bluuebunny/crossref_metadata_2025_split huggingface dataset:
A three‐dimensional layer‐wise constant shear element for general anisotropic shell‐type structures
Authors: Zinno Raffaele , Barbero Ever J. 
Published: August 2005

AbstractThis paper deals with the development of a new three‐dimensional element with two‐dimensional kinematic constraints capable of analysing the mechanical behaviour of the laminated anisotropic shell‐type structures. This element, originally developed for the linear analysis of plates, is extended for the linear analysis of laminated composite shells. The element can represent arbitrarily curved shells with variable number of layers and thicknesses, including ply drop‐off problems. The element was validated in a previous work by the patch test. All the analytical details necessary to make possible the shell analysis are presented here. Examples are reported to show the capability of the element to predict the behaviour of complex structures and a refined computation of the stresses is carried out by integrating the equilibrium equations.
Mathematical boundary integral equation analysis of an embedded shell under dynamic excitations
Authors: Pak Ronald Y. S. , Ji Feng 
Published: August 2005

AbstractA boundary integral equation method is presented for the analysis of a thin cylindrical shell embedded in an elastic half‐space under axisymmetric excitations. By virtue of a set of ring‐load Green's functions for the shell and a group of dynamic fundamental solutions for the semi‐infinite medium, the structure–medium interaction problem of wave propagation is shown to be reducible to a set of coupled boundary integral equations. Through the analysis of an auxiliary pair of Cauchy integral equations, the singularities of the contact stress distributions arc rendered explicit. With a direct incorporation of such analytical features into the formulation, an effective computational procedure is developed which involves an interpolation of regular functions only. Typical results for the dynamic contact load distributions, displacements, and complex compliance functions are included as illustrations. In addition to furnishing quantities of direct engineering interest, this treatment is apt to be useful as a foundation for further rigorous as well as approximate developments for various related physical problems and boundary integral methods.
Finite element analysis of contact–impact between a shell of revolution and a rigid wall
Authors: Gautham B. P. , Ganesan N. 
Published: August 2005

AbstractIn this paper an attempt is made to use a shell theory that includes transverse normal stresses to study the contact–impact behaviour involving thick shells. The problem is solved using the finite element method. The contact criterion is imposed by means of displacement and force constraints. The Lagrangian multipliers technique is used to impose these constraints. The case of a spherical shell impacting a rigid wall with a constant velocity is considered for the analysis. It is shown that the method produces accurate results with less amount of computation than the usual three‐dimensional analyses. The effects of the thickness of shell, velocity of impact and modulus of the material are studied.
Subdomain methods in structural mechanics
Authors: Radi B. , Gelin J. C. , Perriot A. 
Published: August 2005

AbstractThe principle of subdomain methods has been introduced many years ago1 and such methods have been used with success in recent years. In this paper, we discuss some methods used to solve the condensed system resulting from the Schur complement method. We will present the hybrid method and a mechanical application: the contact problem between two deformable solids. In the case of such a problem, we propose two methods: one for the contact with friction and one for the contact without friction. Finally, the results of validation tests for both proposed approaches are given.
A new formulation for the direct dynamic simulation of flexible mechanisms based on the Newton–Euler inverse method
Authors: Verlinden Olivier , Dehombreux Pierre , Conti Calogero , Boucher Serge 
Published: August 2005

AbstractThis paper is concerned with the direct dynamic analysis of mechanisms comprising flexible members.It is first recalled how the time integration of the dynamic equations governing the motion of a flexible mechanism is conditioned by the availability of the so‐called iteration matrix. The latter is obtained not only from the mass matrix, which is sufficient in the rigid case, but also from the stiffness and damping tangent matrices.Hence, in a context based upon relative co‐ordinates where the deformation of the flexible bodies is described by component modes, two formulations, a classical one and a new one, which permit the determination of this iteration matrix are presented. The classical formulation is based upon the Lagrange's theorem. The new one consists in a direct calculation of the residues of the dynamic equations by using the inverse method of Newton–Euler. In this case, the iteration matrix is obtained by a numerical derivation technique which proves well‐conditioned.A first simple example is treated in order to compare the two formulations. A more complex one illustrates the real capabilities of the new formulation.
Ray tracing with a space‐filling finite element mesh
Authors: Favre Jean , Löhner Rainald 
Published: August 2005

AbstractA new ray‐tracing technique is presented which does not work with ray–object intersections per se, but is based on the traversal of an unstructured tetrahedral mesh providing a convex enclosure of a scene of polyhedral objects. The tetrahedral mesh provides tight bounding and an adaptive subdivision of space. This non‐hierarchical data structure is traversed adaptively until one is led directly and unconditionally to the first object intersected. Rendering times are directly related to the average thickness of the enclosing mesh since all tetrahedra are traversed in constant time.Since the proposed algorithm operates directly with volume elements, it allows for volumetric rendering effects. Volume rendering or anisotropic media can be implemented without any further effort. This is an important advantage as compared to usual techniques, which only operate on surface data.Timings for several examples show that the use of this type of ray‐tracing technique, which is more suitable for general purpose visualization codes than traditional techniques, results in CPU times that are comparable with the best ray‐tracing techniques presently used. This is an unexpected and important result, as the vectorization and parallclization of the proposed technique are straightforward, in contrast with traditional ray‐tracing techniques.
Inflation of hyperelastic cylindrical membranes as applied to blow moulding. Part II. Non‐axisymmetric case
Authors: Khayat R. E. , Derdouri A. 
Published: August 2005

AbstractThe non‐axisymmetric confined inflation of an isotropic homogeneous cylindrical membrane is considered in this study. The material is assumed to obey the Mooney–Rivlin constitutive model. The continuum‐based formulation is adopted, with the resulting equilibrium partial differential equations, governing the deformation field, solved using a Galerkin based finite element procedure. Upon contact, the inflating material is assumed to stick to the solid boundary. The dependent variables corresponding to nodes which have contacted are then fixed for subsequent deformation. In an attempt to simulate the inflation stage of the blow‐moulding process, the method is illustrated through some examples of moulded tapered rectangular bottles with centered and off‐centred neck. Examples of initial membranes of uniform and non‐uniform thickness distribution are examined. Experiments are carried out in an attempt to validate the theory, in particular, to compare the predicted and measured final thickness distributions of blow‐moulded containers.
Implicit objective integration for sensitivity analysis in non‐linear solid mechanics
Authors: Leu Liang‐Jenq , Mukherjee Subrata 
Published: August 2005

AbstractIncrementally objective integration schemes are proposed for the accurate and efficient determination of design sensitivity coefficients (DSCs) for solid mechanics problems with both material and geometrical non‐linearities. The derivation of these schemes are based on the direct differentiation of objective schemes that are used in stress analysis for problems of this class. Two widely used objective stress rates, the Jaumann rate and the Green–Naghdi rate, are considered here within the same setting with only minor changes of the integration scheme. Numerical results are presented for a simple shear problem with different material constitutive laws, including a hypoelastic model and a unified isotropic viscoplastic model, for these two objective rates. The numerical results are compared with analytical solutions or direct integration solutions. The close agreement among these solutions demonstrates the accuracy and efficiency of the proposed scheme.
Solution of the slump test using a finite deformation elasto‐plastic Drucker‐Prager model
Authors: Famiglietti C. M. , Prevost J. H. 
Published: August 2005

AbstractDevelopment of a finite deformation elasto‐plasticity model based on the multiplicative decomposition of the deformation gradient is presented and discussed in detail. The formulation presented in this paper includes the derivation of the full set of equations for the Drucker‐Prager yield criterion. The equations, which are not available elsewhere, are developed within a framework using a spectral decomposition approach. Further, expressions for the consistent (algorithmic) tangent moduli in the finite strain regime are developed. Since the finite deformation framework employed to obtain the expressions presented here collapses to the classical infinitesimal plasticity framework when the finite strain assumption is no longer necessary, the finite deformation consistent tangent moduli are compared to the consistent tangent moduli valid for use with infinitesimal plasticity. Validation of the implemented finite deformation elasto‐plastic Drucker‐Prager model is performed through the solution of the concrete slump test. Comparisons between an existing approximate analytical solution and experimental data are presented, and results are discussed in detail.
A qualitative analysis of the behaviour of the Galerkin equations relevant to non‐linear eddy current problems
Authors: Miano Giovanni 
Published: August 2005

AbstractThe Galerkin equations relevant to the eddy currents induced in an iron body are considered. These equations are obtained by formulating the field problem in terms of the magnetic vector potential and by applying the Galerkin method. They are shown to have a unique steady‐state solution if a certain condition on the magnetic constituitive relationship is satisfied. In particular a T‐periodic source gives rise to a unique T‐periodic solution to which all other solutions converge asymptotically independently from the initial conditions. Under the same condition the exponential decay of the ‘transients’ is shown, and an explicit lower and upper bound for its rate is given. These structural properties allow us to exclude a priori that qualitatively different asymptotic behaviours, including even chaotic solutions, may occur. Numerical simulation, when based on qualitative information of this type, enables us to obtain the quantitative properties in an efficient manner. In order to demonstrate the practical use of these results some numerical experiments are presented.
A robust refined quadrilateral plane element
Authors: Wanji Chen , Cheung Y. K. 
Published: August 2005

AbstractBased on a rational choice of the internal incompatible displacement function and a special formulation of the a priori elimination of the internal non‐conforming displacement parameters, a new refined quadrilateral plane element RQ4 has been developed. The present element can be shown to be computationally efficient, accurate and free from locking, and is better than other elements such as the Plan's element HS, the generalized hybrid element QCS6, and the refined hybrid element RGH4, etc. Several numerical examples are given to show the superior performances of the present element RQ4.
Multi‐grid domain decomposition approach for solution of Navier–Stokes equations in primitive variable form
Authors: Ku Hwar‐Ching , Ramaswamy Bala 
Published: August 2005

AbstractA new multi‐grid (two‐grid) pseudospectral element method has been carried out for solution of incompressible flow in terms of primitive variable formulation. The main objective of the proposed method is to apply the multi‐grid technique solving the incompressible flow problems associated with three commonly encountered multi‐grid environments. In domain decomposition terminology, it includes (I) partially overlapped subdomains, each of which has same types of grids; (II) partially overlapped subdomains, each of which has different types of grids; (III) local adaptive subdomains fully overlapped with the original computational domain (composite grids).The approach for flow problems, complex geometry or not, is to first divide the computational domain into a number of subdomains with the inter‐overlapping area (partially or fully overlapped). In categories I and II, the fine‐grid or coarse‐grid subdomains can be defined by their representation, while in category III the fine‐grid or coarse‐grid subdomains are defined as usual. Next, implement the Schwarz Alternating Procedure (SAP) to exchange the data among subdomains, where the coarse‐grid correction is used to remove the high frequency error that occurs when the data interpolation from the fine‐grid subdomain to the coarse‐grid subdomain is conducted. The strategy behind the coarse‐grid correction is to adopt the operator of the divergence of velocity field, which intrinsically links the pressure equation, into this process. The solution of each subdomain can be efficiently solved by the direct (or iterative) eigenfunction expansion technique or preconditioned method with the least storage requirement, i.e. O(N2) in 2‐D.Numerical results of (i) driven cavity flow (Re = 100,400) with Cartesian grids (category I) in each subdomain, (ii) driven cavity flow (Re = 3200) with local adaptive grids (category III) in each subdomain, and (iii) flow over a cylinder (Re = 250) with ‘O’ grids in one subdomain and Cartesian grids in another (category II) will be presented in the paper to account for the versatility of the proposed multi‐grid method.
A posteriori error estimates and adaptivity for finite element solutions in finite elasticity
Authors: Mücke Roland , Whiteman J. R. 
Published: August 2005

AbstractMethods for a posteriori error estimation for finite element solutions are well established and widely used in engineering practice for linear boundary value problems. In contrast here we are concerned with finite elasticity and error estimation and adaptivity in this context. In the paper a brief outline of continuum theory of finite elasticity is first given. Using the residuals in the equilibrium conditions the discretization error of the finite element solution is estimated both locally and globally. The proposed error estimator is physically interpreted in the energy sense. We then present and discuss the convergence behaviour of the discretization error in uniformly and adaptively refined finite element sequences.
A geometrically non‐linear quasi‐conforming nine‐node quadrilateral degenerated solid shell element
Authors: Guan Yupu , Tang Limin 
Published: August 2005

AbstractIn this paper, a geometrically non‐linear quasi‐conforming nine‐node quadrilateral degenerated solid shell element has been constructed from generalization of a linear quasi‐conforming nine‐node quadrilateral degenerated solid shell element,10 based upon the non‐linear quasi‐conforming finite element method. First, the geometrical description and displacement model of the nine‐node quadrilateral degenerated solid shell element is given. Then, the non‐linear quasi‐conforming finite element method is discussed and assumed strains and weighed functions are given. Last, analysis of numerical examples for a clamped square plate, a circular arch, a spherical shell, two cylindrical shells, the patch test and a simply supported square plate is carried out. The results are compared with exact and other finite element solutions. The results indicate that the shell element in the paper is accurate and efficient.
Automatic mesh generation over intersecting surfaces
Authors: Lo S. H. 
Published: August 2005

AbstractA fully automatic general scheme is proposed to determine and analyse the intersections between two groups of surfaces composed of triangular facets. By carefully maintaining the spatial position of the lines of intersection in regenerating mesh locally around surface intersections, pieces of surfaces can be arbitrarily combined and merged. A great variety of objects can be easily created by selectively putting together different surface parts derived from surface intersections. The new algorithm is best applied in conjunction with an existing surface mesh generator to enhance its general capability in dealing with objects built from intersecting surfaces. In fact, it is a powerful surface mesh manipulator, and through the repeated use of the process, complex structures can be rapidly and accurately constructed.
On the solution of non‐linear drying problems in capillary porous media through integral transformation of Luikov equations
Authors: Ribeiro J. W. , Cotta R. M. 
Published: August 2005

AbstractThe generalized integral transform technique is employed to provide hybrid numerical–analytical solutions to the non‐linear Luikov equations, that govern drying within capillary porous media. The coupled equations for moisture and temperature distributions are integral transformed to eliminate the spatial co‐ordinates, yielding an ordinary differential system for the time variation of the transformed potentials, which is readily solved through scientific subroutine libraries with automatic error control schemes. The analytical inversion formula is then recalled to provide explicit expressions for the original potentials at any desired position. The convergence behaviour of the proposed eigenfunction expansions is illustrated, and a parametric study is performed, for the drying of a slab subjected to non‐linear radiative boundary conditions.
The complementary functions method for the element stiffness matrix of arbitrary spatial bars of helicoidal axes
Authors: Haktanir Vebi̇l 
Published: August 2005

AbstractThe statical behaviour of a spatial bar of an elastic and isotropic material under arbitrary distributed loads having a non‐circular helicoidal axis and cross‐section supported elastically by single and/or continuous supports is studied by the stiffness matrix method based on the complementary functions approach. By considering the geometrical compatibility conditions together with the constitutive equations and equations of equilibrium, a set of 12 first‐order differential equations having variable coefficients is obtained for spatial elements of helicoidal axes. The stiffness matrix and the element load vector of a helicoidal bar with a non‐circular axis and arbitrary cross‐section are obtained taking into consideration both the presence of an elastic support and the effects of the axial and shear deformations. For helicoidal staircases, the significance of both axial and shear deformations and eccentricities existing in wide and shallow sections are also investigated. The developed model has been coded in Fortran‐77, which has been applied to various example problems available in the relevant literature, and the results have been compared.
Analysis and optimization of weakly coupled thermoelastoplastic systems with applications to weldment design
Authors: Michaleris Panagiotis , Tortorelli Daniel A. , Vidal Creto A. 
Published: August 2005

AbstractA systematic approach for the design of weakly coupled thermoelastoplastic systems is presented. The Newton–Raphson iteration method is used in the solution process so that analytic design sensitivity formulations may be efficiently derived via the direct differentiation technique. The derived formulations are suitable for finite element implementations. Analysis and sensitivity analysis capabilities are combined with numerical optimization to form an optimum design algorithm. To demonstrate the algorithm, we optimally design a weldment with respect to manufacturing and service life aspects.
Plate spectral elements based upon Reissner–Mindlin theory
Authors: Zrahia Uzi , Bar‐Yoseph Pinhas 
Published: August 2005

AbstractPlate bending spectral elements based upon the Reissner–Mindlin theory is developed for a rectangular plate. Numerical comparison studies for static and eigenvalue problems, demonstrate the excellent performance and robustness of the present method. The improvement in accuracy and computational efficiency in comparison with low order plate bending elements is remarkable and suggests that the proposed approach is an alternative to existing schemes.
Control of the freezing interface morphology in solidification processes in the presence of natural convection
Authors: Zabaras Nicholas , Nguyen T. Hung 
Published: August 2005

AbstractThis paper presents a methodology for the solution of an inverse solidification design problem in the presence of natural convection. In particular, the boundary heat flux q0 in the fixed mold wall, δΩ0, is calculated such that a desired freezing front velocity and shape are obtained. As the front velocity together with the flux history qms on the solid side of the freezing front play a determinant role in the obtained cast structure, the potential applications of the proposed methods to the control of casting processes are enormous.The proposed technique consists of first solving a direct natural convection problem of the liquid phase in an a priori known shrinking cavity, ΩL(t), before solving an ill‐posed inverse design conduction problem in the solid phase in an a priori known growing region, ΩS(t). The direct convection problem is used to evaluate the flux qml in the liquid side of the freezing front. A front tracking deforming finite element technique is employed. The flux qml can be used together with the Stefan condition to provide the freezing interface flux qms in the solid side of the front. As such, two boundary conditions (flux qms and freezing temperature θm) are especified along the (known) freezing interface δΩI(t). The developed design technique uses the adjoint method to calculate in L2 the derivative of the cost functional, ∥θm – θ(x, t; q0)∥, that expresses the square error between the calculated temperature θ(x, t; q0) in the solid phase along δΩI(t) and the given melting temperature. The minimization of this cost functional is performed by the conjugate gradient method via the solutions of the direct, sensitivity and adjoint problems. A front tracking finite element technique is employed in this inverse analysis. Finally, an example is presented for the solidification of a superheated incompressible liquid aluminium, where the effects of natural convection in the moving interface shape are controlled with a proper adjustment of the cooling boundary conditions.