bluuebunny/crossref_metadata_2025_split huggingface dataset:
A simple triangular element for thick and thin plate and shell analysis
Authors: Oñate E. , Zarate F. , Flores F. 
Published: August 2005

AbstractA new plate triangle based on Reissner–Mindlin plate theory is proposed. The element has a standard linear deflection field and an incompatible linear rotation field expressed in terms of the mid‐side rotations. Locking is avoided by introducing an assumed linear shear strain field based on the tangential shear strains at the mid‐sides. The element is free of spurious modes, satisfies the patch test and behaves correctly for thick and thin plate and shell situations. The element degenerates in an explicit manner to a simple discrete Kirchhoff form.
A generalized elastoplastic plate theory and its algorithmic implementation
Authors: Auricchio F. , Taylor R. L. 
Published: August 2005

AbstractIn continuum mechanics within specific classes of problems, one‐ or two‐dimensional theories are often simpler to apply than the more complete three‐dimensional one. This is, for example, the case of thin bodies, such as plates or shells, which may be studied using appropriate two‐dimensionai theories.Within this approach, the reduction of the dimension is traded for a loss of information relative to the motion in the transverse direction. For example, in the case of non‐linear material behaviour, classical plasticity plate theories are usually not able to model the effects related to the spreading of plasticity through the cross‐section.In the present paper we discuss a generalized plasticity plate model, which can be used to reproduce some of the three‐dimensional effects in a two‐dimensional setting. We present the continuous and the discrete time model, including both isotropic and kinematic hardening mechanisms; moreover, the form of the tangent matrix consistent with the discrete model is addressed.Finally, some examples (cantilever beam, clamped circular plate and clamped square plate under monotonic and cyclic loading) are studied numerically using a three‐dimensional classical plasticity theory, a classical plasticity plate theory and the proposed plate theory. The generalized plasticity plate model matches the three‐dimensional response with greater accuracy, than the classical plasticity plate model.
Adaptive finite element analysis of geometrically non‐linear plates and shells, especially buckling
Authors: Stein E. , Seifert B. , Ohnimus S. , Carstensen C. 
Published: August 2005

AbstractBased on both moderate and finite rotation bending theories of thin elastic shells including shear deformation, adaptive non‐linear static finite element analysis is treated within a displacement approach and h‐adaptivity. The a posteriori error indicator given by Rheinboldt, gained by linearization, is investigated in order to decide whether the deformations influence the indicator explicitely and how parameter dependent problems (like the Reissner–Mindlin model) behave in the process of adaptation. In order to achieve overall consistency, dimensional adaptivity (to 3‐D elasticity) is implemented within disturbed subdomains, especially at supports.Results are that Rheinboldt's error indicator is valid under certain restrictions but not directly at bifurcation points and that robustness is not improved by adaptation.Nested quadrilateral finite elements are used for studying pre‐ and post‐buckling states of plates and shells.
Towards automatic adaptive geometrically non‐linear shell analysis. Part I: Implementation of an h‐adaptive mesh refinement procedure
Authors: Okstad Knut Morten , Mathisen Kjell Magne 
Published: August 2005

AbstractEffective methods leading to automated adaptive numerical solutions to geometrically non‐linear shell‐type problems are studied in this work. In particular, procedures for improving the accuracy, the reliability and the computational efficiency of the finite element solutions are of primary interest here. This is addressed using h‐adaptive mesh refinement based on a posteriori error estimation, self‐adaptive methods in global incremental/iterative processes, as well as smart algorithms and heuristic approaches based on methods of knowledge engineering. Seemless integration of h‐adaptive finite element methods with adaptive step‐length control makes it possible to maintain a prescribed accuracy while maintaining the solution efficiency without user intervention throughout the process of a non‐linear analysis. Several examples illustrate the merit and potential of the approach studied herein and confirm the feasibility of developing an automatic adaptive environment for geometrically non‐linear analysis of shell structures.
Wave equation model for solving advection–diffusion equation
Authors: Wu Jiankang 
Published: August 2005

AbstractThis paper presents a Wave Equation Model (WEM) to solve advection dominant Advection–Diffusion (A–D) equation. It is known that the operator‐splitting approach is one of the effective methods to solve A–D equation. In the advection step the numerical solution of the advection equation is often troubled by numerical dispersion or numerical diffusion. Instead of directly solving the first‐order advection equation, the present wave equation model solves a second‐order equivalent wave equation whose solution is identical to that of the first‐order advection equation. Numerical examples of 1‐D and 2‐D with constant flow velocities and varying flow velocities are presented. The truncation error and stability condition of 1‐D wave equation model is given. The Fourier analysis of WEM is carried out. The numerical solutions are in good agreement with the exact solutions. The wave equation model introduces very little numerical oscillation. The numerical diffusion introduced by WEM is cancelled by inverse numerical diffusion introduced by WEM as well. It is found that the numerical solutions of WEM are not sensitive to Courant number under stability constraint. The computational cost is economical for practical applications.
Fully automatic mesh generation for 3‐D domains based upon voxel sets
Authors: Frey Pascal , Sarter Benoît , Gautherie Michel 
Published: August 2005

AbstractFully automatic three‐dimensional mesh generation is an essential and increasingly crucial requirement for finite element solution of partial derivative equations. The results of numerical simulation, more precisely the convergence and accuracy of numerical solutions, closely depends on the quality of the underlying mesh. This work introduces a fully automatic finite element mesh algorithm with simplexes (tetrahedra), adapted to complex geometries described by disctete data.This paper is divided in four sections: (a) brief introduction to discrete geometry is given, as well as the basic definition of the domain of interest; (b) description of the voxel approach to tetrahedronization. The tetrahedronization process uses a divide‐and‐conquer method, which provides small elements on the boundary of the domain of interest. Voxels of the domain are subdivided according to an automatic procedure, which preserves the topology. Specific rules were introduced which allow reducing the number of voxel configurations to be treated, and consequently the computation time; (c) presentation of results and performances of the mesh algorithms. The resulting algorithm demonstrates an n log n growth rate with respect to the number of elements; (d) optimization of the mesh generation process at hand of a ‘finite‐octree’ type of explicit controlling space.
Finite element formulation by parametrized hybrid variational principles: Variable stiffness and removal of locking
Authors: Sze K. Y. 
Published: August 2005

AbstractIn this paper, a new one‐parameter hybrid functional is obtained as a special case of Felippa and Militello's parametrized variational principles. The functional contains stress, strain and compatible displacement as the primary fields. It will be proved that some of the existing variable stiffness formulations fall into the framework of the new functional. Novel applications of the functional are also suggested, mainly for removal of locking. Solid element, destabilized 8‐node and stabilized 9‐plate elements are designed. All of them can handle thin plate/shell analysis. In particular, a prominent method is devised for constructing stabilization vectors. The vectors are explicit linear functions of the nodal coordinates and can be implemented without resorting to Gram–Schmidt orthogonalization or numerical integration. Results of the new elements in popular benchmark tests are encouraging.
Stress analysis of imperfect composite laminates with an interlaminar bonding theory
Authors: Liu Dahsin , Xu Lan , Lu Xianqiang 
Published: August 2005

AbstractDelamination is a major damage mode in laminated composites since it can cause severe structural degradation. Based on an interlaminar shear stress continuity theory and a linear shear slip theory, a so‐called Interlayer Shear Slip Theory was presented in a previous study. This theory was verified to be feasible for shearing‐mode delamination analysis. However, in order to account for opening‐mode delamination in laminated composites, the continuity of interlaminar normal stress and the modelling of normal separation on the composite interface should also be considered. The present study gives a complete discussion on the Interlaminar Bonding Theory. The effects of interlaminar bonding condition on the laminate deformation and stress distribution are also presented. It is concluded from numerical results that the present theory is suitable for analysis of composite laminates with imperfect interfaces.
Implementation of discrete fuzzy structure models in Mathematica
Authors: Sparrow Victor W. , Russell Daniel A. , Rochat Judith L. 
Published: August 2005

AbstractSince Soize introduced the concept of fuzzy structures in structural acoustics there has been little activity clarifying the basic elements which underlie his theory. Soize's papers are not easy reading due to the high level of mathematical formalism. In addition Soize simultaneously bases this fuzzy structure theory on two components: (1) a model for one Degree Of Freedom (DOF) fuzzy oscillators, and (2) a medium frequency solution method developed previously. It is unclear as to the role of the two components, although others have already undertaken a study of the medium frequency method by itself.In the present paper a fundamental analysis of the first component, the one‐DOF fuzzy oscillators, is undertaken. The symbolic manipulation program Mathematica is utilized to gain insight into this component of Soize's fuzzy theory. The resulting Mathematica simulations are easy to use and interpret, and they provide valuable insight into the parameters composing Soize's fuzzy oscillators. It is determined that in many cases of structural acoustics, where there is small damping and a medium to high modal density, the fuzzy mass primarily determines what effect a discrete fuzzy oscillator will have as an attachment.
A local–global model for the non‐linear analysis of locally defective shells of revolution
Authors: Ravichandran R. V. , Sridharan S. , Gould P. L. 
Published: August 2005

AbstractIn this paper a local–global analysis technique is presented for the non‐linear analysis of shells of revolution with a localized material discontinuity in the form of a crack or a cutout. The local zone is modelled using two‐dimensional general shell elements. Axisymmetric shell elements with Fourier description in the circumferential direction are used away from this local zone. In contrast to the earlier work of the authors, the geometric non‐linearity is taken into account in the axisymmetric zone as well. The harmonic coupling in the axisymmetric zone is efficiently handled through the pseudo‐load approach. A special preconditioned conjugate gradient iterative method is employed in conjunction with the arc length method for achieving improved convergence and negotiating the limit points. The attractive features of this methodology are that the tangential stiffness matrix of the structure is never assembled and factorized and that most of the computations are simple matrix–vector multiplications which are carried out efficiently at the element level. Numerical examples are presented to demonstrate the applicability of this method.
Finite element analysis of anisotropic non‐linear incompressible elastic solids by a mixed model
Authors: Srinivasan Ramakrishnan , Perucchio Renato 
Published: August 2005

AbstractA mixed finite element method is presented for geometrically and materially non‐linear analysis of anisotropic incompressible hyperelastic materials. An incremental iteractive total Lagrangian formulation is adopted. The nodal displacements and the hydrostatic pressure are independently interpolated leading to a mixed system of equations, with characteristic zero diagonal terms. Computations are carried out using a three‐dimensional linear displacement, constant pressure element. A mixed penalty approximation is then employed to eliminate the pressure variables at the element level. The anisotropic material handling capability of the formulation is tested through a number of transversely isotropic problems and the results compared to analytical solutions. To demonstrate the applicability of this formulation to model complex anisotropic problems, the inflation of a cut toroidal tube with helical fibre orientation is analysed.
A finite element algorithm for elliptical equations over unstructured domains on a data parallel computer
Authors: Hutchinson Scott A. , Ng Kwong T. , Shadid John N. 
Published: August 2005

AbstractIn the past, most finite element algorithms on data‐parallel computers have been limited to structured problem domains. Here, we consider methods to generalize the finite element method on data‐parallel architectures to unstructured domains. A nodal assembly algorithm is described which effectively allows for both the generation of the sparse interaction matrix (coefficient matrix) and its solution via a preconditioned conjugate‐gradient type routine utilizing several polynomial preconditioners on the Connection Machine 200 (CM‐200). Jacobi preconditioning along with Neumann series and least‐squares polynomial preconditioners are presented and implemented are presented and implemented. Only the Jacobi preconditioner produces an improvement in the convergence time for the problems examined. Several irregular interprocessor communication protocols available on the CM‐200 are investigated in the solution portion of the algorithm, yielding differing performance characteristics. For one such protocol, sustained performance of over two‐hundred MFlops/s, is demonstrated for a test problem on a 512 processing element CM‐200 in slicewise mode. The results are discussed and conclusions are drawn concerning this finite element algorithm.
Problems related to application of eigenstrains in a finite element analysis
Authors: Zhang J. , Katsube N. 
Published: August 2005

AbstractAccorsi has recently proposed a general method for modelling microstructural material discontinuities in a finite element analysis. In this work, it is shown that his method can be significantly simplified. In particular, the transformation strain (eigenstrain) plays no role in his application. Numerical results based on the simplified equations with 8‐node and 9‐node isoparametric elements are presented for the same examples as in his papers. The accuracy of the results is examined in comparison with the solution obtained from a complex mesh model.
The advancing‐front mesh generation method revisited
Authors: George Paul Louis , Seveno Eric 
Published: August 2005

AbstractThis paper presents a mesh generation method of the advancing‐front type which is designed in such a way that the well‐known difficulties of the classical advancing‐front method are not present. The retained solution consists of using the first steps of a Voronoï–Delaunay method to construct a background mesh which is then used to govern the algorithm. The two‐dimensional case is considered in detail and possible extensions to adaption problems and three dimensions are indicated.
Transient analysis of tube rolling processes by a semi‐analytical formulation
Authors: Antúnez H. J. , Idelsohn S. R. 
Published: August 2005

AbstractA semi‐analytical formulation is presented for transient metal‐forming processes which, being axisymmetric in geometry, are subjected to non‐axisymmetric loads and boundary conditions. The problems are described in terms of the flow formulation, and the pseudo‐concentration method (two material based) is used to account for time integration and non‐axisymmetric free surfaces. Proper Fourier series expansion of both the scalar fields defined to identify the free surfaces and of all the variables of the mechanical problem allows the performance of an advective transport–corresponding to time integration–for a non‐axisymmetric velocity field. A block diagonal matrix is obtained for each harmonic component, as it has been achieved for the constant time solution. The new configuration found as a result of this analysis is taken to calculate the velocity field for the incremented time, which in turn is used to perform the following time step.
Stress resultant geometrically non‐linear shell theory with drilling rotations. Part III: Linearized kinematics
Authors: Ibrahimbegović Adnan , Frey François 
Published: August 2005

AbstractA consistent formulation of the geometrically linear shell theory with drilling rotations is obtained by the consistent linearization of the geometrically non‐linear shell theory considered in Parts I and II of this work. It was also shown that the same formulation can be recovered by linearizing the governing variational principle for the three‐dimensional geometrically non‐linear continuum with independent rotation field. In the finite element implementation of the presented shell theory, relying on the modified method of incompatible modes, we were able to construct a four‐node shell element which delivers a very high‐level performance. In order to simplify finite element implementation, a shallow reference configuration is assumed over each shell finite element. This approach does not impair the element performance for the present four‐node element. The results obtained herein match those obtained with the state‐of‐the‐art implementations based on the classical shell theory, over the complete set of standard benchmark problems.
A segregated CFD approach to pipe network analysis
Authors: Greyvenstein G. P. , Laurie D. P. 
Published: August 2005

AbstractThe most popular pipe network algorithms fall into three categories depending on whether node, loop or element solving equations are considered. Although node methods have some advantages over the other two methods, some authors have found the node methods to be more unreliable than the other two classes of methods. Node methods are also used in Computational Fluid Dynamics (CFD) to solve the Navier–Stokes equations. Since significant progress has been made in this field in the recent past it was felt that this should have some bearing on the development of more reliable node methods for pipe network problems. In this paper the well‐known SIMPLE algorrithm of Patankar and Spalding,1 which is Known in CFD as a segregated method, is extended to deal with pipe network problems. The method can deal with both compressible and incompressible flows. Special attention is given to the solution of the pressure correction equation, the stability of the algorithm, sensitivity to initial conditions and convergence parameters. It is shown that the present method is not very sensitive to initial conditions. The method is very reliable and it deals more effectively with compressible flows than the conventional Newton–Raphson method for incompressible flows.
A non‐linear, two‐dimensional, potential‐based analysis of coupled heat and mass transfer in a porous medium
Authors: Thomas H. R. , King S. D. 
Published: August 2005

AbstractThe subject of this paper is the non‐linear analysis of coupled heat and mass transfer in a porous medium, using a potential‐based model of the phenomenon. The work presented describes an extension of the previous work of the authors, to two‐dimensional applications. Problems of greater complexity and engineering significance can hence be solved.Two applications are considered. Results from the first example, a straightforward test case, serve to highlight a number of aspects of coupled heat and mass flow. Furthermore, the problem is used to establish the validity of the numerical solution by comparisons of the results with an independent solution algorithm.The second example consists of the assessment of the ability of the formulation to describe experimentally observed behaviour by means of the simulation of laboratory experimental work. Very good correlation is obtained between numerical and experimental results. Confidence is thus gained in the theoretical basis of the work.Overall it may be concluded that the approach proposed is capable of describing coupled heat and mass transfer in porous materials.
A fast method of numerical quadrature for p‐version finite element matrices
Authors: Hinnant Howard E. 
Published: August 2005

AbstractA new technique of numerical quadrature especially suited for quadrilateral and hexahedron p‐version finite element matrices is presented. This new technique separates the integrand into two parts, and numerically operates on each part separately. The objective of this scheme is to minimize the computational cost of integrating the entire element matrix as opposed to minimizing the cost of integrating a single function. The efficiency of the new technique is compared with Gaussian quadrature and found to take a small fraction of the computational effort.
Finite volume method for stress analysis in complex domains
Authors: Demirdžić I. , Muzaferija S. 
Published: August 2005

AbstractIn this paper an alternative to the widely used finite element method for the solution of stress analysis problems is presented. The method employs a finite volume discretization of solid body equilibrium equation written in an integral form with displacement vector as a dependent variable in conjunction with an efficient iterative procedure for the solution of resulting algebraic equations. It uses unstructured meshes with arbitrary cell topology, which greatly facilitates the solution domain discretization.The method is verified on a number of test cases and it is shown to possess all the geometrical flexibility of the finite element methods and the simplicity and efficiency of the finite volume methods.
A genetic algorithm approach to single and multiobjective structural optimization with discrete–continuous variables
Authors: Dhingra A. K. , Lee B. H. 
Published: August 2005

AbstractA search procedure with a philosophical basis in molecular biology is adapted for solving single and multiobjective structural optimization problems. This procedure, known as a genetic algorithm (GA). utilizes a blending of the principles of natural genetics and natural selection. A lack of dependence on the gradient information makes GAs less susceptible to pitfalls of convergence to a local optimum. To model the multiple objective functions in the problem formulation, a co‐operative game theoretic approach is proposed. Examples dealing with single and multiobjective geometrical design of structures with discrete–continuous design variables, and using artificial genetic search are presented. Simulation results indicate that GAs converge to optimum solutions by searching only a small fraction of the solution space. The optimum solutions obtained using GAs compare favourably with optimum solutions obtained using gradient‐based search techniques. The results indicate that the efficiency and power of GAs can be effectively utilized to solve a broad spectrum of design optimization problems with discrete and continuous variables with similar efficiency.