bluuebunny/crossref_metadata_2025_split huggingface dataset:
Vibration of shear‐deformable rectangular plates using a spline‐function Rayleigh‐Ritz approach
Authors: Wang S. , Dawe D. J. 
Published: August 2005

AbstractThe prediction of the natural frequencies of vibration of rectangular plates or orthotropic laminates is described, through the use of B‐spline functions as trial functions in a Rayleigh‐Ritz approach. Through‐thickness shear deformation effects are included in the analysis and hence assumptions have to be made for the spatial variation over the plate middle surface of each of the lateral deflection and the two rotation components. Two versions of the spline‐function Rayleigh‐Ritz approach are described: in one of these the deflection and rotations are represented by functions of the same polynomial order, whilst in the other a lower‐order representation is used for each rotation component in one of the co‐ordinate directions. It is shown in a number of applications that the former version leads to shear‐locking behaviour whilst the latter version avoids this behaviour and is suitable for the analysis of both thick and thin plates.
Shell elements with drilling degree of freedoms based on micropolar elasticity theory
Authors: Yeh Jyi‐Tyan , Chen Wen‐Hwa 
Published: August 2005

AbstractBased on the theory of micropolar elasticity, new degenerated shell elements with drilling degree of freedoms are presented. The proper stiffness on the drilling degree of freedom is derived and no spurious modes are encountered in these elements. The implementation of these new shell elements on general structural finite element programs has many advantages, especially for the analysis of a folded shell or the treatment of the twist moment normal to the shell. Several numerical examples are carried out to demonstrate the accuracy and applicability of the present elements. The effects of the coupling factor and the body moment induced in magneto‐solid mechanics are also studied.
A posteriori pointwise upper bound error estimates in the finite element method
Authors: Yang J. D. , Kelly D. W. , Isles J. D. 
Published: August 2005

AbstractAn error estimate for the finite element method is presented in this paper. The error is identified as the response to a set of residual forces, and a complementary analysis provides an upper bound estimate of the global energy of the error. The inequality proposed by Babuška and Miller1 is then employed to bound the error in stress and displacement at a point. The formula is derived for two‐dimensional elasticity, but the procedure is general; and can be applied to three‐dimensional and other problems. Numerical experiments using the procedure are carried out and the results are given for the four‐node bilinear compatible element and plane stress.
Buckling of thick skew plates
Authors: Kitipornchai S. , Xiang Y. , Wang C. M. , Liew K. M. 
Published: August 2005

AbstractThe paper considers the elastic buckling of thick skew plates. Up to now, very little work has been done on this subject and the paper aspires to fill this gap. Based on the principle of stationary total potential energy and the recently developed pb‐2 Rayleigh‐Ritz method as a solution procedure, buckling solutions for skew plates of various aspect ratios, skew angles and boundary conditions are determined. The tabulation of these results, not available thus far, should be useful to designers and researchers who may use them as benchmark values to test the validity and convergence of their numerical techniques and softwares for thick plate analysis.
EAS‐elements for two‐dimensional, three‐dimensional, plate and shell structures and their equivalence to HR‐elements
Authors: Andelfinger U. , Ramm E. 
Published: August 2005

AbstractThe enhanced assumed strain (EAS) method, recently proposed by Simo and Rifai13, is used to develop new four‐node membrane, plate and shell elements and eight‐node solid elements. The equivalence of certain EAS‐elements with Hellinger‐Reissner (HR) elements is discussed. For instance, the seven‐parameter element EAS‐7 with 2 × 2 integration is identical to the HR‐element of Pian and Sumihara2. Eight‐node solid elements which are free of volumetric locking and four‐node shell elements which have an improved membrane and bending behaviour, compared to the Bathe‐Dvorkin shell element7, are introduced. Numerical tests for linear elastic problems show an improved performance of the EAS‐elements.
Further development of a three‐node triangular shell element
Authors: Cook Robert D. 
Published: August 2005

AbstractA three‐node triangular shell element having six d.o.f. per node can be economically generated as a flat element that combines well‐known formulations for membrane stiffness and plate bending stiffness. Early elements of this type were inaccurate because the membrane response was poor. Researchers improved the membrane response by adding drilling d.o.f. and by underintegrating the membrane stiffness matrix. More recent research has dealt with the addition of membrane‐bending coupling within individual elements and the suppression of mechanisms. The present work intends to continue the improvement by modifying the membrane stiffness, simplifying the membrane‐bending coupling device and suppressing mechanisms without degrading performance or causing the mesh to lock.
Large displacement transient analysis of flexible structures
Authors: Rice D. L. , Ting E. C. 
Published: August 2005

AbstractA new approach for numerical analysis of flexible space frames subjected to impact forces is presented. The method is particularly effective in the analysis of large‐amplitude vibration and dynamic stability found in extremely flexible structures.The proposed method of analysis is based on a concept of updated material frame, which allows the algorithm of handling large rotations exceeding 360° and extensions longer than 100 per cent without numerical difficulty and the need for iterations. Thus, an efficient explicit integration finite element algorithm can be adopted. The method is convenient for non‐linear and inelastic material models.The basic coding procedure is similar to the popular co‐rotational approach. Existing codes can be easily modified to solve transient dynamic problems. The modification steps necessary for the implementation are outlined in the paper.Several numerical examples are presented. Comparison with the standard co‐rotational approach and large deformation finite element formulations, such as the updated Lagrangian approach, are presented.
An adaptive multigrid technique for three‐dimensional elasticity
Authors: Kočvara Michal 
Published: August 2005

AbstractA program for finite element analysis of 3D linear elasticity problems is described. The program uses quadratic hexahedral elements. The solution process starts on an initial coarse mesh; here error estimators are determined by the standard Babuška‐Rheinboldt method and local refinement is performed by partitioning of indicated elements, each hexahedron into eight new elements. Then the discrete problem is solved on the second mesh and the refinement process proceeds in the following way‐on the ith mesh only the elements caused by refinement on the (i‐1)th mesh can be refined. The control of refinement is the task of the user because the dimension of the discrete problem grows very rapidly in 3D. The discrete problem is being solved by the frontal solution method on the initial mesh and by a newly developed and very efficient local multigrid method on the refined meshes. The program can be successfully used for solving problems with structural singularities, such as re‐entrant corners and moving boundary conditions. A numerical example shows that such problems are solved with the same efficiency as regular problems.
A normal offsetting technique for automatic mesh generation in three dimensions
Authors: Johnston Bruce P. , Sullivan John M. 
Published: August 2005

AbstractA technique, based on a normal offsetting procedure, for the fully automatic generation of meshes suitable for finite element analysis in three dimensions is presented. The method is completely automatic, requiring no user intervention in the process and no special modelling procedures. The method is applied to three‐dimensional solid geometries.The procedure positions nodes in the interior domain of an object by offsetting an initial set of nodes on the object boundary along vectors normal to the boundary to define a layer of new interior point locations. The offset points are processed to ensure good nodal spacing appropriate for generating well‐shaped elements. Following processing, the offset points become a new boundary surrounding the remaining unmeshed region in the interior of the geometric domain. The offsetting procedure is applied again to this new boundary layer to form another offset layer farther into the domain interior. The offset‐process‐offset cycle is repeated until the entire region is filled with nodes. Tetrahedral elements are then formed by triangulation of the nodes.The boundary‐based technique ensures good quality element shapes for analysis in critical boundary regions and facilitates applications involving integration of mesh generation with design geometry databases. Calculation of nodal locations are based on local parameters avoiding the higher‐order time complexities associated with global calculations.
New strategy for assumed stresses for 4‐node hybrid stress membrane element
Authors: Yuan Kuan‐Ya , Huang Yeong‐Shyang , Pian Theodore H. H. 
Published: August 2005

AbstractAn oblique (skew) co‐ordinate system defined at the origin of the isoparametric co‐ordinates is introduced as the reference co‐ordinate system for assumed stresses in the formulation of a 4‐node hybrid membrane element. The initially uncoupled stresses in these reference co‐ordinates can be constrained to satisfy the equilibrium conditions pointwise by using the procedure of Pian and Wu7, when suitable incompatible displacements are introduced. Such strategy allows the element stiffness to be formulated by using either the Hellinger‐Reissner or the complementary energy functional. Numerical results show that the performances of three elements, constructed by using different sets of incompatible displacements in this paper, are practically identical and are all of slightly higher accuracy than that of the Pian‐Sumihara element6.
Calculation of wave forces on offshore structures using parallel computers
Authors: Hardy N. , Downie M. J. , Bettess P. , Graham J. M. R. 
Published: August 2005

AbstractFour methods of implementing Morison wave‐force calculations for offshore tubular‐jacket structures on distributed‐memory parallel hardware are presented The Morison equation is given and the method by which it is used to calculate wave forces on members of an offshore structure is briefly described. A brief background to parallel computing and a description of the transputer hardware and software available to the authors is also given. Program structure and methods of achieving parallelism are explained. A number of test runs on an example structure have been timed and the resulting speed‐ups are discussed.
A finite element analysis of rubber coextrusion using a power‐law model
Authors: Buscaglia Gustavo C. 
Published: August 2005

AbstractA finite element method to simulate coupled thermal viscous coextrusion is presented, with a power‐law viscosity function obtained from viscometric data on rubber composites. It combines, by successive substitution iterations, some well‐known schemes, such as streamline integration for updating interfaces and Lagrange‐Galerkin treatment of the energy equation. Some details of the implementation are discussed. The method is then applied to a comparison of two pre‐forming plates for the dual tuber head extruder of Farrel Corporation. Both the normal stress and the temperature at the interface suggest that the presence of a deflector deteriorates the adherence properties. This prediction is in agreement with operational experience.
Applications of a super element model for non‐linear analysis of stiffened box structures
Authors: Jiang J. , Olson M. D. 
Published: August 2005

AbstractNumerical investigations are carried out to verify the new super element model developed in Reference 1 for non‐linear analysis of stiffened box structures. The results presented here are obtained from a variety of examples which are chosen to illustrate the accuracy and convergence of the model in various applications. Good agreement is obtained for most of the problems considered and the present formulation is found to be accurate and economical for preliminary engineering design.
The construction of an optimal weakly divergence‐free macroelement
Authors: Ye Xiu , Hall Charles A. 
Published: August 2005

AbstractThe divergence‐free finite element method (DFFEM) is a method to find an approximate solution of the Navier‐Stokes equations in a divergence‐free space. That is, the continuity equation is satisfied a priori. DFFEM eliminates the pressure from the calculations and reduces significantly the dimension of the system to be solved at each time step. For the standard 8‐node velocity and 4‐node pressure DFFEM, an optimal basis for the weakly divergence‐free subspace is constructed such that each basis function has non‐zero support on at most nine contiguous elements. Given this basis, weakly divergence‐free macroelements are constructed.
A six‐noded element for analysing power‐type singularities under thermal loads
Authors: Dutta Bijan K. 
Published: August 2005

AbstractThe shape functions of a 6‐noded triangular element have been derived to model power‐type singularities under thermal loads. A number of case studies have been presented, which involve variable‐order singularities under mechanical and thermal loads. The results show the usefulness of the element.
New basis functions and computational procedures for p‐version finite element analysis
Authors: Carnevali P. , Morris R. B. , Tsuji Y. , Taylor G. 
Published: August 2005

AbstractNew basis functions and solution procedures for p‐version finite element analysis are described. They are used in a highly efficient p‐version finite element solver for linear elastostatics and dynamics, which has been used in an industrial environment for over two years. Using two sample applications it is shown that, using the techniques proposed here, p‐version finite element analysis can have a substantially lower computational cost, for given accuracy, than standard finite element methods. This makes the industrial applicability of p‐version finite element analysis much wider than is commonly believed.
A computational procedure for flexible beams with frictional contact constraints
Authors: Sun S. M. , Natori M. C. , Park K. C. 
Published: August 2005

AbstractThis paper deals with the application of a parametric quadratic programming (PQP) method to the numerical solution of large‐deflection beams involving frictional contact constraints. The flexibility of the structure is modelled by an intrinsic spatial beam theory which is approximated by transverse‐shear deformable linear beam elements. The linear complementary problem (LCP) without the penalty function resulting from PQP is made part of a Newton‐Raphson search. The tool for solving the complementary equations is Lemke's algorithm, in which frictional contact conditions are enforced and new contact surfaces are updated during iteration. Applying the resulting contact element, a more accurate approximation of the contact point can be guaranteed, and the contact force can be directly computed by the adjacent beam elements. Three numerical examples are analysed to show the effectiveness and validity of the method.
Stress computation and consistent tangent operator using non‐linear kinematic hardening models
Authors: Hartmann Stefan , Haupt Peter 
Published: August 2005

AbstractOne possibility of formulating the tinite element method is founded on the principle of virtual displacement, in which we want to include a rate‐independent elastoplastic constitutive model based on the assumption of a yield surface. The constitutive equations result from the assumptions of small deformations, Hooke's law for the elastic domain, the normality rule for the evolution of plastic strains, the von Mises yield condition and a special kind of kinematic hardening due to Armstrong and Frederick,1 in which linear kinematic hardening is generalized with a saturation term. We show that it is not generally recommendable to propose large load steps. To this end, we investigate the influences of the non‐linear kinematic hardening model on the stress computation and the resulting consistent elastoplastic tangent operator. The main topics of this paper are: (1) development of a problem‐optimized backward Euler method with regard to the kinematic hardening model, (2) study of the influence of the saturation term on the numerical accuracy through isoerror maps and (3) computation of the consistent elastoplastic tangent operator.
Discrete micromechanics of elastoplastic crystals
Authors: Borja Ronaldo I. , Wren Jon R. 
Published: August 2005

AbstractThe theoretical prediction of elastoplastic behaviour of single crystals is a basic problem which is central to the prediction of the overall behaviour of the crystal aggregate. It is generally well known that quasi‐static and isothermal plastic deformation in single crystals arises almost solely from slip on specific crystallographic planes, and that this process occurs when the resolved shear stress on a critical slip system reaches a certain maximum value. What is not obvious is how one can identify the specific slip systems activated by a given load increment, since the process usually involves selection from a pool of linearly dependent slip systems. In this paper we use small‐deformation multisurface plasticity theory to phrase properly the problem of crystal slips at infinitesimal increments. We then describe an ‘ultimate’ algorithm for systematically identifying the active slip systems at finite increments. We arrive at the following major conclusions when the ultimate algorithm is applied to f.c.c. crystals: For perfectly plastic crystals the combination of active slip systems may or may not be unique; however, the imposition of the discrete Kuhn‐Tucker conditions is sufficient to determine the (unique) final crystal stresses. For Taylor hardening crystals in which active and latent slip systems harden by the same amount, the discrete Kuhn‐Tucker conditions are also sufficient to make the mathematical problem of crystal stress integration well posed, i.e. the final stresses can be determined uniquely albeit the combination of active slip systems may not be unique. To illustrate the latter point, an accurate return‐mapping algorithm for perfectly plastic and Taylor hardening crystals is described and tested against the ultimate algorithm to demoustrate numerically that it is possible to generate different combinations of active slip systems and yet produce identical final stresses.
Physically correct penalty‐like formulations for accurate pressure calculation in finite element algorithms of the Navier‐Stokes equations
Authors: Dyne B. R. , Heinrich J. C. 
Published: August 2005

AbstractFinite element algorithms for incompressible fluids, in particular the penalty function method, are re‐examined and re‐formulated based on physically consistent approximations to the mass conservation equation. These approximations lead to methods that satisfy all fluid conditions under the assumption of slightly compressible flow and directly yield approximations to the pressure field that are free from spurious oscillations. Penalty function‐type algorithms are developed for direct steady‐state calculations and for time‐dependent simulations of viscous incompressible flows that are based on the bilinear isoparametric quadrilateral element and circumvent the Ladyszhenskaya, Babuska and Brezzi (LBB) condition. Further‐more, methods that eliminate pressure oscillations in the low Mach number region of high‐speed compressible flows are obtained. These methods are tested in examples that show their superior performance in approximating the pressure field.
Fully implicit integration and consistent tangent modulus in elasto‐plasticity
Authors: Doghri Issam 
Published: August 2005

AbstractThis paper deals with the numerical integration of a class of rate‐independent elasto‐plastic models. The backward Euler scheme is used to integrate the rate constitutive relations. The non‐linear equations obtained are solved by the Newton method. The consistent tangent modulus is obtained by exact linearization of the algorithm. In the case of J2 elasto‐plasticity with non‐linear isotropic hardening and non‐linear kinematic hardening (Chaboche‐Marquis model), explicit formulas are derived, without any approximations.
A parametric study on achieving the same final shape by numerical experimentation using a shape optimization process subject to different initial conditions
Authors: Gates A. A. 
Published: August 2005

AbstractA finite element based shape optimization program has been developed for three‐dimensional shell structures which allows for multiple edge movement and large shape changes. This program automatically performs shape optimization by linking together adaptive mesh generation, substructuring and optimization algorithms with a commercial finite element analysis program, MSC/NASTRAN. This paper examines the robustness of the shape optimization program by varying the initial shape and design parameters for three examples. This is performed to determine the conditions under which similar optimum shapes will be generated for different initial conditions.
A Streamline‐Upwind‐Full‐Galerkin method for space–time convection dominated ‐transport problems
Authors: Perrochet P. 
Published: August 2005

AbstractAn original space‐time finite element approach for the solution of the diffusion‐convection equation is proposed in this paper. A slight manipulation of the differential equation suggests that transient transport problems may in fact be seen as ‘steady‐state space‐time transport problems’, accurately and easily soluble by the standard Galerkin technique. However, concerning convective transport involving sharp fronts or coarse discretization, it is shown that implementation of dissipation along space‐time trajectories significantly improves the solutions. Classical comparative test problems are run to establish the performances of this method, and to show the limits of the more sophisticated Petrov and Taylor‐Galerkin schemes. Evocation of a possible space‐time anisotropy generated by usual finite difference time‐stepping procedures, as well as comparative analysis of amplification matrices, help to understand the accuracy and the robustness of the proposed approach.
H‐Adaptive finite element methods for dynamic problems, with emphasis on localization
Authors: Belytschko T. , Tabbara M. 
Published: August 2005

AbstractH‐adaptive procedures for the finite element solution of transient solid mechanics problems are studied, with particular emphasis on problems involving localization due to material instability. Various types of error criteria are examined and it is shown that for problems involving plastic response or localization, an error criterion based on an L2‐projection of strains is the most effective for the constant strain elements considered here. Examples of one‐dimensional and two‐dimensional localization (shear band formation) problems are given.