bluuebunny/crossref_metadata_2025 huggingface dataset:
The evaluation of the error term in some numerical quadrature formulae
Authors: Smith H. V.
Published: August 2005

A method, based on the trapezoidal rule, is described for the numerical evalution of the error term arising in some numerical quadrature formulae.
Finite difference energy techniques for arbitrary meshes applied to linear plate problems
Authors: Pavlin V. , Perrone N.
Published: August 2005

A new energy based finite difference analytical technique is introduced. The method incorporates certain energy concepts and the ability to use arbitrary, irregular meshes within the framework of the Finite Difference Method. This formulation reduces any governing partial differential equations to a set of difference equations containing partial derivatives up to and including the second order. Further, certain strong similarities with the popular Finite Element Method are shown and the ability to solve problems with irregular boundaries is discussed. To demonstrate the Finite Difference Energy Method several plate bending problems are solved.
A finite element approach to subsonic aerodynamics
Authors: Habashi W. G.
Published: August 2005

A study of the application of the Finite Element Method to compressible potential flows, typified by the airfoil problem, is undertaken. Some novel approaches, believed to simplify solution techniques, are presented.

The solutions use two pseudo‐variational integrals, appropriate to subsonic flows, and possessing a physical iterative basis. With constant‐derivatives triangular elements formulated for cylindrical co‐ordinates, accurate solutions are easily obtained for the flow over a circular cylinder. For arbitrary airfoils a simple mapping is used to transform them into near circles. An appropriate mesh is then constructed in the mapped plane. The paper then presents two solution approaches by which this non‐linear problem is solved in both the near circle plane and the airfoil plane.
Matrix‐MP method for the analysis of inelastic arch structures
Authors: Ronca P. , Cohn M. Z.
Published: August 2005

A general matrix formulation and mathematical programming techniques are used for the analysis of arch bridge structures in the inelastic range. Discretization of the structural model and of the constitutive laws of the material enables the solution of a number of engineering problems by a unified computer program. The capability of the method includes and limit load and deformation analysis, historical load–deformation analysis and shakedown load analysis. All these problmes but the last one are covered in the paper and are illustrated in the example of an actual reinforced concrete arch bridge with a stiffening girder.
Large displacement analysis of three‐dimensional beam structures
Authors: Bathe Klaus‐Jürgen , Bolourchi Saïd
Published: August 2005

An updated Lagrangian and a total Lagrangian formulation of a three‐dimensional beam element are presented for large displacement and large rotation analysis. It is shown that the two formulations yield identical element stiffness matrices and nodal point force vectors, and that the updated Lagragian formulation is computationally more effective. This formulation has been implemented and the resulted of some sample analyses are given.
On comparing the accuracy of some finite difference methods for parabolic partial differential equations
Authors: Towler B. F. , Yang R. Y. K.
Published: August 2005

Methods for comparing the accuracy of numerical methods for the solution of parabolic partial differential equations are briefly surveyed. Criteria for a more systematic comparison are proposed and applied to an accuracy comparison of the classical and the modified Saul'yev methods and the Crank–Nicholson method on a simple linear problem. The results obtained, which include observation of the existence of optimal spatial mesh size for the two Saul'yev methods, are discussed.
Design‐oriented analysis of imperfect truss structures—part I—accurate analysis
Authors: Rosen Aviv , Schmit Lucien A.
Published: August 2005

An accurate nonlinear analysis procedure for calculating the displacement stresses and system buckling loads of geometrically imperfect truss structures is developed. The investigation considers both local and system imperfections. This nonlinear analysis takes first‐order geometrically nonlinear effects into account. The accuracy of the analysis procedure is confirmed by comparison with analytical and experimental results for truss structures drawn from the literature. The results show that local and system imperfections can have strong influence on the behaviour of truss structures and therefore should be taken into account. It is shown that nonlinear effects play a major role in the phenomena and therefore simplified analyses that neglect nonlinear effects are inadequate.
The finite element method in the solution of unbounded potential flows
Authors: Habashi Wagdi G.
Published: August 2005

A simple, yet effective, finite element approach to aerodynamic problems is presented. A better approximation of the geometry is obtained by the mapping of airfoils into near‐circles. The mapping serves in homogenizing the gradients of the problem by magnifying regions of high gradients such as the leading and trailing edges while geometrically condensing the lower gradient regions on the main part of the airfoil. The mapping also permits the use of an effective automated mesh generation scheme that greatly reduces the amount of preparatory work involved in finite elements. To limit the size of the solution domain, an asymptotic analytical solution, with unknown coefficients, is assumed on a finite radius outer contour. The coefficients are obtained along with the finite element nodal unknowns. An accrued advantage of this patching asymptotic procedure is its ability to obtain the lift as a solution variable without having to resort to the numerical integration of the pressure field over the body. Solutions to non‐lifting and lifting bodies are obtained.
Modelling the load transfer in threaded connections by the finite element method
Authors: Bretl John L. , Cook Robert D.
Published: August 2005

We introduce a finite element model for stress analysis of threaded connections. Instead of modelling individual threads, the thread zone is replaced by a layer of elements with orthotropic properties. The principal directions of orthotropy depend upon the thread geometry and upon the direction of load, which is not necessarily known a priori. Both conventional and tapered threads are considered. The latter problem is nonlinear, as the number of threads in contact is a function of the load. Numerical results for conventional and tapered threads agree well with theoretical and exeprimental results in the literature.
Plastic (or visco‐plastic) behaviour of axisymmetric bodies subjected to non‐symmetric loading—semi‐analytical finite element solution
Authors: Winnicki L. A. , Zienkiewicz O. C.
Published: August 2005

A combination of a two‐dimensional finite element process and a Fourier series in the third dimension, well known in linear applications, is shown to be a possible and efficient way of analysing plastic and visco‐plastic behaviour. The economy of the process as contrasted with full three‐dimensional solutions is illustrated.
Inclusion of hybrid deformation elements in the class of simple deformation models
Authors: Wissmann Johannes W. , Specht Bernhard
Published: August 2005

Hybrid elements for the representation of elastic media are based upon extended variational principle. In the discretization process the hybrid deformation model requires an expansion of the displacement field as well as of the Lagrange multipliers at the boundary. Using an extension of the common shape function concept, these hybrid elements can be reduced to the basis of the simple minimum principle of potential energy with only one expansion of the displacements. An application to plate elements is given and a discussion about some consequences of the approach.
A frontal procedure using skyline storage
Authors: Thompson Erik , Shimazaki Yoji
Published: August 2005

A frontal‐skyline method is presented which allows for compact skyline storage while using the frontal method. It is shown that the method requires the same minimum core storage as the frontal method and fewer transfers to and from disc than the blocked‐skyline method. Subroutines necessary for its implementation with finite element codes are given.
Singular finite elements for the fracture analysis of V‐notched plate
Authors: Lin K. Y. , Tong Pin
Published: August 2005

Special accurate and efficient hybrid elements were developed to account for notch‐tip singularities of type rγ, where γ can be complex. Proper normalization of the notch‐tip element size was used to minimize the oscillation of the assumed function around the boundaries of the element and to improve the accuracy of the solution. Examples of various notch angles and sizes are presented.
Solution of the poisson equation: Comparison of the Galerkin and control‐volume methods
Authors: Ramadhyani S. , Patankar S. V.
Published: August 2005

The two‐dimensional Poisson equation is solved by the finite element method which uses rectangular elements and the bilinear shape function. Two kinds of weighting functions are employed, which correspond to the Galerkin method and the control‐volume method. The results for three test problems, for which exact analytical solutions are available, show that the control‐volume method leads to errors that are about one‐half of the errors given by the Galerkin method. Incidentally, the five‐point finite difference method is found to give errors which are nearly equal to those for the Galerkin method.
Space–time elements for the shock wave propagation problem
Authors: Cella A. , Lucchesi M. , Pasquinelli G.
Published: August 2005

A space–time finite element procedure is presented that integrates on time the equations of nonlinear dynamics. When a shock occurs and subsequently propagates, the space–time procedure gives accurate and stable numerical results, without after‐shock wiggling, at relatively low costs of computation.

The procedure is implicit. The good performance is to be attributed to the capability of the space‐time elements to cope with discontinuities in the velocity by the simple use of reduced numerical integration.

The numerical solution of the Fermi–Pasta–Ulam problem is discussed.
Finite elements based on energy orthogonal functions
Authors: Bergan P. G.
Published: August 2005

It is shown how the convergence requirements for a finite element may be written as a set of linear constraints on the stiffness matrix. It is then attempted to construct a best possible stiffness matrix. The constraint equations restrict the way in which these stiffness terms may be chosen; however, there is normally still room for improving or optimizing an element. It is demonstrated how an element stiffness matrix may be found using rigid body, constant strain and higher order deformation modes. Further, it is shown how the constraint equations may be exploited in deriving an ‘energy orthogonality theorem’. This theorem opens the door to a whole new class of simple finite elements which automatically satisfy the convergence requirements. Examples of deriving plane stress and plate bending elements are given.
Four‐node quadrilateral stress membrane element with rotational stiffness
Authors: Robinson John
Published: August 2005

A four‐node quadrilateral membrane element with 12 degrees‐of‐freedom and based on stress assumptions is presented. The element has a rotational degree‐of‐freedom at each node associated with a moment.
A scheme for the automatic generation of triangular finite elements
Authors: Sadek Edward A.
Published: August 2005

This paper describes a method for the automatic triangulation of arbitrary multilateral plane domains. In addition, the method can be used in connection with that suggested by Zienkiewicz and Phillips4 for the subdivision of curved‐boundary domains. The method can be described as general fully automatic and computer oriented. A Fortran computer program has been prepared by the author. Output can be of interactive, graphical or alphanumerical form. The program has been applied to a number of cases. The resulting triangulations are always satisfactory, even when vigorous changes of mesh sizes are encountered.
Direct search solution of an inverse problem in elastoplasticity: Identification of cohesion, friction angle and in situ stress by pressure tunnel tests
Authors: Gioda Giancacrlo , Maier Giulio
Published: August 2005

The identification (or ‘calibration’ or ‘inverse’) problem with in this paper, can be outlined as follows. The ‘real system’ is a deep rock formation which can be regarded as isotropic and elastoplastic. A mathematical‐numerical model, intended for the analysis of its response to excavations, rests on the assumption of an elastic‐perfectly plastic Mohr–Coulomb constitutive law and of a homogeneous isotropic initial (in situ) stress state. The values of cohesion, friction angle and initial stress to be introduced in this model are identified by minimizing a measure of the discrepancy (error) between theoretical and experimental relationship (pressure vs. average diameter increase), concerning a standard pressure tunnel test carried out well inside the nonlinear range. For the error minimization process, two very general ‘search techniques’ are adopted and discussed from the computational standpoint: the flexible polyhedron (modified simplex) strategy and the alternating variable strategy in the Rosenbrock version. Both are found to be adequate for solving this inverse problem, when the mathematical model has to be use as a ‘black box’ in a purely numerical identification process.
Some computational aspects of elastic‐plastic large strain analysis
Authors: Nagtegaal J. C. , De Jong J. E.
Published: August 2005

The governing equations for large strain analysis of elastic‐plastic problems are reconsidered. An improved form of these equations is derived, which is valid for small increments of strain and large increments of rotation. Special attention is paid to the integration procedures for these equations in the deformation history. It is shown that the tangent modulus procedure for integration of the constitutive equations is conditionally stable, and that implicit methods, such as the ‘mean normal’ method, are to be preferred. A novel procedure is introduced for the treatment of nonlinear geometric effects. The performance of various element types is examined, with specific attention to effects of ‘locking’ and distortion. Several applications are discussed to illustrate the various aspects of the formulation developed ein this paper.
‘Infinite domain’ elements
Authors: Beer G. , Meek J. L.
Published: August 2005

A parametric element is formulated which enables the economic modelling of ‘infinite domain’ type problmes. A typical problem is an opening in a stress field in an infinite medium, either in two or three dimensions. The strategy is to model around the opening with two or three layers of conventional isoparametric finite elements and surround these with a single layer of ‘infinite domain’ elements.

Several sample problems has been analysed for circular, square and spherical openings in infinite media, and the results compared with either theoretical or boundary element solutions which include the ‘infinite’ boundary in their solution technique.
High order three‐dimensional hybrid‐stress elements for thick‐plate analysis
Authors: Spilker R. L.
Published: August 2005

Two alternative hybrid‐stress based three‐dimensional elements are presented. These elements are intended for use in the analysis of thick plates for which the through‐thickness variation of displacement and stress may be of high order, and in which a single element is to be used through the thickness of the plate. For both elements, the displacement assumption allows for cubic through‐thickness variation in the inplane displacements, and quadratic through‐thickness variation for the transverse displacement. The elements differ in the stress assumption used. In the first element, the z variations in the stress components are chosen to be consistent with the z variations of the strain distribution calculated from the displacement assumption, and the traction boundary conditions at the upper and lower surfaces are satisfied in the weighted integral sense. In the second element, the z variations in the stress components are chosen to achieve consistency with respect to the equilibrium equations, and the traction‐free conditions at the upper and lower surface of the plate are satisfied exactly. The example problem of a semi‐infinite, simply‐supported thick plate under transverse sinusoidal loading is considered. Results obtained by using each of these elements are compared with available elasticity and approximate solutions, and an assessment of the relative merits and range of applicability of each element is made.
Techniques for thermal sensitivity analysis
Authors: Haftka Raphael T.
Published: August 2005

Techniques for computing the sensitivity of temperatures to changes in design variables needed for designing thermal protection systems are considered. It is shown that the choice of the most efficient technique depends on the ratio of number of temperature constraints to the number of design variabies, as well as on the thermal analysis method employed. The analysis is specialized to the case of a structure modelled by finite elements, and an example of an insulation panel is used demonstrate the techniques.
Simplified analysis of linear fluid‐structure interaction
Authors: Müller W. Cristoph
Published: August 2005

An approximation method is presented for the analysis for the interaction of a structure with a compressible linear fluid. The method uses the fact that the eigenvalues of the dry structure are higher than the corresponding eigenvalues of a structure in contact with an incompressible fluid, and the corresponding eigenvalues of a structure in contact with a compressible fluid are even lower. The proof of this theorem is given. It is shown that in both the compressible and incompressible cases the number of degress‐of‐freedom can be reduced to the number of boundary points which results in a substantial saving of core memory space and computing time. A sample problem is given to demonstrate the good results of the approximation methods for a low quotient of the eigenfrequencies divided by the square of the speed of sound.
Alternative integration formulae for triangular finite elements
Authors: Reddy C. T. , Shippy D. J.
Published: August 2005

Some new formulae are presented for numerical integration over triangular regions. These formulae, which are triangularly symmetric, involve four, six, and seven integration points, respectively. They were derived by determining co‐ordinates and weight factors for which polynomial functions of up to a certain degree are integrated exactly. The effectiveness of the formulae is demonstrated by applying them to the integration of five non‐polynomial functions, two of which are singular within the region of integration. Results obtained with the new formulae are compared with results obtained with other, comparable formulae. It is seen that the new formulae are more accurate than some existing ones with the same numbers of points.
Improved hybrid‐stress axisymmetric elements includng behaviour for nearly incompressible materials
Authors: Spilker Robert L.
Published: August 2005

A series of 4‐node axisymmetric solid‐of‐revolution elements with quadrilateral cross‐section are developed based on the hybrid‐stress finite element model. The displacement interpolation is identical, and the elements differ in the stress field chosen; alternative schemes for selection of stress distribution are investigated. The performance of these elements is assessed and compared for the example problems of a thick cylinder and thick sphere under internal pressure. Of particular importance are convergence, intra‐element stress distributions, and element performance as the incompressible state is approached.
Dynamic stress concentration studies by boundary integrals and Laplace transform
Authors: Manolis G. D. , Beskos D. E.
Published: August 2005

The dynamic stress field and its concentrations around holes of arbitrary shape in infinitely extended bodies under plane stress or plane strain conditions are numerically determined. The material may be linear elastic or viscoelastic, while the dynamic load consists of plane compressional waves of harmonic or general transient nature. The method consists of applying the Laplace transform with respect to time to the governing equations of motion and formulating and solving the problem numerically in the transfomed domain by the boundary integral equation method. The stress field can then be obtaind by a numerical inversion of the trasformed solution. The correspondence principle is invoked for the case of viscoelastic material behavious. The method is simplified for the case of harmonic waves where no numerical inversion is involved.
Simplified direct optimization of tubular truss structures
Authors: Felton Lewis P. , Fuchs Moshe B.
Published: August 2005

The general problem of optimum design of trusses composed of tubular elements requires the determination of cross‐sectional dimensions for each element which satisfy a set of side constraints on those dimensions as well as Euler and local buckling constraints. A formulation is presented which eliminates the necessity to use mathematical programming methods for the determination of feasible cross‐sectional dimensions. The minimization problem is shown to be expressible in terms of area variables only, with each area subject to bounds which are functions of truss stiffness but which may be obtained by explicit analysis of the element ‘desing space’ for any design. This‘direct’ formulation is completely general and compatible with any minimization algorithm. The formulation also leads to a simple and efficient recursive procedure for producing near‐optimal fully‐constrained designs. Several examples illustrate results obtained by both the direct and recursive procedures.
Locking of thin plate/shell elements
Authors: Tsach Uri
Published: August 2005

Often, finite element solutions of thin plate/shell elements become very stiff and the displacement field solutions diverge from those predicted by Kirchhoff's theory. This phenomenon is known as the locking phenomenon. A theoretical fomulation demonstrating its existence is developed, and results of finite element analysis of a single element and mesh are discussed. This leads to a sufficient and necessary criterion which must be satisfied to avoid the locking phenomenon.
Finite difference approximation for ordinary derivatives
Authors: Lau P. C. M.
Published: August 2005

This paper deals with constructing finite difference formulaes for approximating ordinary derivatives in a uniform or non‐uniform mesh. The corresponding order of truncation error is also established. The accuracy and versatility of the proposed formulae are illustrated through numerical solution to two‐point boundary value problems.
Liner and nonlinear elastic analysis of cracked plate: Application of a penalty function and superposition method
Authors: Yagawa G. , Aizawa T. , Ando Y.
Published: August 2005

Cracked plates of power hardening material under plane strain and incompressibility conditions are investigated in this work by using a penalty function and superposition method. The present numerical method is found to be quite efficient for the relevant problems if the hardening exponent of material is not so large.
High‐order curved finite elements
Authors: Wachspress E. L.
Published: August 2005

Recent finite element analysis of adaptive refinement has focused attention on high‐order approximation within elements. High‐order approximation may be attained over curved elements with either rational basis functions expressed directly in the global co‐ordinates or with a particular class of isoparametric basis functions. Theory for construction of high‐order rational bases yields modifications to the blending method for a special class of elements in order to achieve higher order approximation within these elements.
A new technique for the evaluation of the temperatures arising from some geometries which commonly occur in microelectronics
Authors: Dean D. J.
Published: August 2005

This paper presents a series summation computation method for calculating temperatures arising from some geometries which commonly occur in microelectronics. The method, which is suitable for use with pocket calculators, involves an exchange of terms with those of a known series. At each stage of the summation a state of convergence (SOC) is calculated in terms of the maximum possible error, thus enabling the calculation to be terminated as soon as the required accuracy has been obtained.
A fast stiffness formulation for finite element analysis of two‐dimensional solids
Authors: Sloan S. W.
Published: August 2005

This paper describes and efficient method for computing two‐dimensional element stiffness matrices. It is a generalization of the algorithm given by Taylor. 1Theory is developed for elements which are loaded under plane stress, plane strain or axisymmetric conditions, and two FORTRAN IV subroutines are included. These subroutines, which are presented in a modular form, are applicable to any type of serendipity, Lagrangian or triangular element, and may be incorporated into a user's library. Alternatively, if desired, the relevant code may be embedded directly into existing stiffness generation routines.
Improved iteration strategy for nonlinear structures
Authors: Powell Graham , Simons Jeffrey
Published: August 2005

A solution strategy for the analysis of nonlinear structures is described. The strategy is a simple extension of existing Newton‐type procedures, and can easily be incorporated into existing computer programs.

Earlier work which contributed to the development of the strategy is reviewed and the theory of the procedure is presented. Six examples, covering several different types of structural behaviour are described. These examples suggest that the strategy is remarkably stable and efficient.
A general formulation for coupled thermal flow of metals using finite elements
Authors: Zienkiewicz O. C. , Oñae E. , Heinrich J. C.
Published: August 2005

A finite element formulation to deal with the flow of metals coupled with thermal effects in presented. The deformation process of the metal is treated using the visco‐plastic flow approach and the solution technique for the coupled problem implies a simultaneous solution for velocities and temperatures. Some aspects of the numerical solution of the problem are given and in the last part of the paper some examples of steady‐state extrusion and rolling problems showing the applicability of the method are shown.
An algorithm for the calculation of poisson's equation in 2‐d semiconductor problems
Authors: Polak S. J. , Wachters A. , Vaes H. M. J. , De Beer A. , Den Heyer C.
Published: August 2005

A robust algorithm is described for the solution of the highly nonlinear potential problem in the analysis of semiconductors under a zero current assumption. Some examples are given showing the use of the algorithm.
A boundary integral equation method for plate flexure with conditions inside the domain
Authors: Bezine G.
Published: August 2005

A method for solving boundary value problems for thin plate flexure as described by Kirchhoff's theory is proposed. An integral formulation leads to a system of boundary integral equations involving values of deflection, slope, bending moment and transverse shear force along the edge. A discretization leading to a matrix formulation is proposed. To solve problems with inner conditions in the plate domain, an elimination of boundary unknowns proves successful. The degenerate case where the boundary is free (which leads to a non‐invertible matrix) is investigated. Three examples illustrate the efficiency of the method.
Transmitting boundaries for time‐harmonic elastodynamics on infinite domains
Authors: Murakami H. , Shioya S. , Yamada R. , Luco J. Enrique
Published: August 2005

A 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 generalized numerical approximation for the two‐dimensional Laplacian operator
Authors: Okon E. E.
Published: August 2005

A numerical approximation for the two‐dimensional Laplacian operator at a point is derived for the general case in which the point is surrounded by an arbitrary number of arbitrarily located coplanar nodes. The expression obtained is shown to generalize the usual Cartesian finite difference expression.
Further developments in transient and pseudo‐transient analysis of Mindlin plates
Authors: Pica A. , Hinton E.
Published: August 2005

Some recent developments are presented on a unified approach to the static and transient dynamic geometrically nonlinear analysis of Mindlin plates with initial imperfections.
A preprocessor for the finite element program SAP IV
Authors: Haugeneder E. , Prochazka W. , Tavolato P.
Published: August 2005

The 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

A 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

Finite 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

Two 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

A 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

A 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

A 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

To 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

The 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

Optimal 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

Several 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

A 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

A 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

In 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

A 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

A 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

A 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

Presented 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

An 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

An 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.