bluuebunny/crossref_metadata_2025_split huggingface dataset:
Structural dynamics analysis using an unsymmetric block Lanczos algorithm
Authors: Kim Hyoung M. , Craig Roy R. 
Published: August 2005

AbstractThis paper describes the way in which an unsymmetric block Lanczos algorithm can be employed for approximate eigensolutions or dynamic response solutions for large systems having arbitrary damping and/or repeated (or closely spaced) eigenvalues. To reduce a square, unsymmetric matrix which may have repeated eigenvalues to block‐tridiagonal form, an unsymmetric block Lanczos algorithm is developed. Right and left Lanczos vectors, generated by the reduction process, are employed to define the reduced‐order model based on a discrete analytical model of general linear, time‐invariant dynamic systems. A special type of starting vector is also introduced, which automatically includes the static displacement. This reduced‐order model is employed to compute approximate eigenvalues/vectors and dynamic responses of the original system. To verify the proposed algorithm, examples of an 8‐DOF beam‐rotor system are provided for eigensolutions and dynamic responses due to step and random external forces. These examples showed promising results, indicating that the proposed algorithm is worthy of further study.
Evaluation of the constant strain triangle with drilling rotations
Authors: Allman D. J. 
Published: August 2005

AbstractThe performance of the constant strain triangle with added ‘drilling’ rotations is evaluated by solving a variety of plane test problems. Numerical results confirm that the new element is always superior to the standard constant strain triangle and that it is of similar accuracy to the best available alternative triangular elements of other authors. It is, however, less accurate than some rectangular elements which include drilling rotations.
Some recent developments in numerical modelling of fracture toughness in brittle matrix composites
Authors: Hom C. L. , Mataga P. A. , McMeeking R. M. 
Published: August 2005

AbstractFinite element analysis was used to study the fracture toughening of a ceramic by a stress induced dilatant transformation of second phase particles. The finite element method was based on a continuum theory which modelled the composite as subcritical material. Transient crack growth was simulated in the finite element mesh by a nodal release technique. The crack's remote tensile opening load was adjusted to maintain the near‐tip energy release rate at the level necessary for crack advance. The transformation zone surrounding the crack developed as the crack propagated through the composite. Resistance curves were computed from the analysis; and the results show that during crack advance maximum toughness is achieved before a steady state is reached.The toughening effect of a crack‐bridging ductile phase in a brittle material may be predicted if ligament deformation is characterized. A plastically deforming ligament constrained by surrounding elastic matrix material is modelled using finite elements and the relevant toughness enhancement information extracted. Comparison is made to model experiments as well as to toughness measured for technologically important materials. The results suggest that debonding along the interface between the ligament and the matrix may enhance the toughening effect of a ductile phase.
Homogenization and pre‐integration techniques for multilayer composite and sandwich finite element models
Authors: Laschet G. , Jeusette J. P. , Beckers P. 
Published: August 2005

AbstractThe multilayer degenerated 3‐D shell element, for which the stiffness matrix is calculated by numerical integration ply by ply, gives accurate results even for moderately thick composite panels, but needs an important linear and non‐linear generation time when the number of plies is high (N > 10). In order to reduce this time some pre‐integration and homogenization techniques are investigated. Different pre‐integration methods have been reviewed and discussed. Then, two new homogenization methods, based on a series expansion of an equivalent Hooke matrix over the thickness, are presented. Next, simple numerical validation tests of these new methods are discussed, indicating necessary further investigations. Finally, a general discussion about the properties of the pre‐integration and homogenization techniques tends to define their respective application domain.
On refined computational models of composite laminates
Authors: Reddy J. N. 
Published: August 2005

AbstractFinite element models of the continuum‐based theories and two‐dimensional plate/shell theories used in the analysis of composite laminates are reviewed. The classical and shear deformation theories up to the third‐order are presented in a single theory. Results of linear and non‐linear bending, natural vibration and stability of composite laminates are presented for various boundary conditions and lamination schemes. Computational modelling issues related to composite laminates, such as locking, symmetry considerations, boundary conditions, and geometric non‐linearity effects on displacements, buckling loads and frequencies are discussed. It is shown that the use of quarter plate models can introduce significant errors into the solution of certain laminates, the non‐linear effects are important even at small ratio of the transverse deflection to the thickness of antisymmetric laminates with pinned edges, and that the conventional eigenvalue approach for the determination of buckling loads of composite laminates can be overly conservative.
Analysis of viscoelastic structural elements in the frequency domain
Authors: De Wilde W. P. , Cardon A. H. 
Published: August 2005

AbstractThe paper presents a formulation in the frequency domain for the viscoelastic material behaviour of structural elements. This approach is equally valid for deterministic forces, but also in the case of probabilistic descriptions of those forces. The method takes advantage of readily available experimental data and shows how to introduce them in e.g. finite element formulations.
A comparison of direct and preconditioned iterative techniques for sparse, unsymmetric systems of linear equations
Authors: Brussino Giacomo , Sonnad Vijay 
Published: August 2005

AbstractIn this paper we compare direct and preconditioned iterative methods for the solution of nonsymmetric, sparse systems of linear algebraic equations. These problems occur in finite difference and finite element simulations of semiconductor devices, and fluid flow problems.We consider five iterative methods that appear to be the most promising for this class of problems: the biconjugate gradient method, the conjugate gradient squared method, the generalized minimal residual method, the generalized conjugate residual method and the method of orthogonal minimization. Each of these methods was tested using similar preconditioning (incomplete LU factorization) on a set of large, sparse matrices arising from finite element simulation of semiconductor devices. Results are shown where we compare the computation time and memory requirements for each of these methods against one another, as well as against a direct method that uses LU factorization to solve these problems.The results of our numerical experiments show that preconditioned iterative methods are a practical alternative to direct methods in the solution of large, sparse systems of equations, and can offer significant savings in storage and CPU time.
Effective and practical h–p‐version adaptive analysis procedures for the finite element method
Authors: Zienkiewicz O. C. , Zhu J. Z. , Gong N. G. 
Published: August 2005

AbstractTwo practical and effective, h–p‐type, finite element adaptive procedures are presented. The procedures allow not only the final global energy norm error to be well estimated using hierarchic p‐refinement, but in addition give a nearly optimal mesh. The design of this is guided by the local information computed on the previous mesh. The desired accuracy can always be obtained within one or at most two h–p‐refinements.The rate of convergence of the adaptive h–p‐version analysis procedures has been tested for some examples and found to be very strong.The presented procedures can easily be incorporated into existing p‐ or h‐type code structures.
Crypto‐DOF finite elements
Authors: Kanarachos A. , Provatidis Ch. 
Published: August 2005

AbstractNew finite elements, called crypto‐DOF elements, are introduced, utilizing degrees of freedom that satisfy the differential equation but do not appear explicitly in the discrete equations. The crypto‐DOF elements can be advantageous in adaptive finite element techniques, and to approximate singular‐type eigensolutions (e.g. in convective diffusion or stress concentration problems) without altering the original mesh or introducing new degrees of freedom. In this paper the crypto‐DOF elements, the construction of crypto‐DOF element families and selected numerical results are presented.
Conforming boundary elements in plane elasticity for shape design sensitivity
Authors: Saigal Sunil , Aithal R. , Kane J. H. 
Published: August 2005

AbstractThe structural design sensitivity analysis of a two‐dimensional continuum using conforming (continuous) boundary elements is investigated. Implicit differentiation of the discretized boundary integral equations is performed to obtain design sensitivities in an efficient manner by avoiding the factorization of the perturbed matrices. A singular formulation of the boundary element method is used. Implicit differentiation of the boundary integral equations produces terms that contain derivatives of the fundamental solutions employed in the analysis. The behaviour of the singularity of these derivatives of the boundary element kernel functions with respect to the design variables is investigated. A rigid body motion technique is presented to obtain the singular terms in the resulting sensitivity matrices, thus avoiding the problems associated with their numerical integration. A formulation for obtaining the design sensitivities of the continua under body forces of the gravitational and centrifugal types is also presented. The design sensitivity results are seen to be of the same order of accuracy as the boundary element analysis results. Numerical data comparing the performance of conforming and non‐conforming formulations in the calculation of design sensitivities are also presented. The accuracy of the present results is demonstrated through comparisons with existing analytical results.
Partial hybrid stress element for the analysis of thick laminated composite plates
Authors: Jing Hung‐Sying , Liao Ming‐Liang 
Published: August 2005

AbstractA new element—a partial hybrid stress element—is proposed in this paper for the analysis of thick laminated composite plates. The variational principle of this element can be derived from the Hellinger–Reissner principle through dividing six stress components into a flexural part (σx, σy, σxy, σz) and a transverse shear part (τxy, τyz). The element stiffness matrix can be formulated by assuming a stress field only for transverse shear stresses, while all the others are obtained from an assumed displacement field. Consequently, this new element combines the benefits of the conventional displacement method and the hybrid stress method. A twenty‐node hexahedron element is employed in each layer for the displacement field. For the assumed transverse shear stress field, only the traction‐free boundary conditions and interface traction continuity are satisfied. The equilibrium equation is enforced by the variational principle. Hence, the complicated work of searching an equilibrating stress field for all the six stress components in the hybrid stress method can be avoided. Furthermore, the interlaminar traction discontinuity, especially transverse shear, encountered by the conventional displacement method and higher‐order plate element for laminated plate analysis can also be overcome. Examples are illustrated to demonstrate the accuracy and efficiency of this proposed partial hybrid stress element.
A geometrically non‐linear tensorial formulation of a skewed quadrilateral thin shell finite element
Authors: Yang Henry T. Y. , Wu Y. C. 
Published: August 2005

AbstractA 48‐degree‐of‐freedom (d.o.f.) skewed quadrilateral thin shell finite element, including the effect of geometrical non‐linearity, is formulated and appropriate numerical procedures are adopted for the development of an efficient approach for the static and dynamic analysis of general thin shell structures. The element surface is described by a variable‐order polynomial in curvilinear co‐ordinates. The displacement functions are described by bicubic Hermitian polynomials in curvilinear co‐ordinates. The directions of the curvilinear co‐ordinates at each nodal point are uniquely defined to coincide with the directions of the boundaries of the element. In the present case of a skewed quadrilateral with non‐orthogonal curvilinear coordinates, the coupling terms of the metric tensor and curvature tensor of the surface no longer vanish, such as in the case of orthogonal co‐ordinates. The tensor form is used in the setup of the shape functions, geometric derivatives, stiffness matrix and computer code. This allows for the treatment of shells with irregular shapes and variable curvatures. To evaluate the efficiency and accuracy of this formulation, a systematic list of examples is chosen: (i) linear and non‐linear static analysis of square and rhombic plates, cylindrical and spherical shells; (ii) linear vibrations of trapezoidal flat and curved plates; (iii) large amplitude vibrations of a rhombic plate. For the square plate and cylindrical and spherical shell, shewed element meshes with various distortion angles are used to study the effect of the distortion angles on the accuracy of the results and to demonstrate the versatility of the present element. All results are compared with alternative available solutions including those obtained using regular rectangular meshes. Pinched thin cylindrical and spherical shells are studied using different skewed meshes and various Gauss integration meshes, and no membrane locking phenomenon is observed.
Fast algorithm for assembling blocks of global equations in FE programs
Authors: Ondris Ľubomír 
Published: August 2005

AbstractA new method for assembling blocks of global equations in FE programs is presented. The method has been implemented in SAP IV, the well‐known FE program.The new assembling process consists of two phases. First, for each pair of blocks, the numbers of active elements are determined in ascending order. Then, from the sequential file containing element matrices, active records only are read and processed, the non‐active ones being skipped.The most important features of the new method as compared to the method previously used are the following: (i) it saves up to 2/3 of the CPU‐time for assembling, (ii) the amount of data on an auxiliary file is negligible, (iii) it does not require any additional high speed storage, (iv) it can be directly applied in any FE program with blocks using the constant bandwidth row storage scheme, (v) after some modifications it can be applied also in FE programs with blocks using the skyline column storage scheme.The full source code in FORTRAN IV is given in Appendix II.
Hypersingular integrals in boundary element fracture analysis
Authors: Gray L. J. , Martha Luiz F. , Ingraffea A. R. 
Published: August 2005

AbstractA new general purpose boundary element method for domains with cracks has been recently developed. This technique avoids the use of a multi‐domain decomposition by including an additional integral equation expressing the boundary condition on the crack. The principal requirement of this technique is the analytic determination of certain hypersingular integrals of the Green's function which arise from this equation. In order to establish the applicability of this method for fracture, these integrals are evaluated herein for the Kelvin solution of the three‐dimensional Navier equations of linear elasticity. Numerical results for fracture problems using the single‐domain boundary element analysis are also presented.
Tangent constitutive matrices for inelastic finite element analysis
Authors: Riggs H. R. , Powell G. H. 
Published: August 2005

AbstractA general formulation is presented for the tangent constitutive matrices of rate‐independent material models which assume that the strain increment consists of two components. One component is related to the stress increment through a known constitutive matrix, while the other component results from deformation mechanisms not reflected in the constitutive matrix. The procedure to modify the known matrix for these additional strains is specified. The formulation is a generalization of the well‐known procedure used in plasticity to modify the elastic constitutive matrix for plastic deformation. Application to both the classical and endochronic theories of plasticity and to a smeared crack theory is illustrated.
Effects of spatial discretization on dispersion and spurious oscillations in elastic wave propagation
Authors: Jiang Lei , Rogers Robert J. 
Published: August 2005

AbstractThe dispersive and spurious oscillation properties of one‐dimensional uniform finite element meshes are investigated using the information provided by the frequency response functions of the finite element meshes. The modal superposition method, in which the effects of temporal discretization are eliminated, is employed to integrate the discretized equations of motion. Compared with the commonly used complex variable method, this approach reveals more clearly the physical essence of the dispersion and spurious oscillation phenomena. A series of interesting results is obtained.
An efficient L2 Galerkin finite element method for multi‐dimensional non‐linear hyperbolic systems
Authors: Bar‐Yoseph Pinhas , Elata David 
Published: August 2005

AbstractAn L2 Galerkin approximation is obtained by the use of specially chosen spaces of trial and test functions. The method combines the features of the orthogonal collocation and Galerkin finite element methods. This new algorithm can be more efficient by orders of magnitude than conventional discontinuous Galerkin finite element procedures in solving non‐linear problems which require frequent reformulation of the coefficient matrices and right‐hand‐side vectors.
A boundary element algorithm using compatible boundary displacements and tractions
Authors: Piltner R. , Taylor R. L. 
Published: August 2005

AbstractWith the aid of Muskhelishvili's complex plane elasticity solution representation compatible displacement and stress fields are constructed. The complex functions in these formulas are represented by Cauchy integrals, which are discretized along the boundary with the aid of complex shape functions for each boundary element. The constructed displacement and stress functions satisfy the Navier equations and the equilibrium equations, respectively. The use of fifth order complex basis functions with continuous second complex derivatives gives numerical results of high accuracy.
Least‐squares characteristics and finite elements for advection–dispersion simulation
Authors: Li C. W. 
Published: August 2005

AbstractThe method of characteristics is combined with the method of least‐squares to solve the advection equation within the finite element framework. Fourier mode analysis shows that the numerical scheme is stable and accurate even when a linear basis function is used. However, in practical application, the involvement of using numerical quadrature in this method can produce numerical instability, depending on the value of the Courant number used. It is found that using C1 continuous Hermitian cubic basis functions in the scheme reduces the degree of instability significantly and produces high accuracy. When being used in a split‐operator approach, this method combines naturally with the standard finite element method and results in a highly accurate scheme for advection–dispersion simulation.
Advanced time‐domain formulation of BEM for two‐dimensional transient elastodynamics
Authors: Israil A. S. M. , Banerjee P. K. 
Published: August 2005

AbstractIn this paper, a new formulation for two‐dimensional time‐domain transient elastodynamic analysis by the Boundary Element Method (BEM) is presented. The traction kernel is derived by using the causality of the waves and the resulting kernel is explicit and much simpler than the ones that have appeared in the recent literature. An appropriate set of linear time interpolation functions together with quadratic spatial variations are incorporated. Moreover, the algorithm has a capability of handling problems with multiply connected regions. All of these advanced features have resulted in an efficient formulation capable of producing very accurate results and represent significant improvements over the present level of sophistication in this area. This above algorithm is now a part of the general purpose BEM code known as GPBEST.
On the use of one point and two points singularity elements in the analysis of kinked cracks
Authors: Dutta B. K. , Maiti S. K. , Kakodkar A. 
Published: August 2005

AbstractA 3‐noded triangular two singular points finite element is proposed to model two variable order singularities lying at close proximities as in the case of a kinked crack. The element meets the rigid body mode and the interelement compatibility of the convergence criteria. A degenerate form of the element is a one point variable order singularity element, which meets all the convergence requirements. A number of kinked crack problems have been analysed using the new element and its degenerate form. The computed results are compared with analytical solutions. The accuracy of the results is found to be good.
The numerical simulation of electron transmission through a two‐dimensional quantum device by the finite element method
Authors: Kirkner David J. , Lent Craig S. , Sivaprakasam Srinivas 
Published: August 2005

AbstractIn this paper we present a method for numerically solving the Schrödinger equation for the problem of electron transmission through a quantum device defined on a two‐dimensional domain. An important aspect of our formulation is the treatment of the boundary conditions at the contact–device interfaces, allowing the problem to be discretized on the device domain only. With the FEM aproach that we employ, the nature of the potential field does not effect the computational expense (for smoothly varying fields). We examine a sample problem of a symmetric cavity in a wave‐guide structure.
A class of mixed assumed strain methods and the method of incompatible modes
Authors: Simo J. C. , Rifai M. S. 
Published: August 2005

AbstractA three‐field mixed formulation in terms of displacements, stresses and an enhanced strain field is presented which encompasses, as a particular case, the classical method of incompatible modes. Within this frame‐work, incompatible elements arise as particular ‘compatible’ mixed approximations of the enhanced strain field. The conditions that the stress interpolation contain piece‐wise constant functions and be L2‐ortho‐gonal to the enhanced strain interpolation, ensure satisfaction of the patch test and allow the elimination of the stress field from the formulation. The preceding conditions are formulated in a form particularly convenient for element design. As an illustration of the methodology three new elements are developed and shown to exhibit good performance: a plane 3D elastic/plastic QUAD, an axisymmetric element and a thick plate bending QUAD. The formulation described herein is suitable for non‐linear analysis.