bluuebunny/crossref_metadata_2025_split huggingface dataset:
An implicit time integration scheme for inelastic constitutive equations with internal state variables
Authors: Cordts Detlef , Kollmann Franz G. 
Published: August 2005

AbstractIn a broad class of inelastic constitutive models for the deformation of metals the inelastic strain rates are functions of the current state of stress and internal state variables only. All known models are in some regions of application mathematically stiff and therefore difficult to integrate. The unconditionally stable implicit Euler rule is used for integration. It leads to a system of highly nonlinear algebraic equations which have to be solved by an iterative process. The general Newton‐Raphson method, which converges under very broad conditions, requires repeated solution of the finite element system and is infeasible for large inelastic problems. But for the inelastic strains and internal state variables the Jacobian can be computed analytically and therefore the NRI can be used. For the stresses the Jacobian cannot be computed analytically and therefore the accelerated Jacobi iteration is used. A new method for computing the relaxation parameter is introduced which increases the rate of convergence significantly. The new algorithm is applied on Hart's model. A comparison with prior computations using an approximation is made.
Hybrid stress reduced‐Mindlin elements for thin multilayer plates
Authors: Spilker R. L. , Jakobs D. M. 
Published: August 2005

AbstractA hybrid‐stress formulation of isoparametric elements for the analysis of thin multilayer laminated composite plates is presented. The element displacement behaviour is characterized by laminate reference surface inplane and transverse displacements and laminate non‐normal cross‐section rotations; as a result, simple Co interpolation of displacement and rotation can be used, and the number of degrees‐of‐freedom is independent of the number of layers. All components of stress are included and are related to a set of laminate stress parameters, the number of which is independent of the number of layers. Attention is restricted here to thin laminates, for which it is shown that the contributions of transverse shear stress and transverse normal stress to the internal complementary energy can be neglected. As a result of this reduction, a modified stiffness‐formation algorithm can be used which provides a significant improvement in computational efficiency. The formulation presented is used to develop an 8‐node isoparametric thin multilayer plate element. The resulting element is naturally invariant, of correct rank, and non‐locking in the thin plate limit.
Exact eigenvalue calculations for structures with rotationally periodic substructures
Authors: Williams F. W. 
Published: August 2005

AbstractThe theory presented enables rotationally periodic (i.e. cyclically symmetric) three‐dimensional substructures to be included when using existing algorithms to ensure that no eigenvalues are missed when the stiffness matrix method of structural analysis is used, where the eigenvalues are the natural frequencies of undamped free vibration analyses or the critical load factors of buckling problems. A substructure can be connected in any required way to a parent structure which shares its rotational periodicity, or can be connected by nodes at each end of its axis of periodicity to any parent structure, i.e. the parent structure need not be periodic. The theory uses complex arithmetic, involves only one of the rotationally repeating portions of the substructure, allows nodes and members to coincide with the axis of rotational periodicity, permits efficient multi‐level use of rotationally periodic substructures, and gives ‘exact’ eigenvalues if the member equations used are those obtained by solving appropriate differential equations. The competitiveness of the method is illustrated by approximate predictions of computation times and savings for two structures which contain rotationally periodic substructures.
Solution of two‐point boundary value problems using splines
Authors: Tewarson R. P. , Zhang Yin 
Published: August 2005

AbstractCubic spline on quintic spline interpolations are used to approximate the derivative terms for use in two high order numerical schemes for the solution of two‐point boundary value ordinary differential equations. The use of splines leads to solutions that reflect the smoothness of the slopes of the differential equations. Results of some computational experiments are given.
A field consistent three‐noded quadratic curved axisymmetric shell element
Authors: Prathap G. , Babu C. Ramesh 
Published: August 2005

AbstractA curved three‐noded quadratic isoparametric axisymmetric thick shell element is developed. Field‐consistency interpretations allow various configurations of the element to be designed so as to satisfy specific problem needs. Typical applications demonstrate the versatility and accuracy of this element in its different problem‐specific forms.
Finite deformation post‐buckling analysis involving inelasticity and contact constraints
Authors: Simo J. C. , Wriggers P. , Schweizerhof K. H. , Taylor R. L. 
Published: August 2005

AbstractThis paper is concerned with the numerical solution of large deflection structural problems involving finite strains, subject to contact constraints and unilateral boundary conditions, and exhibiting inelastic constitutive response. First, a three‐dimensional finite strain beam model is summarized, and its numerical implementation in the two‐dimensional case is discussed. Next, a penalty formulation for the solution of contact problems is presented and the correct expression for consistent tangent matrix is developed. Finally, basic strategies for tracing limit points are reviewed and a modification of the arc‐length method is proposed. The good performance of the procedures discussed is illustrated by means of numerical examples.
p‐adaptive boundary elements
Authors: Alarcon E. , Reverter A. 
Published: August 2005

AbstractThis paper presents the implementation of an adaptive philosophy to plane potential problems, using the direct boundary element method. After some considerations about the state of the art and a discussion of the standard approach features, the possibility of separately treating the modelling of variables and their interpolation through hierarchical shape functions is analysed. Then the proposed indicators and estimators are given, followed by a description of a small computer program written for an IBM PC. Finally, some examples show the kind of results to be expected.
Effect of rotary inertia on vibration of tapered beams
Authors: Gupta Arvind K. 
Published: August 2005

AbstractRotary inertia and dynamic‐correction rotary inertia matrices for a linearly tapered beam element of any cross‐sectional shape are derived in explicit form. Exact expressions for the required displacement functions are used in the derivation of these matrices. Variation of area and moment of inertia of the cross‐section along the axis of the element are exactly represented by simple functions involving shape factors. Vibration analysis results of a tapered cantilever beam of I‐section, obtained with and without the rotary inertia matrices are compared and effect of rotary inertia on vibration of tapered beams discussed.
Dynamic stress intensity factors studied by boundary integro‐differential equations
Authors: Sládek J. , Sládek V. 
Published: August 2005

AbstractThe boundary integro‐differential equation method is illustrated by two numerical examples concerning the study of the dynamic stress intensity factor around a penny‐shaped crack in an infinite elastic body. Harmonic and impact load on the crack surface has been considered. Applying the Laplace transform with respect to time to the governing equations of motion the problem is solved in the transformed domain by the boundary integro‐differential equations. The Laplace transformed general transient problem can be used to solve the steady‐state problem as a special case where no numerical inversion is involved.
Modelling of radiation damping in fluids by finite elements
Authors: Sharan Shailendra K. 
Published: August 2005

AbstractA very efficient technique is presented to model the effects of radiation damping in the computation of added mass for the dynamic analysis of submerged structures. The structure is assumed to be surrounded by an infinite, incompressible and inviscid fluid field and the effect of the free surface is neglected. The technique is implemented in the finite element analysis of two‐dimensional problems, assuming pressure to be the nodal unknown. The implementation procedure is quite simple and the symmetrical and banded form of the matrix of coefficients remains unchanged. With the use of the proposed radiation condition, the fluid field may be truncated at a relatively very short distance from the solid—fluid interface. This results in great computational advantages. Furthermore, a guideline is suggested for the selection of the geometry and the location of the truncation boundary to enhance the computational efficiency. The effectiveness and efficiency of the technique is demonstrated by analysing several cases for different geometries of the solid—fluid interface and the truncation boundary.
Finite layer analysis of layered elastic materials using a flexibility approach. Part 2—Circular and rectangular loadings
Authors: Small J. C. , Booker J. R. 
Published: August 2005

AbstractThe finite layer techniques introduced in Part 1 of this paper are extended to allow the analysis of circular or general loadings applied to horizontally layered anisotropic materials. The analysis is considerably simplified through the use of Hankel transforms (circular loadings) and double Fourier transformations (general loadings).Once again an exact flexibility matrix is found for each finite layer, and it is shown that this flexibility matrix has precisely the same form whether the loading is a strip, circular or general loading. The flexibility matrix has the advantage of not becoming singular for incompressible materials as is the case for the stiffness matrices used in a conventional finite strip analysis.Examples are given of the behaviour of circular and general (rectangular) loadings applied to multilayered anisotropic materials. It is also shown by means of an example, that the method is extremely useful for analysis of problems involving incompressible materials.
A finite element and experimental study of rigid‐plastic compression
Authors: Houlston R. , Vickers G. W. , Anderson D. L. 
Published: August 2005

AbstractThis paper is concerned with the effect of material properties, boundary friction, and inertia on the flow and strain patterns in material undergoing large plane strain compression. Experimental results are presented for both the rapid compression of Plasticine and the quasi‐static compression of aluminium. In addition, a finite element code for rigid‐plastic material behaviour is discussed, and approximate procedures are described for both in‐plane and platen friction. Provision in the code was also made for strain hardening and strain rate sensitive material properties, and inertia effects. Comparison of the finite element and experimental results showed good agreement. Finite element calculations revealed that in‐plane friction had a very significant effect on the strain patterns observed in the Plasticine experiments. Finite element calculations also showed that strain hardening was of fundamental importance in determining the strain patterns that were observed to occur in the quasi‐static compression of aluminium.
Failures of local approximation in finite‐element methods
Authors: Kurtze Douglas A. 
Published: August 2005

AbstractIt is shown that standard finite‐element discretizations of second‐order differential equations (i.e. Galerkin and subdomain methods) using conforming linear elements may fail to approximate the original equation locally if the finite‐element grid is irregular or if subdomains are chosen improperly. This failure of local approximation can lead to spurious computational results when subdomain methods are used, but these difficulties can be averted by a judicious choice of subdomains. The conditions which the subdomains must satisfy in order for local approximation to hold are derived and used to construct an algorithm for choosing them properly. The relation of these local results to the global convergence properties of the Galerkin method is discussed.
Dynamic response of rigid strip‐foundations by a time‐domain boundary element method
Authors: Spyrakos C. C. , Beskos D. E. 
Published: August 2005

AbstractThe dynamic response of rigid strip‐foundations placed on or embedded in a homogeneous, isotropic, linear elastic half‐space under conditions of plane strain to either external forces or obliquely incident seismic waves of arbitrary time variation is numerically obtained. The above mixed boundary‐value problems are treated by the time domain boundary element method which is used in a step‐by‐step timewise fashion to provide the foundation response to a rectangular impulse. Numerical examples are presented in detail to demonstrate the use and importance of the proposed method. The method appears to be more advantageous than frequency domain techniques, because it provides the transient foundation response in a natural and direct way and can form the basis for extension to the non‐linear case.
Wave propagation in anisotropic layered media
Authors: Kausel Eduardo 
Published: August 2005

AbstractThe determination of the natural modes of wave propagation in an anisotropic layered medium requires the solution of a transcendental eigenvalue problem that is usually approached numerically with the aid of search techniques. Such computations require great effort. The method presented in this paper provides an alternate solution to this problem in terms of a quadratic eigenvalue problem involving tridiagonal matrices, for which the eigenvalues can be found with great speed and accuracy. The technique is then illustrated by means of an example involving a cross‐anisotropic Gibson solid.
A solution of the eigenproblem for undamped gyroscopic systems with the Lanczos algorithm
Authors: Bauchau O. A. 
Published: August 2005

AbstractThis paper presents an efficient numerical solution of the quadratic eigenproblem arising in the analysis of gyroscopic systems. Such problems are known to reduce to a generalized linear eigenproblem defined by two real non‐singular matrices, one symmetric and one skew‐symmetric. For this class of problems, the general Lanczos algorithm for unsymmetric matrices is shown to simplify considerably and yields an efficient solution of the problem. Full advantage can be taken of the sparsity of the matrices and of the specific nature of gyroscopic systems. Numerical examples are presented, which demonstrate the efficiency and accuracy of the solution procedure.
Finite element method for non‐linear forced vibrations of circular plates
Authors: Decha‐Umphai Kamolphan , Mei Chuh 
Published: August 2005

AbstractGeometric non‐linearities for large amplitude free and forced vibrations of circular plates are investigated. In‐plane displacement and in‐plane inertia are included in the formulation. The finite element method is used. An harmonic force matrix for non‐linear forced vibration analysis is introduced and derived. Various out‐of‐plane and in‐plane boundary conditions are considered. The relations of amplitude and frequency ratio for different boundary conditions and various load conditions are presented.
A boundary element method for determining the effect of holes on the stress distribution around a crack
Authors: Ang W. T. , Clements D. L. 
Published: August 2005

AbstractA boundary integral procedure is obtained for examining the effect of a finite number of holes on the crack tip stress intensity factors for a plane crack in a homogeneous anisotropic elastic material. Numerical results for specific examples involving a transversely isotropic material are given.
Comparison of finite element techniques for solidification problems
Authors: Dalhuijsen A. J. , Segal A. 
Published: August 2005

AbstractThe accuracies of the computed temperatures of a liquid in a corner region under freezing conditions are compared for various fixed‐grid finite element techniques using the analytical solution for this problem as a reference.In the finite element formulation of the problem different time‐stepping schemes are compared: the implicit Euler‐backward algorithm combined with an iterative scheme and two three‐time‐level methods—the Lees algorithm and a Dupont algorithm, which are both applied as non‐iterative schemes.Furthermore, different methods for handling the evolution of latent heat are examined: an approximation method suggested by Lemmon and one suggested by Del Giudice, both using the enthalpy formulation as well as a fictitious heat‐flow method presented by Rolph and Bathe.Results of calculations performed with the consistent heat‐capacity matrix are compared with those performed with a lumped heat‐capacity matrix.
A time—memory trade‐off frontwidth reduction algorithm for finite element analysis
Authors: Webb J. P. , Froncioni A. 
Published: August 2005

AbstractA frontwidth reduction algorithm is presented with an execution time which may be traded against its primary memory requirement, making it possible to optimize the performance of the algorithm on a particular computer. With an amount of primary memory O(E1/2), where E is the number of elements, the execution time of the algorithm is O(E3/2), in two or three dimensions. The algorithm has two parts: first, new node‐based data structures are derived from the conventional element list, then these structures are used to reorder the elements for reduced frontwidth.
A sixth‐order multiderivative method for two beam problems
Authors: Twizell E. H. , Tirmizi S. I. A. 
Published: August 2005

AbstractA sixth‐order method is developed and analysed for the numerical solution of the linear fourth‐order boundary value problem for which the boundary conditions are given in terms of functional values and (i) first‐order derivatives (the clamped‐clamped beam problem) or (ii) second‐order derivatives (the simple‐simple beam problem). The method is tested on a number of problems from the literature.
Grid optimization for the boundary element method
Authors: Ingber Marc S. , Mitra Ambar K. 
Published: August 2005

AbstractThe quality of solution obtained using the boundary element method (BEM) is dependent on how the boundary is discretized. This is particularly true in domains of complex geometry. A rule for grid optimization for the BEM is derived on the bases of an asymptotic measure of the boundary element error that preserves the number of elements (degrees of freedom). Three example problems are provided to show the advantages of grid optimization in terms of accuracy and cost.
Concurrent Cholesky factorization of positive definite banded Hermitian‐matrices
Authors: Utku S. , Salama M. , Melosh R. J. 
Published: August 2005

AbstractFirst the Cholesky factorization is extended to cover uniformly partitioned banded positive definite matrices of rank n which may be real symmetric or Hermitian. Then two stratagems are given for the use of the algorithm in concurrent machines where the number of processing elements is less than required to factor the matrix in as few serial steps as possible, and where uniformly high efficiency is expected from all processing elements. Expressions are given for the efficiency factor e appearing in the speed‐up expression g = eN, and these are specialized for the N node hypercube machine as a function of partition size s, the number N of processing elements of the hypercube machine, and the cost μ of interelement transmission relative to computation. It is shown that efficiency factor e is inversely proportional to μ/s, and that e is almost independent of N when N is large and μ/s = 0. The task is completed in n/s serial steps with no limit on n. The half bandwidth b of the matrix is 2Ns.
Parallel solution of closely coupled systems
Authors: Utku S. , Salama M. 
Published: August 2005

AbstractThe odd—even permutation and associated unitary transformations for reordering the matrix coefficient A is employed as a means of breaking the strong seriality which is characteristic of closely coupled systems. The nested dissection technique is also reviewed, and the equivalence between reordering A and dissecting its network is established. The effect of transforming A with odd—even permutation on its topology and the topology of its Cholesky factors is discussed. This leads to the construction of directed graphs showing the computational steps required for factoring A, their precedence relationships and their sequential and concurrent assignment to the available processors. Expressions for the speed‐up and efficiency of using N processors in parallel relative to the sequential use of a single processor are derived from the directed graph. Similar expressions are also derived when the number of available processors is fewer than required.
Performance of some SQP algorithms on structural design problems
Authors: Thanedar P. B. , Arora J. S. , Tseng C. H. , Lim O. K. , Park G. J. 
Published: August 2005

AbstractThis paper describes the basic ideas of sequential quadratic programming (SQP) algorithms for design optimization. There are two fundamental differences between the various algorithms: (i) the difinition of the QP subproblem solved at each iteration, and (ii) the descent function used during step size determination. The performances of the algorithms can change dramatically depending on how the two steps are executed. Numerical implementation details of various computational steps are discussed. Three programs based on SQP algorithms are used to solve 17 structural design problems having 7 to 96 design variables and 10 to 1051 performance constraints besides design variable bounds. Based on the performance of these programs, efficient procedures to execute various steps of the SQP methods are determined. It is concluded that the potential constraint strategy, where only a subset of the constraints is used to define the QP subproblem, is essential for large scale engineering design applications. With this strategy the SQP methods are quite robust and have great potential for routine application in engineering design.
Gradients of behaviour constraints and reanalysis via the integrated force method
Authors: Patnaik S. N. , Gallagher Richard H. 
Published: August 2005

AbstractA matrix formulation of structural analysis, known as the integrated force method (IFM) is an attempt to establish an approach in which internal forces are the unknowns. Gradients of such behaviour constraints as stress, displacement and frequency can be obtained in closed form via the IFM. Closed form reanalysis formulae can also be generated. Computational experiments reported here show that reanalysis and gradient generation can be performed efficiently by this approach.