bluuebunny/crossref_metadata_2025_split huggingface dataset:
A study of incremental‐iterative strategies for non‐linear analyses
Authors: Clarke Murray J. , Hancock Gregory J. 
Published: August 2005

AbstractThe paper describes a study of incremental‐iterative solution techniques for geometrically non‐linear analyses. The solution methods documented are based on a modified Newton‐Raphson approach, meaning that the tangent stiffness matrix is computed at the commencement of each load step but is then held constant throughout the equilibrium iterations. A consistent mathematical notation is employed in the description of the iterative and load incrementation strategies, enabling the simple inclusion of several solution options in a computer program. The iterative strategies investigated are iteration at constant load, iteration at constant displacement, iteration at constant ‘arc‐length’, iteration at constant external work, iteration at minimum unbalanced displacement norm, iteration at minimum unbalanced force norm and iteration at constant ‘weighted response’. The load incrementation schemes investigated include strategies based on the number of iterations required to achieve convergence in the previous load step, strategies based on the ‘current stiffness parameter’ and a strategy based on a parabolic approximation to the load‐deflection response. Criteria for detecting when the applied external load increment should reverse sign are described.A challenging example of a circular arch exhibiting snap‐through (load limit point) behaviour and snap‐back (displacement limit point) behaviour is solved using several different iterative and load incrementation strategies. The performance of the solution schemes is evaluated and conclusions are drawn.
Curved shell elements based on hierarchical p‐approximation in the thickness direction for linear static analysis of laminated composites
Authors: Surana Karan S. , Sorem Robert M. 
Published: August 2005

AbstractThis paper presents a new curved shell finite element formulation for linear static analysis of laminated composite plates and shells, where the displacement approximation in the direction of the shell thickness can be of an arbitrary polynomial order p, thereby permitting strains of at least (p ‐ 1) order. This is accomplished by introducing additional nodal variables in the element displacement approximation corresponding to the Lagrange interpolating polynomials in the element thickness direction. The resulting element displacement approximation has an important hierarchical property i.e. the approximation functions and the generalized nodal variables corresponding to an approximation order p are a subset of those corresponding to an approximation order (p + 1). The element formulation ensures C0 continuity or smoothness of displacements across the interelement boundaries.The element properties (stiffness matrix and equivalent load vectors) are derived using the principle of virtual work and the hierarchical element approximation. The formulation is extended for generally orthotropic material behaviour where the material directions are not necessarily parallel to the global axes. Further extension of this formulation for laminated composites is accomplished by incorporating the material properties of each lamina by numerically integrating the element stiffness matrix for each lamina. The formulation has no restriction on either the number of laminas or the layup pattern of the laminas. Each lamina can be generally orthotropic, and the material directions and the lamina thicknesses may vary from point to point within each lamina. The geometry of the laminated shell element is described by the co‐ordinates of the nodes lying on the middle surface of the element and the lamina thicknesses at each node. The formulation permits any desired order displacement or strain approximation in the shell thickness direction without remodelling.Numerical examples are presented to demonstrate the accuracy, efficiency, and overall superiority of the present formulation. The results obtained from the present formulation are compared with those available in the literature as well as the analytical solutions.
A robust self‐starting explicit computational methodology for structural dynamic applications: Architecture and representations
Authors: Tamma Kumar K. , Namburu Raju R. 
Published: August 2005

AbstractConventional approaches for computational structural dynamics (CSD) relevant to time‐integration methods involve first employing the classical Galerkin formulations for the spatial discretization to yield a set of ordinary differential equations in time and then employing finite difference approximations for deriving the appropriate step‐by‐step algorithms. And, almost all of the widely advocated (existing) step‐by‐step schemes for structural dynamics require an initial acceleration vector to be specified (evaluated) in addition to displacement and velocity vectors for starting the schemes. Unlike the above, in this paper we introduce new representations and architecture towards providing not only direct self‐starting features with the elimination of acceleration computations but also for enhancing the computational architecture itself via several other inherent distinguishing characteristics. Thereby, a robust and effective methodology of computation is presented which is an extension of our previous efforts (see Tamma and Namburu3). In particular, to illustrate the basic concepts, in this paper we focus attention on the development of explicit time‐integration formulations. The methodology involves expressing the governing dynamic equations of motion in conservation form, and firstly temporal discretization is accomplished in the spirit of Lax–Wendroff‐type formulations. Therein, discretization in space is accomplished by introducing stress‐based representations and employing the classical Galerkin scheme, and, quite naturally, we advocate employing finite elements as the principal computational tool because of its several inherent advantages. The stability and accuracy of the proposed formulations and the several added distinguishing features are briefly highlighted. Considerations on the effects of damping are additionally included and the introduction of general boundary conditions in a natural setting permits an effective generalized architecture for general applications. Numerical test models are presented to validate the overall developments for computational structural dynamics.
A finite element model for non‐linear shells of revolution with finite rotations
Authors: Wagner W. 
Published: August 2005

AbstractThe axisymmetric behaviour of geometrically non‐linear elastic shells of revolution with finite rotations is discussed. In contrast to the approach of Reissner and to standard classical shell theories a new straightforward strategy is derived for the formulation of fully non‐linear strain measures in the axisymmetric case. Within this approach the computation of the deformed director vector d is a main assumption which is essential to describe the fully non‐linear bending behaviour. A Total Lagrangian Description is chosen to represent the large displacements. As an illustrative example the finite element formulation for a simple two‐node conical element is given. A consistent linearization of the weak form leads to a quadratically convergence behaviour. The discussed shell examples under proportional loading show the good performance of the derived finite element formulation.
A numerical integration scheme for finite element method based on symbolic manipulation
Authors: Yagawa G. , Ye G.‐W. , Yoshimura S. 
Published: August 2005

AbstractThis paper is concerned with the improvement of the efficiency and accuracy of the usual numerical integration procedures for the finite element method. A modified numerical integration scheme based on both the symbolic manipulation system and the numerical integration formula is proposed. Its efficiency for the integration of complicated rational or irrational expressions is demonstrated through several numerical examples. To verify its effectiveness in the calculation of the finite element stiffness matrix, a simple numerical example is also presented.
Development of an automatic, two‐dimensional finite element mesh generator using quadrilateral elements and Bezier curve boundary definition
Authors: Talbert Jeffrey A. , Parkinson Alan R. 
Published: August 2005

AbstractThis paper describes the development of an automatic, two‐dimensional, quadrilateral element mesh generator. The methodology is based on the looping algorithm developed in part by Dr M. L. C. Sluiter. Bezier curves are used to define the boundaries of the parts to be meshed. The required interaction by the user is reduced to specifying the boundary geometry, the preferred element size and the refinement coefficient. Transition elements are automatically generated between regions of varying element sizes. The ability to offset specified boundary curves insures well‐conditioned elements along the boundary. Meshes for several sample geometries are presented to illustrate the versatility of the mesh generator.
Two‐level approximation concept in structural synthesis
Authors: Zhou M. , Xia R. W. 
Published: August 2005

AbstractA new concept for complex structural optimization problems is presented. Based on investigation of the mechanical nature of the studied problem, a set of basic mechanical characteristics can be introduced as the generalized variables. A high‐quality explicit first‐level approximate problem FA is formed by first‐order Taylor series expansion of the behaviour constraints in terms of the generalized variables. The FA is explicit but highly non‐linear with respect to design variables. Therefore, a second‐level approximation is introduced to solve the FA by considering a sequence of second‐level approximate problems SA in the design variable space. This approach is a Two‐Level Approximation Concept. Its application to space frame synthesis shows its good grasp of the mechanical nature of the problem. The computational results for several examples show that the method presented in this paper is very efficient.
On special points on load‐displacement paths in the prebuckling domain of thin shells
Authors: Mang H. A. 
Published: August 2005

AbstractPoints on load‐displacement paths of thin shells subjected to proportional loading, at which the second and/or the third derivative of the displacement components with respect to the load parameter vanishes, are termed ‘special points’. Such points represent global characteristics of the state of deformation of the shell in the sense that for the respective values of the load parameter the mentioned rate(s) of all displacement components at all points of the shell must vanish. It will be shown that special points on load‐displacement paths correspond to special points of one order lower on the Det KT–λ diagram, where Det KT is the determinant of the tangent stiffness matrix within the framework of the finite element method and λ is a dimensionless load parameter. Points of inflection on load‐displacement diagrams, for example, correspond to extreme values on the Det KT–λ diagram. The main reason for the occupation with special points on load‐displacement paths is that points of inflection and flat points on these paths correspond to special points on eigenvalue curves in the context of accompanying linear stability analyses of geometrically non‐linear prebuckling analyses of thin shells by the finite element method, investigated in a companion paper.
Exact block diagonalization of large eigenvalue problems for structures with symmetry
Authors: Healey T. J. , Treacy J. A. 
Published: August 2005

AbstractWe consider large eigenvalue problems for skeletal structures with symmetry. We present an algorithm, based upon a novel combination of group‐theoretic ideas and substructuring techniques, that block‐diagonalizes such systems exactly and efficiently. The procedure requires only the structural matrices of a repeating substructure, together with the symmetry modes, which are obtained from symmetry considerations alone. We first present a simple paradigmatic example and then follow with several non‐trivial applications involving large lattice structures.
Graded tetrahedral finite element meshes
Authors: Field David A. , Smith Warren D. 
Published: August 2005

AbstractVertices in the body centred cubic (bcc) lattice are used to create a tetrahedral spatial decomposition. With this spatial decomposition an octree approach is combined with Delaunay triangulations to decompose solids into tetrahedral finite element meshes. Solids must have their surfaces triangulated and the vertices in the triangulation are finite element nodes. Local densities of interior tetrahedra are controlled by the densities of surface triangles. Accuracy of the decomposition into finite elements depends on the accuracy of the surface triangulation which can be constructed with state of the art computer aided design systems.
Frictional contact problems of kinked cracks modelled by a boundary integral method
Authors: Zang W. L. , Gudmundson P. 
Published: August 2005

AbstractA numerical method is presented for the solution of two dimensional crack problems including the effects of crack kinks and frictional contact between crack faces. The metod is based on an integral equation for the resultant forces along a crack. Coulomb friction between contacting crack surfaces is taken into account. The numerical implementation is demonstrated by considerations of surface and sub‐surface piece‐wise straight line cracks in a half‐plane. Numerical results are presented to illustrate the efficiency and the reliability of the presented method.
A perturbation analysis and finite element approximate model for free surface flow over curved beds
Authors: Berger R. C. , Carey G. F. 
Published: August 2005

AbstractA perturbation analysis is developed for 1‐D shallow water flow over a curved bed for applications such as spillways. The perturbation approach leads to a new formulation of the problem with associated weak integral statement and approximation using finite elements. The flow may exhibit a hydraulic jump in the downstream regime. An artificial dissipation technique is introduced to stabilize the non‐linear problem and suppress numerical oscillations. Numerical results demonstrate the performance of the model and compare it with the steep‐slope shallow water formulation corresponding to the model with zero curvature.
An Eulerian approach for die compaction processes
Authors: Brekelmans W. A. M. , Janssen J. D. , Van De Ven A. A. F. , De With G. 
Published: August 2005

AbstractFor the analysis of deformation processes the Eulerian approach is usually formulated in material velocities. To describe the die compaction of compressible media, this paper presents an Eulerian simulation method, basically expressed in displacements. The material behaviour is modelled by the theory of elastoplasticity. Frictional interaction with the surroundings is included. As a spatially fixed finite element mesh is applied, rezoning is governed by the process specification and not, as in the Lagrangian approach, by the mesh distortion. The solution scheme, using a Newton‐Raphson algorithm, is considered in detail. A consistent iteration procedure is derived. Examples demonstrate the merits of the method developed.
The multiple Reciprocity boundary element method in elasticity: A new approach for transforming domain integrals to the boundary
Authors: Neves A. C. , Brebbia C. A. 
Published: August 2005

AbstractThis paper presents a new boundary element approach to transform domain integrals into equivalent boundary integrals. The technique, called the Multiple Reciprocity Method, is applied to 2‐D elasticity problems and operates on domain integrals resulting from different types of body forces such as gravitational and centrifugal forces, as well as loadings due to linear and quadratic temperature distributions. Numerical examples are presented to demonstrate the accuracy and efficiency of the method.
Simple and efficient shear flexible two‐node arch/beam and four‐node cylindrical shell/plate finite elements
Authors: Shi Guangyu , Voyiadjis George Z. 
Published: August 2005

AbstractSeveral simple and accurate C° two‐node arch/beam and four‐node cylindrical shell/plate finite elements are presented in this paper. The formulation used here is based on the refined theory of thick cylindrical shells and the quasi‐conforming element technique. Unlike most C° elements, the element stiffness matrix presented here is given explicitly. In spite of their simplicity, these C° finite elements posseses linear bending strains and are free from the deficiencies existing in curved C° elements such as shear and membrane locking, spurious kinematic modes and numerical ill‐conditioning. These finite elements are valid not only for thick/thin beams and plates, but also for arches/straight beams and cylindrical shells/plates. Furthermore, these C° elements can automatically reduce to the corresponding C1 beam and plate elements and give the C° beam element obtained by the reduced integration as a special case. Several numerical examples indicate that the simple two‐node arch/beam and four‐node cylindrical shell/plate elements given in this paper are superior to the existing C° elements with the same element degrees of freedom. Only the formulation of the rectangular cylindrical shell and plate element is presented in this paper. The formulation of an arbitrarily quadrilateral plate element will be presented in a follow‐up paper32.
Finite element formulations that include particular solutions of governing equations
Authors: Tabarrok B. , Xiong Y. 
Published: August 2005

AbstractThe correspondence between the homogeneous and particular solutions of differential equations and the related solutions of the discrete equations is brought to light in this study. Guided by this correspondence, the trial functions for finite elements are written in two parts—one the homogeneous and the other a prescribed particular solution. It is shown that this approach allows one to simplify the computations of element matrices and also yields better results, throughout the element, than those obtained by the conventional approach. Two simple examples are provided for illustration.
Scattering of elastic waves by a crack with spring‐mass contact
Authors: Hirose S. , Kitahara M. 
Published: August 2005

AbstractThe scattering problem of elastic waves by a crack with spring‐mass contact is investigated. Such a crack may be regarded as a simplified model of a thin elastic inclusion. Boundary integral equations are formulated for both displacement and traction on crack faces and are solved numerically. Numerical results are presented for stress intensity factors, crack‐opening displacements and scattering cross‐sections. Our results are in good agreement with other published solutions. It is also found that the effect of a mass can not be neglected in evaluation of scattering cross‐sections, even if the mass is small.
Geometrical representation and integration in BIE analysis
Authors: Walker S. P. 
Published: August 2005

AbstractBoundary representation by straight lines and circular arcs is described, and the error introduced through the common representation of circular arc boundaries by quadratic geometrical shape functions is investigated. This error is shown to be in some cases the major contributor to the total error. An even more significant advantage of exact boundary representation is that it permits many of the required integrations to be performed analytically, rather than by using Gaussian quadrature. For example, all integrations in any rectilinear domain can then be evaluated analytically. This generally produces an increase in accuracy, and a saving in the computing time required to assemble the coefficient matrices. In slender domains both this increase in accuracy and saving in computing time are very marked, as analytical integrations permit the use of very much coarser discretization than would be required for numerical quadrature.
Modified formulations for nine‐d.o.f. plane triangles that include vertex rotations
Authors: Cook Robert D. 
Published: August 2005

AbstractThis paper considers various procedures that yield improved stiffness matrices for plane triangular elements. Each element has nine d.o.f. and vertex nodes only. Some of the resulting elements are non‐classical constant strain triangles while others have more competent displacement fields. Numerical examples suggest that the nine‐d.o.f. element can either be formulated more efficiently or made more accurate, but probably not both at the same time.
Large deflection elastic‐plastic analysis of cylindrical shells using the finite strip method
Authors: Kumar Pravin , Olson M. D. , Anderson D. L. 
Published: August 2005

AbstractThe finite strip method is extended to the non‐linear, static analysis of cylindrical shells. Large deflection effects are incorporated via first‐order non‐linearities in the strain‐displacement relations, and material non‐linearities are included via the von Mises yield criteria and associated flow rule. Numerical results are presented for various example problems including the diaphragm supported cylindrical shell‐roof problem, an axisymmetric cylindrical shell loaded by radial pressure, the cylindrical shell‐roof problem with clamped curved ends and a pressure loaded cylindrical panel clamped all round. The results are compared with known results from analytical and/or finite element analyses. The results indicate that a single bending mode in the strip direction is sufficient in most cases to yield engineering accuracy for preliminary design purposes.
A design optimization procedure to minimize fillet bending stresses in an epicyclic gear system
Authors: Andrews J. D. 
Published: August 2005

AbstractThis paper presents the development of a design algorithm for epicyclic gear systems. The criterion on which the design performance is assessed is the maximum tensile stress induced in the fillets of the sun, planet and annulus gears. From an initial set of prescribed real and integer design parameters the finite element method is used to determine the maximum tensile fillet stresses in each gear. An objective function is formulated to represent the total stress in the system by combining the maximum fillet stresses in each component. A sequential procedure is then used to minimize the objective function subject to equality, inequality and integer function constraints.The finite element method is used to evaluate the stresses in the gear teeth and iterative application of the analysis and optimization stages converges to produce a design vector such that the maximum stress produced in all components of the system is minimized.Since the effectiveness of each design is assessed using the finite element method, the factorized stiffness matrix is reused to calculate the design derivatives. This makes the processes very efficient in its use of computer resources.
Closed form stiffness matrices and error estimators for plane hierarchic triangular elements
Authors: Lawrence Kent L. , Nambiar Rajiv V. , Bergmann Brad 
Published: August 2005

AbstractClosed form expressions for the stiffness matrix and a simple error estimator and error indicator are derived for plane straight sided triangular finite elements in elasticity problems. The calculation of the error estimator is performed on an element by element basis, and is found to be very accurate and efficient. In general, the solutions for benchmark problems using the error indicators for selective refinement of the regions show accelerated convergence when compared to the convergence rate of solutions using uniform mesh refinement. Evaluation of the stiffness matrices and error estimators using explicit formulations is found to be several times faster than numerical integration.