bluuebunny/crossref_metadata_2025_split huggingface dataset:
Design‐oriented analysis of imperfect truss structures—part I—accurate analysis
Authors: Rosen Aviv , Schmit Lucien A. 
Published: August 2005

AbstractAn 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

AbstractA 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

AbstractWe 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

AbstractA 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

AbstractHybrid 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

AbstractA 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

AbstractSpecial 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

AbstractThe 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

AbstractA 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

AbstractIt 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.
A scheme for the automatic generation of triangular finite elements
Authors: Sadek Edward A. 
Published: August 2005

AbstractThis 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

AbstractThe 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

AbstractThe 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

AbstractA 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

AbstractTwo 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

AbstractTechniques 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

AbstractAn 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

AbstractSome 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

AbstractA 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

AbstractThe 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

AbstractThe 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

AbstractOften, 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.
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

AbstractCracked 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

AbstractRecent 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

AbstractThis 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

AbstractThis 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

AbstractA 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

AbstractA 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

AbstractA 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

AbstractA 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.