bluuebunny/crossref_metadata_2025_split huggingface dataset:
Contact forces in the non‐linear dynamic analysis of tracked vehicles
Authors: Nakanishi Toshikazu , Shabana A. A. 
Published: August 2005

AbstractIt is known that when two springs are connected in series, the stiffness coefficient of an equivalent system that consists of one spring is less than the stiffness coefficients of the original springs. Experimental observations indicate that this fact can be very useful in determining the overall vibration characteristics of tracked vehicles. This simple fact is used in this investigation to develop a computer aided analysis procedure for the dynamic simulation of large‐scale tracked vehicles. The track is considered as a closed kinematic chain that consists of rigid bodies connected by revolute joints. The contacts between the track links and the rollers, the sprocket, and the idler are represented by non‐linear continuous force models. The stiffness and damping coefficients in these contact force models are determined by studying the viberation characteristics of the tracked vehicle. The tooth of the sprocket is defined using three surfaces. These are the left, the bottom, and the fight surfaces. Three successive transformations are used to define the contact kinematic relationships between the sprocket teeth and the pins of the track links. The equations of motions of the vehicle are formulated using the Lagrangian approach. Non‐linear constraint equations that describe mechanical joints and specified motion trajectories in the system are adjoined to the differential equations of motion using the technique of Lagrange multipliers. The resulting mixed system of differential and algebraic equations is solved numerically using a direct numerical integration method. A Newton–Raphson algorithm is used to check on the violations in the kinematic constraints. The results presented in this paper are obtained using a 54 body planer tracked vehicle in which the track consists of 42 rigid links connected by revolute joints.
An iterative solution scheme for systems of boundary element equations
Authors: Davey K. , Rosindale I. 
Published: August 2005

AbstractIn this paper an iterative scheme of first order is developed for the purpose of solving linear systems of equations. In particular, systems that are derived from boundary integral equations are investigated. The iterative schemes to be considered are of the form Ex(k+1) = Dx(k) + d, where E and D are square matrices. It will be assumed that E is a lower matrix, i.e. the coefficients above the central diagonal are zero. It will be shown that by considering matrix D embedded in a vector space and reducing its size with respect to a chosen metric, that convergence rates can be substantially improved. Equation ordering and parameter matrices are used to reduce the magnitude of D. A number of examples are tested to illustrate the importance of the choice of metric, equation ordering and the parameter matrix. Computation times are determined for both the iterative procedure and Gauss elimination indicating the usefulness of iteration which can be orders of magnitude faster.
The monomial method: Extensions, variations, and performance issues
Authors: Burns Scott A. 
Published: August 2005

AbstractThe monomial method solves systems of non‐linear algebraic equations by constructing a sequence of approximating monomial (single‐term polynomial) systems, much as Newton's method generates a sequence of linear systems to do this. Since the monomial system becomes linear through a logarithmic transformation of variables, the monomial method can be considered to be an alternative linearization scheme. Although the monomial method is closely related to Newton's method, it exhibits many special invariance properties not shared by Newton's method that enhance performance. This paper first briefly reviews the monomial method and its special properties. Two new versions of the algorithm are presented, both of which, are simplified and computationally more efficient to implement in comparison to the original algorithm. The monomial method is also extended to apply to certain non‐algebraic systems. Since the monomial method can be interpreted as Newton's method applied to a three‐part reformulation of the algebraic system, graphical experiments are presented which investigate the role that each part of the reformulation plays in contributing to the enchanced performance. Finally, instances in which difficulties have arisen using the monomial method are discussed.
An intrinsic beam model based on a helicoidal approximation—Part II: Linearization and finite element implementation
Authors: Borri Marco , Bottasso Carlo 
Published: August 2005

AbstractThe helicoidal beam model developed in the first part of this work is applied here to the development of a mixed finite element for space‐curved and twisted beams undergoing large displacements and finite rotations. Starting from the governing weak form expressed by the principle of virtual work, a consistent linearization is obtained in the following and a novel updated Lagrangian finite element implementation is thoroughly discussed.The unique features and the distinguishing properties previously claimed for the helicoidal model are shown here to imply remarkable numerical consequences. For this purpose, meaningful example problems regarding the non‐linear static response of beams are addressed in the following and the results are compared with those available from the literature.Furthermore, a finite element in time for the rigid body dynamic problem is developed within the framework of the helicoidal geometry. The underlying philosophy of this novel finite element for dynamics is the realization of the helicoidal decomposition of the rigid body motion within a time step.
Instantaneous response of elastic thin‐walled structures to rapid heating
Authors: Chen Xiaoqin , Mohan Ram V. , Tamma Kumar K. 
Published: August 2005

AbstractA generalized modelling and analysis approach of thermally induced coupled vibrations of elastic thin‐walled configurations with arbitrary open cross‐sections are presented in conjunction with a unified implicit transient methodology. Limited research which takes into account the influence of rapid thermal heating effects on structures involving various forms of coupling appears in the literature. As a consequence, the dynamic response of such thin‐walled structures of arbitrary open cross‐section to rapid heating are described here. Effects involving triple, double, and no coupling between bending and torsional vibrations caused by sudden heating on these structures are examined. Numerical test cases are presented which describe the influence of sudden heating on elastic thin‐walled structures of arbitrary open cross‐sections.
Combined micro‐ and macromechanical considerations of layered composite shells
Authors: Rammerstorfer Franz G. , Starlinger Alois , Dorninger Konrad 
Published: August 2005

AbstractThis contribution deals with a computational treatment of the non‐linear behaviour of composite sandwich shells with extremely thin face layers and a relatively thick orthotropic core, and multi‐layered fiber reinforced polymer or metal matrix composite shells. Special emphasis is laid on algorithms which allow the consideration of local effects, like face layer wrinkling in sandwich shells and progressive damage or microplasticity in fibre composites, by semi‐analytical approaches implemented into a finite element formulation. This leads to the advantage that the shell structure must be discretized only up to an element mesh density which is sufficient for describing the global deformation and stability behaviour.
Wavelet–Galerkin solutions for one‐dimensional partial differential equations
Authors: Amaratunga Kevin , Williams John R. , Qian Sam , Weiss John 
Published: August 2005

AbstractIn this paper we describe how wavelets may be used to solve partial differential equations. These problems are currently solved by techniques such as finite differences, finite elements and multi‐grid. The wavelet method, however, offers several advantages over traditional methods. Wavelets have the ability to represent functions at different levels of resolution, thereby providing a logical means of developing a hierarchy of solutions. Furthermore, compactly supported wavelets (such as those due to Daubechies1) are localized in space, which means that the solution can be refined in regions of high gradient, e.g. stress concentrations, without having to regenerate the mesh for the entire problem.In order to demonstrate the wavelet technique, we consider the one‐dimensional counterpart of Helmholtz's equation. By comparison with a simple finite difference solution to this problem with periodic boundary conditions, we show how a wavelet technique may be efficiently developed. Dirichlet boundary conditions are then imposed, using the capacitance matrix method described by Proskurowski and Widlund2 and others. The convergence rates of the wavelet solutions are examined and they are found to compare extremely favourably to the finite difference solutions. Preliminary investigations also indicate that the wavelet technique is a strong contender to the finite element method, at least for problems with simple geometries.
A least‐squares front‐tracking finite element method analysis of phase change with natural convection
Authors: McDaniel David J. , Zabaras Nicholas 
Published: August 2005

AbstractThis paper focuses on the numerical modelling of phase‐change processes with natural convection. In particular, two‐dimensional solidification and melting problems are studied for pure metals using an energy preserving deforming finite element model. The transient Navier–Stokes equations for incompressible fluid flow are solved simultaneously with the transient heat flow equations and the Stefan condition. A least‐squares variational finite element method formulation is implemented for both the heat flow and fluid flow equations. The Boussinesq approximation is used to generate the bulk fluid motion in the melt. The mesh motion and mesh generation schemes are performed dynamically using a transfinite mapping. The consistent penalty method is used for modelling incompressibility. The effect of natural convection on the solid/liquid interface motion, the solidification rate and the temperature gradients is found to be important. The proposed method does not possess some of the false diffusion problems associated with the standard Galerkin formulations and it is shown to produce accurate numerical solutions for convection dominated phase‐change problems.
Finite element formulation for a baffled, fluid‐loaded, finite cylindrical shell
Authors: Grosh Karl , Pinsky Peter M. , Malhotra Manish , Rao Vinay S. 
Published: August 2005

AbstractA new method for obtaining the response of a baffled, fluid‐loaded, finite cylindrical shell using the finite element method is presented. The Galerkin finite element formulation for this problem utilizes a Neumann Green's function representation of the pressure loading on the shell. By representing the pressure loading in this manner, only the structure need be discretized. Both 𝒞0 and 𝒞1 finite element discretizations of the shell are considered. The finite element results are compared with the analytic solutions of the fluid‐loaded cylinder which are obtained using an expansion of the displacement in terms of the in vacuo modes of the Naghdi–Cooper and Flügge shell theories.
Hybrid finite element formulation for periodic piezoelectric arrays subjected to fluid loading
Authors: Chin Liang‐Chi , Varadan Vasundara V. , Varadan Vijay K. 
Published: August 2005

AbstractThe effect of fluid loading on a structure embedded with a periodic distribution of piezoelectric transducers is considered in a hybrid formulation that involves a finite element formulation for the structure and transducers that is coupled to an analytical series representation of the acoustic field in the fluid. The passive fluid loading redefines the stiffness matrix via a radiation impedance term. Modal analysis of the array can be effected for elastic vibrations, open and close circuited electrical boundary conditions. General damping in the stiffness as well as dielectric constants is considered. Sensor and actuator equations are then formulated. The actuator equations permit computation of the displacement and stress distribution in the transducer and structure when a known voltage is applied to the transducer electrodes. The sensor equation is illustrated for the case of a known incident plane harmonic wave obliquely incident on the array. The voltage induced in the transducer elements can then be computed.
The domain composition method applied to Poisson's equation in two dimensions
Authors: Charlesworth W. W. , Cox J. J. , Anderson D. C. 
Published: August 2005

AbstractDomain composition, a recently described method for formulating continuum field problems, removes certain restrictions on the construction of finite element models such that it is possible to solve a finite element problem without using a global compatible mesh. The domain composition method couples or otherwise constrains meshes in local regions to obtain a solution equivalent to that produced by conventional finite element methods. In particular, the domain composition method enables finite element models to be formulated with overlapping elements. Several advantages come from this, including an ability to automatically generate a finite element model from a solid geometric model, an ability to use a variety of element types in a single finite element model and an ability to exactly match element boundaries to the local geometry. This paper shows in detail a finite element formulation of Poisson's equation using domain composition and presents certain key algorithms that incorporate the domain composition method into well‐established finite element procedures.
On the application of multi‐step integration methods to infinitesimal elastoplasticity
Authors: Papadopoulos Panayiotis , Taylor Robert L. 
Published: August 2005

AbstractThis article proposes an implicit algorithm for time integration of the differential/algebraic equations of small‐deformation elastoplasticity in strain space. The algorithm employs a two‐step backwards differentiation formula and a standard operator‐split procedure. Second‐order accuracy and non‐linear stability are established under appropriate constitutive restrictions. The algorithm is implemented for the model of J2‐plasticity and numerical simulations are conducted that illustrate its applicability and accuracy.
Enhanced superconvergent patch recovery incorporating equilibrium and boundary conditions
Authors: Wiberg Nils‐Erik , Abdulwahab Fethi , Ziukas Saulius 
Published: August 2005

AbstractPatch recovery based on superconvergent derivatives and equilibrium (SPRE), an enhancement of the Superconvergent Patch Recovery (SPR), is studied for linear elasticity problems. The paper also presents a further improvement for recovery of derivatives near boundaries, SPREB, where either tractions or displacements are prescribed. This is made by inclusion of weighted residual errors at boundary points in the patch recovery. A pronounced improvement in the post processed gradients of the finite element solution is observed by this method.
A postprocessed error estimate and an adaptive procedure for the semidiscrete finite element method in dynamic analysis
Authors: Wiberg N.‐E. , Li X. D. 
Published: August 2005

AbstractIn the paper we present a postprocessed type of a posteriori error estimate and a h‐version adaptive procedure for the semidiscrete finite element method in dynamic analysis. In space the super‐convergent patch recovery technique is used for determining higher‐order accurate stresses and, thus, a spatial error estimate. In time a postprocessing technique is developed for obtaining a local error estimate for one step time integration schemes (the HHT‐α method). Coupling the error estimate with a mesh generator, a h‐version adaptive finite element procedure is presented for two‐dimensional dynamic analysis. It updates the spatial mesh and time step automatically so that the discretization errors are controlled within specified tolerances. Numerical studies on different problems are presented for demonstrating the performances of the proposed adaptive procedure.
Inelastic post‐buckling analysis of truss structures by dynamic relaxation method
Authors: Ramesh G. , Krishnamoorthy C. S. 
Published: August 2005

AbstractThe paper presents the inelastic post‐buckling analysis of truss structures by the Dynamic Relaxation (DR) method. A simplified inelastic finite element formulation for truss element and new algorithms are proposed for Elastic Post‐Buckling (EPB) analysis and Inelastic Post‐Buckling (IEPB) analysis using the DR method. The post‐buckling paths for elastic, EPB and IEPB analyses are completely traced using the variable‐arc‐length method. Four numerical examples are presented to illustrate the application of the proposed algorithms.
Optimal shape design for thin‐walled beam cross‐sections
Authors: Schramm Uwe , Pilkey Walter D. 
Published: August 2005

AbstractProblems of shape optimization for thin‐walled beam cross‐sections are investigated. In particular, shape optimization under torsional loading is treated. The shape of the beam cross‐section is described by non‐uniform rational B‐splines (NURBs). Biquadratic and p‐version finite elements are used to calculate the warping function. The definition of the element geometry is carried out by isoparametric and B‐spline mappings. Both methods are discussed and compared. For structural shape optimization the B‐spline mapping in connection with the p‐version finite elements is very efficient. The optimization is implemented using convex linearisation and a dual method of mathematical programming. Sensitivity analysis is performed analytically. Sample calculations are included.
Spatial stability and free vibration of shear flexible thin‐walled elastic beams. II: Numerical approach
Authors: Kim Moon‐Young , Chang Sung‐Pil , Kim Sung‐Bo 
Published: August 2005

AbstractIn a companion paper,1 equations of motion and closed‐form solutions for spatial stability and free vibration analysis of shear flexible thin‐walled elastic beams were analytically derived from the linearized Hellinger–Reissner principle. In this paper, elastic and geometric stiffness matrices and consistent mass matrix for finite element analysis are evaluated by using isoparametric and Hermitian interpolation polynomials. Isoparametric interpolation functions with 2, 3 and 4 nodes per element are utilized in isoparametric beam elements, and in Hermitian beam elements, the third‐ and fifth‐order Hermitian polynomials including shear deformation effects are newly derived and applied for the calculation of element matrices. In order to verify the validity of the finite element formulation, both analytic and numerical solutions for spatial buckling and free vibration problems including shear effects are presented and compared.
Dynamic stability of stiffened laminated composite plates and shells subjected to in‐plane pulsating forces
Authors: Liao Chung‐Li , Cheng Chu‐Ren 
Published: August 2005

AbstractThe dynamic stability of laminated composite stiffened or non‐stiffened plates and shells due to periodic in‐plane forces at boundaries is investigated in this paper. A three‐dimensional (3‐D) degenerated shell element and a 3‐D degenerated curved beam element are used to model plates/shells and stiffeners, respectively. The characteristic equations to find the natural frequencies, buckling loads and their corresponding mode shapes are obtained from the finite element equation of motion. Then, the method of Hill's infinite determinants or the method of multiple scales is applied to analyse the dynamic instability regions. Numerical results are presented to demonstrate the effects of various parameters, such as skew angle, lamination scheme, stiffened scheme, in‐plane force type and curvature of cylindrical shell, on the dynamic stability of stiffened and non‐stiffened plates and shells subjected to in‐plane pulsating forces at boundaries.
A finite element analysis of the singular stress fields in anisotropic materials loaded in antiplane shear
Authors: Pageau Stephane S. , Joseph Paul F. , Biggers Sherrill B. 
Published: August 2005

AbstractA finite element formulation is developed to determine the order and angular variation of singular stress states at material and geometric discontinuities in anisotropic materials subject to antiplane shear loading. The displacement field of the sectorial element is quadratic in the angular co‐ordinate direction and asymptotic in the radial direction measured from the singular point. The formulation of Yamada and Okumura14 for in‐plane problems is adapted for this purpose. The simplicity and accuracy of the formulation are demonstrated by comparison to several analytical antiplane shear solutions for both isotropic and anisotropic multi‐material wedges and junctions with and without disbonds. The nature and speed of convergence of the eigensolution suggests that the solution presented here could be used in developing enriched elements for accurate and computationally efficient evaluation of stress intensity factors in problems having complex global geometries.
A modification of the Petrov–Galerkin method for the transient convection–diffusion equation
Authors: Cardle James A. 
Published: August 2005

AbstractA variation of the Petrov–Galerkin method of solution of a partial differential equation is presented in which the weight function applied to the time derivative term of the transient convection–diffusion equation is different from the weight function applied to the special derivatives. This allows for the formulation of fourth‐order explicit and centred difference schemes. Comparison with analytic solutions show that these methods are able to capture steep wave fronts. The ability of the explicit method to capture wave fronts increases as the amount of convective transport increases.
Hierarchal triangular elements using orthogonal polynomials
Authors: Webb J. P. , Abouchacra R. 
Published: August 2005

AbstractHierarchal elements are finite elements which have the useful property that elements with different polynomial orders can be used together in the same mesh without causing discontinuities. This paper introduces a new hierarchal triangular element in which the basis functions are constructed from orthogonal polynomials—Jacobi polynomials. The resulting element is shown to be better conditioned than the earlier hierarchal element of Rossow and Katz.1 Recursive formulas allow the complete set of basis functions for an element to be efficiently evaluated at a given point. In addition, the formulas can be used to generate pre‐computed (universal) matrices. Examples are given of universal matrices, up to order 4, for the generalized Helmholtz equation. An electromagnetic problem involving a length of transmission line is used to show the usefulness of the new elements.
An algorithm for optimization of non‐linear shell structures
Authors: Ringertz Ulf Torbjörn 
Published: August 2005

AbstractAn algorithm for optimal design of non‐linear shell structures is presented. The algorithm uses numerical optimization techniques and nonlinear finite element analysis to find a minimum weight structure subject to equilibrium conditions, stability constraints and displacement constraints. A barrier transformation is used to treat an apparent non‐smoothness arising from posing the stability constraints in terms of the eigenvalues of the Hessian of the potential energy of the structure. A sequential quadratic programming strategy is used to solve the resulting non‐linear optimization problem. Matrix sparsity in the constraint Jacobian is exploited because of the large number of variables. The usefulness of the proposed algorithm is demonstrated by minimizing the weight of a number of stiffened thin shell structures.