bluuebunny/crossref_metadata_2025_split huggingface dataset:
Shell theory versus degeneration—a comparison in large rotation finite element analysis
Authors: Buechter Norbert , Ramm Ekkehard 
Published: November 2005

AbstractThe first part of this study addresses the controversy ‘degenerated solid approach’ versus ‘shell theory’. It is shown that both formulations differ only in the kind of discretization if they are based on the same mechanical assumptions. In particular for degenerated shell elements different versions of explicit integration across the thickness are discussed. Among these are the approximation ‘Jacobian across the thickness is constant’, proven to be too restrictive, and the series expansion of the inverse Jacobian which turns out to be unnecessary although it leads to equations of the same order as those of a ‘best first approximation’ of a shell theory.The second part deals with the description of large rotations. It is demonstrated for problems formulated in three components of a rotation vector that a straightforward derivation results in a symmetric tangent stiffness matrix. However, a modified version is also added leading to an unsymmetric matrix already discussed in the literature. For shell problems with only two rotational variables both formulations coincide.
A universal method for including shear deformation in thin plate elements
Authors: Yuqiu Long , Fei Xi 
Published: November 2005

AbstractA universal method which can be used to generalize thin plate elements to thick ones without adding any extra degree of freedom (DOF) is presented in this paper. To illustrate this method, a rectangular moderately thick plate element with 12 DOF is constructed on the basis of the well known thin plate ACM element. The element can be used in the analysis of both thin and thick plates. Shear locking is avoided.
A simplified analysis of plate structures using Trefftz‐functions
Authors: Hochard Ch. , Proslier L. 
Published: November 2005

AbstractThis paper presents a method for a quick evaluation of stresses and displacements in a plate structure for elastostatic problems. First, an approximation is built from the mathematical structure of the solutions for starshaped domains, which is representative of long wavelength effects. Second, a variational formulation consistent with this approximation is proposed. Finally, two alternative procedures for coupling adjacent domains are demonstrated.
On a highly robust spurious‐mode filtering method for uniformly reduced‐integrated shell elements
Authors: Vu‐quoc L. , Hoff C. 
Published: November 2005

AbstractIn structural elements that allow shear deformation, uniformly reduced integration is used to avoid shear and membrane locking. The spurious modes of an underintegrated stiffness matrix can be filtered using perturbation methods. Although finite elements with perturbed stiffness show very good results, the displacements still conceal a component of spurious modes, albeit with very small magnitude depending on the perturbation factor. To desensitize the numerical results completely from the perturbation factor, a projection of the applied force is proposed to complement the perturbation of the stiffness such that spurious modes are not excited, thus providing robustness to the filtering of spurious modes. The proposed methodology is general in nature, but is applied in this paper to a 9‐node shell element with uniformly reduced integration as an illustration. The perturbation of the stiffness matrix and the projection of the force vector are performed at the element level, avoiding expensive local‐global transformations. As a consequence of the force projection, the perturbation factor for the stiffness can be arbitrarily small, and the element yields accurate results for a wide range of shell thickness.
Computation of MPD flows and comparison with experimental results
Authors: Sleziona P. C. , Auweter‐Kurtz M. , Schrade H. O. 
Published: November 2005

AbstractFor several years, experimental investigations with magnetoplasmadynamic (MPD) thrusters have been conducted at the Institute for Space Systems (IRS). In order to achieve a better understanding of these thrusters, numerical procedures to calculate these MPD accelerators have been applied. A theoretical model for the calculation of the current, electron temperature and flow distribution in self‐field MPD thrusters has been developed. The extended Ohm's law has been applied to calculate the current contour lines, the electron energy equation is taken to calculate the electron temperature distribution and a two‐dimensional flow code is used to obtain the velocity, pressure and heavy particles temperature distributions. With both temperature distributions, a thermal non‐equilibrium in the plasma flow is obtained. The gas dynamic equations are solved by a finite volume code EUFLEX, which was transformed to cylindrical co‐ordinates and extended for the implementation of j × B and heat source terms. The electromagnetic discharge equation and the electron energy equation are transformed into curvilinear co‐ordinates and solved for the steady phase by a modified Gauss–Seidel algorithm. A comparison of the numerical and experimental results for different currents is presented and discussed.
A BEM approach to model heat flow during crystallization
Authors: Erhun Mehmet , Advani Suresh G. 
Published: November 2005

AbstractIn most polymer processing applications such as injection moulding, fibre spinning and extrusion, crystallization plays an important role. The energy flow at the solid‐liquid interface during crystallization controls the kinetics and subsequently influences the morphology of the transforming material. Our approach is based on the classical phase‐change problem. The governing transient heat conduction equations in the liquid and the solid domains are solved using a boundary element method (BEM) with a time dependent fundamental solution to determine the temperature distribution. The boundary energy equation is used to predict the movement of the front. The crystallization kinetics are introduced through a mathematical model based on the cooling rate of a hypothetical control volume in the solid (crystalline) domain and the changes in the crystallinity are expressed in terms of the varying interface temperature. First, we verified the BEM formulation and implementation by comparing the results of two examples with an analytical and a finite difference method in one‐dimension. Next, we investigated the effects of the crystallization kinetics by allowing the interface temperature to vary during the crystallization process. The results show that the crystallization front movement is slowed considerably when the kinetics are taken into account. Also, depending on the cooling rate and the parameters in the kinetics model, there may be undercooling during the process.
The multiple reciprocity method applied to thermal stress problems
Authors: Neves A. C. , Brebbia C. A. 
Published: November 2005

AbstractIn this paper, the multiple reciprocity boundary element method is applied to transform domain integrals due to thermal loadings into equivalent boundary integrals. The resulting formulation is restricted to two‐dimensional elastic and isotropic materials with any steady‐state temperature distribution, including internal heat generation. Several numerical examples are presented to validate the formulation and demonstrate the accuracy of the method.
Efficient and reliable accelerated constant stiffness algorithms for the solution of non‐linear problems
Authors: Chen Chang‐New 
Published: November 2005

AbstractThe paper relates to a secant‐relation‐based acceleration method used to improve the modified Newton‐Raphson scheme in which the constant stiffness matrix formed at the first iteration step is adopted to make incremental predictions for all iteration steps. An accelerator defined by minimizing a certain globally defined system error is used to scale the incremental response vector obtained by the modified Newton‐Raphson prediction in iteratively updating the response vector. The performance of acceleration is dependent on the method used to evaluate the system error. A consistent approach of evaluating the system error leads to obtaining a consistent accelerator. Another approach evaluates the system error less consistently, which results in obtaining a less consistent accelerator. Numerical results of non‐linear finite element analyses will be presented to show the effectiveness of this approach and to demonstrate the conclusion made by theoretical investigation regarding the convergency performances of the two accelerators proposed.
The C° structural finite elements reformulated
Authors: Briassoulis D. 
Published: November 2005

AbstractA new formulation was recently proposed by the present author aimed at removing the shear and membrane locking mechanisms from the C° structural elements. The performance achieved was shown to be excellent, completely eliminating all locking problems. In some cases of C° plate and shell element applications; however, the proposed formulation was shown to yield flexible (softer than expected) models. Analysis of this behaviour revealed the presence of an internal moment redistribution mechanism with the classical formulation. The absence of this mechanism from the new formulation was found to be responsible for the potential introduction of softening effects in the elastic finite element models. In the present paper, the internal moment redistribution effect is examined analytically and the key component responsible for its development is isolated. The new formulation, as originally proposed for the C° structural elements, is modified so that the internal moment redistribution mechanism is retained, yet, with all locking mechanisms being rejected. The proposed formulation has been subjected recently to extensive numerical investigation with excellent results.
Inverse stefan problem: Tracking of the interface position from measurements on the solid phase
Authors: Bénard C. , Afshari A. 
Published: November 2005

AbstractThis study presents a sequential algorithm for the identification of the position s of the moving boundary of a variable one‐dimensional or two‐dimensional domain from discrete measurements, temperatures and fluxes, collected at the fixed boundary. The inverse problem is solved by minimization, with respect to s, of a penalized output least square criterion defined on a sliding time horizon of length τ. At every time step, several iterations are performed to estimate the unknown s. Each iteration consists in a guess of s, a computation of the corresponding value of the output y (direct model) and the criterion J, and a step towards a new estimation of s. The impact of the different parameters, space and time discretization intervals, regularization coefficient, dimension of the unknown parameter s, length of the observation horizon, choice of the observed output (temperature or flux) and choice of the direct model is thoroughly analysed for an analytical test case.
The conjugate formulation of a radiation induced transient natural convection boundary layer
Authors: Li Xianming , Durbetaki Pandeli 
Published: November 2005

AbstractThe vertical surface of a non‐reactive semi‐infinite solid is suddenly heated by a radiative heat flux source. The surface temperature increases and a thermal wave penetrates the solid. At the same time, the hot surface heats the neighbouring air, which begins to move upward under the influence of gravity. The events in both domains are closely connected and the compressible fluid in the boundary layer establishes a hydrodynamic and thermal coupling. Such coupling and the non‐linearity in this problem require a special solution approach. A numerical technique was selected, which is based on the finite control volume method developed by Patankar and Spalding. The Patankar–Spalding method was modified to accommodate both the solid domain and the gas phase domain simultaneously. The conjugate formulation for the transient combined solid phase and gaseous boundary layer was investigated. It was found that the new conjugate method provided reliable solutions to the current problem. Furthermore, the analysis revealed that the time required for the surface temperature to attain a specified value was inversely proportional to the square of the radiative heat flux.
Implementation of a lamina‐based constitutive relationship for analysing thick composites
Authors: Zywicz Edward 
Published: November 2005

AbstractThe finite element implementation of a lamina‐based elastic constitutive relation appropriate for describing the three‐dimensional (3‐D) behaviour of fibre composite laminated media is presented. Unconstrained by the two‐dimensional restrictions accompanying plate and shell theories, this approach resolves the macro 3‐D deformation fields found in 'thick' laminated or filament wound composites without requiring each lamina to be individually discretized to assign material properties. In rectangular isoparametric solid elements where laminae locally parallel an element 'face', the implementation represents 'exactly' the elastic laminate behaviour by replacing the discrete lamina stiffnesses with continuous polynomial moduli functions. Attributable directly to the lamina constitutive relationship used, appropriate for fibre‐dominated material systems, the implementation automatically preserves interlaminar continuity of tractions and displacements within each element for laminates assembled from a single lamina type. The order of the effective moduli functions is determined by the element kinematics and by requiring identical net mid‐surface elemental forces and moments. In general, this representation substantially reduces the number of stored variables and through‐thickness integrations required, and allows 'exact' integration by higher‐order Gaussian quadrature. Additionally a single element may span any portion or number of laminae, thus allowing nearly arbitrary meshing and solution resolution. Several numerical examples using 3‐D 8‐node isoparametric solid elements demonstrate the approach's convergence and overall behaviour.
Use of boundary element method for the determination of tool shape in electrochemical machining
Authors: Das Shuvra , Mitra Ambar K. 
Published: November 2005

AbstractThe problem of cathode shape determination for a given anode shape in electrochemical machining is considered. An algorithm based on the boundary integral equation technique and non‐linear optimization for this inverse problem is developed. The additional flux condition at the anode is used as the constraint in this ill‐posed problem. Through an iterative process, the shape of the cathode is determined by minimizing a functional. The algorithm is tested on two examples. It is shown that the algorithm is consistently superior compared to published numerical techniques based on the embedding method or the method of the lines.
reduction of equilibrium, compatibility and flexibility matrices, in the force method
Authors: Pellegrino S. , Kwan A. S. K. , Van Heerden T. F. 
Published: November 2005

AbstractThis paper develops analytical expressions and numerical for reducing the structural matrices which are used in the Force Method of structural analysis. Two simple examples illustrate the calculations for pin‐jointed trusses.Two advanced applications, a beam cross consisting of two coplanar beams which are linked by a shear connector, and an equilibrium linear‐stress finite element, are also presented.
Some theoretical aspects in computational analysis of adhesive lap joints
Authors: Destuynder P. , Michavila F. , Santos A. , Ousset Y. 
Published: November 2005

AbstractThis paper is devoted to the numerical analysis of bidimensional bonded lap joints. For this purpose, the stress singularities occurring at the intersections of the adherend‐adhesive interfaces with the free edges are first investigated and a method for computing both the order and the intensity factor of these singularities is described briefly. After that, a simplified model, in which the adhesive domain is reduced to a line, is derived by using an asymptotic expansion method. Then, assuming that the assembly debonding is produced by a macro‐crack propagation in the adhesive, the associated energy release rate is computed. Finally, a homogenization technique is used in order to take into account a preliminary adhesive damage consisting of periodic micro‐cracks. Some numerical results are presented.
How to recognize the order of infinitesimal mechanisms: A numerical approach
Authors: Salerno Ginevra 
Published: November 2005

AbstractStructures presenting kinematical inderterminacy are usually called mechanisms. This paper is entirely concerned with assemblies which reveal themselves to be mechanisms at a null value of the load. Among them a first distinction is made between infinitesimal and finite ones, the former being characterized by one or several directions of lower (but not zero) stiffness, whereas the latter show at least one finite admissible displacement for which none of the bars undergoes any elongation. Moreover, there exists the possibility to make a further distinction among the infinitesimal mechanisms, according to which is the order of the stiffness along the direction considered above. The way of evaluating this order is to perform a local analysis of the strain energy of the assembly, once the displacement field is parametrized in terms of a suitable parameter. By means of a finite element technique, this analysis can be easily performed through the numerical approach presented in this report.
Creep deformation structural analysis using an efficient numerical algorithm
Authors: Whirley Robert G. , Henshall Gregory A. 
Published: November 2005

AbstractThis paper presents a fast numerical algorithm for the implementation of material models for creep into finite element codes. First, an overview of existing algorithms for transient and steady‐state creep is given. Next, a new formulation is presented which reduces the constitutive integration to the solution of a scalar non‐linear algebraic equation. A solution is shown to exist without the need for subincrementation. Details of the numerical algorithm are then discussed. The paper closes with several numerical examples which illustrate the speed, robustness and accuracy of the proposed procedure as implemented in the Lawrence Livermore National Laboratory finite element codes NIKE2D and NIKE3D.
The use of orthogonal projections to handle constraints with applications to incompressible four‐node quadrilateral elements
Authors: Hueck Ulrich , Schreyer Howard L. 
Published: November 2005

AbstractLinear equality multipoint constraint conditions define a vector space which is used to construct an orthogonal projection operator. Another orthogonal projection operator follows from the complement to the constrained vector space. A procedure is developed in which these operators are used in a systematic fashion to solve a set of algebraic equations subject to a set of multipoint constraints. In addition to elementary examples to illustrate the procedure, a problem associated with an incompressible, isotropic, elastic material is solved using four‐node quadrilateral finite elements. The method of orthogonal projections provides the insight to show that, with the application of the incompressibility constraint, convergence is obtained for any arbitrary value of Poisson's ratio chosen sufficiently far from the value of one‐half, which is the value normally associated with incompressibility. The bending performance of the incompressible four‐node quadrilateral can be adjusted with artificial values of Poisson's ratio. The result is that calculations are performed with full numerical quadrature of the element, and mesh locking, hourglass instabilities and subsequent modifications to the element stiffness matrix are avoided.
A multigrid method for the generalized symmetric eigenvalue problem: Part II—performance evaluation
Authors: Hwang T. , Parsons I. D. 
Published: November 2005

AbstractThe behaviour of the multigrid method is studied by solving some simple test problems. Optimum choices for some of the parameters are discussed, together with effective techniques for solving the coarse mesh correction equation. The effects of ill‐conditioning on the performance of the algorithm are examined. In particular, thin shells and non‐uniform meshes are observed to slow convergence. The solution of practical, large scale problems demonstrates the utility and speed of the proposed multigrid method. For example, the first 10 eigensolutions of a stiffened plate problem with 193 536 degrees‐of‐freedom were computed in 1.6 CPU hours using 42 Mbytes of memory on a Convex C240.
Seismic response analysis of alluvial valley with two dipping layers by a boundary element‐finite element coupling method
Authors: Abe Kazuhisa , Yoshida Yutaka 
Published: November 2005

AbstractA coupling process of time‐domain boundary element method and finite element method is constituted for analysis of the dynamic response of an alluvial valley. Since the characteristics of these two methods are different from each other, the time increment of the boundary element method is set to be an integer multiple of the finite element method, and a combination of a linear interpolation of boundary element equations at two successive time steps with a finite element equation is proposed. Using this procedure, responses of alluvial valleys with two dipping layers are analysed for a vertically incident SV wave, and influence of the lower layer on these responses is investigated. It is found that the presence of the additional lower layer affects not only the reflected waves but also the surface waves. Furthermore, when an outcropping lower layer exists at the basin edges, the valley suffers an amplification of motion and an extreme increase in strains. These results show that a small difference in the layer at the basin edge is significant in analysing dynamic responses of an alluvial valley.
Boundary element analysis of thin plates internally bounded by rigid patches
Authors: Hartley Gilbert A. , Abdel‐Akher Ahmed , Chen Peilei 
Published: November 2005

AbstractProcedures are described for modelling a structural system consisting of thin Kirchhoff plates with internal patch areas capable of displacing as rigid flat surfaces. The physical prototype for these patches could be interconnection points for one‐dimensional frame type elements of various shapes and layout, rigidly connected at these finite size 'joints' in the plate. The numerical procedure for modelling the thin plate is the Direct Boundary Element Method (DBEM) and a simple overview of this procedure is provided. Potential trouble spots, of which the user should be aware, are described.The paper will be of interest to structural engineers for analysis of frames having both plate and simple frame elements, for example, building frames; and also to researchers seeking the greater detail that this refined procedure can provide. As a practical tool, the methods described are computationally competitive with existing procedures, including the more rugged approaches used by building structural engineers for dynamic and torsional analysis.
An enthalpy control‐volume—unstructured‐mesh (cv—um) algorithm for solidification by conduction only
Authors: Chow P. , Cross M. 
Published: November 2005

AbstractRecently, control volume methods have been developed for fluid flow and heat transfer on unstructured meshes. This approach has been extended here to implement the enthalpy based solidification algorithm on an unstructured mesh. A range of two‐dimensional test problems are solved using triangular and quadrilateral cells (or elements). The accuracy of the CV–UM algorithms compare favourably with the structured‐mesh algorithm, though the former algorithms require 1.5–3 times as much CPU as the latter. This overhead is associated with the extra work caused by the unstructuredness of the mesh; the number of sweeps to achieve convergence is roughly comparable for all algorithms. The CV–UM algorithms should perform well on complex geometry problems and, therefore, show potential to be a productive technique in casting solidification analysis.