed, which can be evaluated only from the finite element solutions calculated. The validity of the present theory is verified by numerical examples.
Band algorithm for unsymmetric matrices in finite element and semi‐discrete methods
Authors: Gopalakrishnan T. C. , Palaniappan A. B. 
Published: August 2005

AbstractA compact FORTRAN subroutine for reducing unsymmetric band matrices (in‐core solution) is presented. As usual, the zeros inside the band are skipped during the Gauss elimination. However, the theme of the paper is centred on a new approach in applying the above‐mentioned band solver to transient problems. The approach results in considerable saving of computational time while also achieving reduction in memory space. This double advantage makes it particularly useful in handling dynamic real world problems. Extension of the use of the algorithm to moving boundary problems is indicated.
Permutation rules for simplex finite elements
Authors: Silvester Peter P. 
Published: August 2005

AbstractSimplicial finite elements have many symmetries, which are commonly exploited in programs to save computing time and storage. All possible permutations of the interpolation functions of an N‐simplex can be expressed in terms of N basic permutation operations. The relevant permutation matrices are given for triangles up to order 20 and tetrahedra up to order 10.