bluuebunny/crossref_metadata_2025 huggingface dataset:
A numerical study of the deviation of the crack ending at the interface in a multilayer
Authors: El Abdi R.
Published: November 2005

The study of the deviation of a crack reaching the interface separating two materials in a multilayer in a 4‐point deflection is considered. This study is based on the use of special isoparametric finite elements.1 (The elements surrounding the crack tip have nodes placed at a distance α from the crack tip, and in this way we impose a singularity of the stresses in the neighbourhood of the crack.)

The Erdogan2 criterion that estimates the deviation angle shows that this angle is a function of the initial angle of the crack, and the properties of each component of the multilayer.
An implicit finite‐element method for high‐speed flows
Authors: Hassan O. , Morgan K. , Peraire J.
Published: November 2005

A fast algorithm is presented for constructing continuous lines, made up of element sides, which pass once through each node of a general unstructured triangular mesh and which are generally aligned in prescribed directions. The lines are used as the basis of an adaptive fully implicit unstructured grid procedure for the solution of two‐dimensional problems of steady compressible inviscid and laminar viscous high‐speed flows, where the equation system is solved by line relaxation using a block tridiagonal equation solver. For three‐dimensional laminar viscous simulations it is proposed to utilize an implicit/explicit finite‐element formulation. In the vicinity of solid walls a grid exhibiting structure in the normal direction is employed while, away from this region, the grid will be totally unstructured. In the structured region, lines in the normal direction to the wall are readily identified, while lines in the surfaces parallel to the solid wall are constructed using the proposed two‐dimensional procedure. The implicit algorithm is then used in the structured region and the equation solution is achieved via line relaxation. An explicit form of the solution algorithm is used elsewhere. To illustrate the performance of the proposed method, solutions are obtained for both transonic inviscid and transonic and hypersonic laminar viscous problems in two dimensions. The application of the proposed procedure to the solution of three‐dimensional hypersonic laminar viscous flow over a double ellipsoid configuration is also described.
New predictor/corrector algorithms with improved energy balance for a recent formulation of dynamic vehicle/structure interaction
Authors: Vu‐Quoc L. , Olsson M.
Published: November 2005

A new class of predictor/corrector algorithms is proposed to solve the complex system of differential equations that arises from a Galerkin spatial discretization of the equations of motion in a recent formulation of dynamic vehicle/structure interaction. The applicability of the concept of a building‐block vehicle/structure interaction model developed in our previous work—where the vehicle nominal motion is not prescribed a priori, but is part of the unknown motion of the system—is demonstrated through the construction of a simple vehicle model. In the new algorithms, the presence of the accelerations of the vehicle component is eliminated in the predictor structural equations, making these equations different from the corrector structural equations. The special treatment of the predicted axial motion that provides an artificial damping to eliminate unstable oscillations in the numerical results as proposed in the old algorithms is avoided. Accurate results from numerical simulations using the new algorithms are obtained, and there are no unstable oscillations that were observed in some other predictor/corrector schemes. The system energy balance is also better preserved compared with the old algorithms.
Phase‐space representation of iterative design processes
Authors: Burns Scott A.
Published: November 2005

A large variety of design optimization methods have been proposed in recent years. Comparison of the relative performance of each method is a difficult task, and attempts to do so are often based on a limited number of numerical experiments. Recently, a ‘basins of attraction’ construction has been proposed as a graphical tool for investigating global performance of iterative design optimization methods, and as a basis for comparison of different methods. The phase‐space representation presented in this paper is a companion to the basins of attraction construction. Basins of attraction reveal the relationship between starting design and final outcome of the solution process; the phase‐space construction reveals that nature of the paths connecting the starting design and final outcome. The two constructions complement one another in summarizing the performance of design optimization processes. Both constructions are demonstrated in this paper, applied to the optimal design of an elastic grillage structure using Newton's method and the stress ratio method.
A numerical method for the solution of two‐dimensional inverse heat conduction problems
Authors: Reinhardt H.‐J.
Published: November 2005

A numerical method for the solution of inverse heat conduction problems in two‐dimensional rectangular domains is established and its performance is demonstrated by computational results. The present method extends Beck's8 method to two spatial dimensions and also utilizes future times in order to stabilize the ill‐posedness of the underlying problems. The approach relies on a line approximation of the elliptic part of the parabolic differential equation leading to a system of one‐dimensional problems which can be decoupled.
On the numerical integration of a class of pressure‐dependent plasticity models with mixed hardening
Authors: Lee J. H. , Zhang Y.
Published: November 2005

Radial return algorithms, for both three‐dimensional and plane stress situations, are developed for a class of pressure‐dependent plasticity models (formulated in state variables) with mixed hardening. The consistent tangent matrix has been developed which, among other advantages, does not require numerical inversion. The algorithms, for Gurson's mixed hardening model, are incorporated in a finite element program to solve several simple uniaxial tension problems. When compared with numerically integrated solutions, the results from the finite element analysis show excellent agreement. Finally, results of the axisymmetric necking problem, using Gurson's mixed hardening model, are presented as an example of application.
A comparative study of the behaviour of a direct solver and a preconditioned iterative solver for the equations arising from the discretization by Chebyshev collocation of a second‐order partial differential equation on a square
Authors: Kjellmert Bo
Published: November 2005

The behaviour is compared of two solvers for the discrete equations arising from the discretization using Chebyshev collocation of a second‐order linear partial differential equation on a square. The alternative solvers considered are a direct solver and an iterative solver based on preconditioning with the matrix arising from finite‐difference discretization of the governing equation. The total error of the collocation derivatives and the separate contributions from round‐off and discretization error are examined. The efficiency of the two solvers is compared. The iterative solver is more efficient than the direct solver on fine grids for equations similar to the Poisson equation, provided that there are Dirichlet boundary conditions on at least three of the sides of the square.
Forced harmonic vibration of rotating beam systems in space analysed by use of exact finite elements
Authors: Lundblad H. Mikael
Published: November 2005

A general computational technique is developed for the accurate analysis of forced non‐synchronous harmonic vibration of linear structures rotating with constant speed about a fixed axis in the inertial space. The structures studied are built up from piecewise uniform straight Rayleigh‐Timoshenko beam members having coinciding cross‐sectional centres of geometry, shear and mass, and vibrating in coupled tension, torsion, bending and shearing. Hysteretic and viscous dampings in the beam material and in a Winkler‐type ambient medium are considered. Rigid bodies and modal bodies and also discrete masses, springs and dampers can be included in the structure. The six coupled scalar partial linear differential equations governing the motion of a loaded beam are established in a corotating local co‐ordinate system. A transcendentally frequency‐dependent non‐symmetric complex‐valued 12 × 12 stiffness matrix is derived, over a state‐space analogy and an associated eigenproblem, for a harmonically vibrating beam member non‐synchronously excited at its ends. This matrix is exact in the sense that no assumed shape functions and no lumped masses are used. The general computational technique is here applied to a simple beam rotating about (1) its longitudinal axis and (2) about a transverse axis. The study clarifies the influence of gyroscopic effects and of material and support dampings on the dynamical behaviour of the beam at different rotational speeds and forcing frequencies. Resonance frequencies are found. Frequency response functions and frequency maps are plotted.
A comparison of adaptive‐grid redistribution and embedding for steady transonic flows
Authors: Dannenhoffer John F.
Published: November 2005

In recent years, numerical analysts have increasingly turned to adaptive‐grid techniques to efficiently obtain highly‐accurate solutions to partial‐differential equations. This paper presents a comparison of two distinct grid‐adaptation approaches, grid‐point redistribution and grid‐embedding, applied to two‐dimensional, steady, inviscid, shocked flows. Grid redistribution is accomplished through a control function approach applied to the elliptic‐grid generator while the embedding approach consists of a fixed global grid and an automatically chosen number of irregularly shaped, embedded regions. For both techniques, the Euler flow equations are integrated to steady state using Ni's Lax‐Wendroff‐type integrator to predict the flow fields about a variety of isolated airfoil configurations. The application of a common integration scheme as well as a common adaptive control function leads to a direct comparison of the effectiveness of the two adaptation approaches for the types of problems tested.
Shape reconstruction and volume meshing for complex solids
Authors: Baker Timothy J.
Published: November 2005

The reconstruction of a solid surface from a series of cross‐sections and the generation of a volume mesh that conforms with a prescribed surface are issues that arise in numerous applications. We describe an approach to both these problems that is based on the generation of a tetrahedral mesh which automatically captures a triangulation of the surface points. A simple algorithm for introducing a set of interior points permits a simple partition of the volume mesh into two disjoint sets of tetrahedra such that one set determines the interior of the solid while the second determines the exterior.
Multi‐domain two‐ and three‐dimensional thermoelasticity by BEM
Authors: Deb A. , Banerjee P. K.
Published: November 2005

A computationally advantageous multi‐domain boundary element formulation is presented for uncoupled thermoelastic analysis of two‐ and three‐dimensional isotropic media. Particular integrals capable of representing exactly a quadratic temperature distribution in both two and three dimensions are employed. These particular integrals are derived using an orderly approach. When temperature data are provided at discrete points, the best fit quadratic distribution is generated in the least square error sense which, together with a multi‐domain approach, makes it possible to represent an arbitrary temperature distribution within acceptable bounds. Numerical examples are given to show the efficiency and effectiveness of the present formulation, which is now incorporated in a general purpose boundary element code named GPBEST.
Efficient and accurate four‐node quadrilateral C0 plate bending element based on assumed strain fields
Authors: Shi Guangyu , Voyiadjis George Z.
Published: November 2005

Based on the assumed element strain fields and the interrelated displacement‐rotation interpolations, a four‐node (12 dof) quadrilateral C0 finite element, designated as QCCP‐2, for the analysis of thick/thin plates is developed in this paper. The four‐node C0 plate element presented here possesses a linear bending strain field, and the element stiffness matrices are given explicitly. Therefore, the present four‐node C0 plate element is more efficient and accurate than the existing four‐node C0 plate elements where the constant strain stiffness matrices are obtained by numerical integration. By the use of the interrelated displacement‐rotation interpolations, QCCP‐2 is capable of automatically satisfying the Kirchhoff assumption for the case of thin plates. Consequently, QCCP‐2 is not only free of shear locking, but also free from the numerical ill‐conditioning. Furthermore, QCCP‐2 passes the patch test of thin plates. The four‐node quadrilateral C0 elements presented here can automatically reduce to the corresponding three‐node triangular elements. Several numerical examples are given to demonstrate the efficiency and accuracy of the C0 plate bending element QCCP‐2.
Numerical simulation of mechanical systems using methods for differential‐algebraic equations
Authors: Anantharaman Martin , Hiller Manfred
Published: November 2005

A simple approach to the numerical simulation of mechanical systems consisting of rigid and flexible bodies is presented. The mechanical system may consist of rigid bodies, different types of flexible bodies, joints and actuators and may have arbitrary topological structure with kinematical loops. The equations of motion are formulated as a large sparse system of equations in absolute co‐ordinates as well as relative co‐ordinates. These equations are numerically integrated as a system of differential‐algebraic equations using modern numerical methods.
A decoupled flexible‐relative co‐ordinate recursive approach for flexible multibody dynamics
Authors: Lai Hao‐Jan , Haug Edward J. , Kim Sung‐Soo , Bae Dae‐Sung
Published: November 2005

An extended kinematic graph concept and a variational‐vector calculus approach are employed to develop a new recursive formulation for the dynamic analysis of flexible multibody systems. The extended graph concept introduced defines frames and transformations between frames as nodes and edges, respectively, rather than the more traditional body and joint convention. Kinematic relationships between adjacent flexible bodies are derived, using joint relative co‐ordinates and a state vector notation that represents both translational and rotational components of velocity. Deformation kinematics are formulated in terms of modal co‐ordinates, under small deformation assumptions. Joint relative co‐ordinates are decoupled from deformation modal co‐ordinates in both kinematic relations and in the recursive dynamics algorithm, leading to a significant reduction in the dimension of matrices that must be inverted. Dynamic analysis of a flexible closed‐loop spatial robot is performed to illustrate the efficiency of the algorithm.
On a stress resultant geometrically exact shell model. Part VI: Conserving algorithms for non‐linear dynamics
Authors: Simo J. C. , Rifai M. S. , Fox D. D.
Published: November 2005

In Parts I to V of the present work, the formulation and finite element implementation of a non‐linear stress resultant shell model are considered in detail. This paper is concerned with the extension of these results to incorporate completely general non‐linear dynamic response. Of special interest here is the dynamics of very flexible shells undergoing large overall motion which conserves the total linear and angular momentum and, for the Hamiltonian case, the total energy. A main goal of this paper is the design of non‐linear time‐stepping algorithms, and the construction of finite element interpolations, which preserve exactly these fundamental constants of motion. It is shown that only a very special class of algorithms, namely a formulation of the mid‐point rule in conservation form, exactly preserves the total linear and angular momentum. For the Hamiltonian case, a somewhat surprising result is proved: regardless of the degree of non‐linearity in the stored‐energy function, a generalized mid‐point rule algorithm always exists which exactly conserves energy The conservation properties of a time‐stepping algorithm need not, and in general will not, be preserved by the spatial discretization. Precise conditions which ensure preservation of these conservation properties are derived. A number of numerical simulations are presented which illustrate the exact conservation properties of the proposed methodology.
Finite‐rotation shell elements for the analysis of finite‐rotation shell problems
Authors: Başar Yavuz , Ding Yunhe
Published: November 2005

For the analysis of shell structures with finite displacements and rotations displacement‐based and mixed finite‐rotation shell elements are developed starting from consistent tensorial shell theories. The constraints for the description of the deformed normal vector have been considered at the element level as subsidiary conditions so that finite rotations in arbitrary strongly nonlinear situations can be considered without any difficulty. The efficiency of the finite‐rotation elements is demonstrated by numerical examples.
A Taylor—Galerkin finite element method for non‐Newtonian flows
Authors: Tamaddon‐Jahromi H. R. , Ding D. , Webster M. F. , Townsend P.
Published: November 2005

Some recent results are reviewed that indicate the appropriate nature of Taylor–Galerkin based algorithms for solving model convection–diffusion problems accurately in time and for simulating more complex non‐Newtonian flows, such as those arising in the polymer industry. Initially attention is given therefore to linear and non‐linear convection–diffusion model problems in two space dimensions, and then to transient problems involving heating effects. Newtonian and generalized Newtonian models are considered for both power‐law and Carreau models for various parameters. Effects of shear‐rate changes and temperature variations through transient build up periods are discussed in relation to their influence on the viscosity and viscous heating for thermal Péclet numbers of 1 and 100.
A logic for simple Petrov–Galerkin weighting functions
Authors: Freund J. , Salonen E.‐M.
Published: November 2005

Weak form for the solution of the complete second order boundary value problem in one‐dimensional case is derived in a way, which should be easy to comprehend. The starting point is the boundary value problem extended with suitable jump conditions. The aim is a convenient form for numerical calculations and weighting functions giving accurate nodal values. The connections with SUPG‐, GLS‐ and GGLS‐method is discussed with reinvention explaining the selections of ‘free’ parameters related to these methods. Finally some ideas to extend the methods to two‐dimensional cases are presented.
A finite element formulation of the large sliding contact
Authors: Schreppers G. J. M. A. , Brekelmans W. A. M. , Sauren A. A. H. J.
Published: November 2005

A finite element formulation for the large sliding contact problem is discussed. With respect to a set of two material points the free and contacting state are distinguished. Because of the possibly occurring large slidings, the two points contact conditions are transformed to contact conditions with respect to larger sets of points, the so‐called contact units. An incremental solution strategy is presented which calculates the equilibrium solution that obeys these contact conditions using an iterative procedure. Part of this strategy is the identification of actual sets of contacting material points. The performance of the algorithm is demonstrated by some case‐studies.
Newton‐like methods with limited storage, for the solution of elasto‐viscoplasticity problems
Authors: Reed M. B.
Published: November 2005

Quasi‐Newton and Secant‐Newton methods have been successful in solving problems of elasto‐plasticity. In this paper these methods are applied to elasto‐viscoplastic analyses, in an algorithm coupling the global solution for displacement increments with local Newton‐Raphson stress iteration at each sampling point. The familiar rank‐two DFP and BFGS methods are generalized to the Broyden family of algorithms, and this generalization is also used to produce a Secant‐Newton algorithm corresponding to Hoshino's method. Consideration is given to the most effective strategy when only a limited number of Quasi‐Newton iterates may be stored; overwriting, re‐start or continuation in Secant‐Newton form. Results are presented for a tunnelling problem using both plane strain and axisymmetric formulations.
Boundary element approach for dynamic poroelastic problems
Authors: Dominguez José
Published: November 2005

A Boundary Element approach for dynamic poroelastic problems in the frequency domain is presented. The technique is based on an integral equation formulation in terms of solid displacements and fluid stress. The analogy between dynamic poroelasticity and thermoelasticity in the frequency domain is used to obtain the fundamental solution. The Boundary Elements formulation is developed and the numerical aspects related to the integration of the fundamental solution kernels analysed. A computer code for two‐dimensional problems is implemented and validated by solving two basic problems. The obtained numerical results are compared with the corresponding exact solutions.
A shear locking free isoparametric three‐node triangular finite element for moderately‐thick and thin plates
Authors: Kabir Humayun R. H.
Published: November 2005

A shear locking free isoparametric three‐node triangular plate bending element, KEYA, is developed. Reissner/Mindlin theory that incorporates transverse shear deformation is assumed in the plate formulation. Numerical results include patch tests, convergence of transverse displacement and stress resultants, and variations of them for various parametric effects on cantilever, simply supported and clamped plates.
Analysis and evaluation of singular integrals by the invariant imbedding approach
Authors: Rosen Dan , Cormack Donald E.
Published: November 2005

The invariant imbedding formulae for evaluating singular integrals on flat domains are used to analyse the singular integrals which arise in the Boundary Element Method.

Although all orders of singularity are considered, the primary objective of the paper is the evaluation of Cauchy principal value integrals (CPV). Conditions for boundedness of the CPV aré derived, and evaluation techniques are presented for situations in which the singular point lies on, or is in close proximity to, an element boundary. Specific cases analysed include straight and curved element boundaries, and corners. Other numerical aspects of the formulae are also discussed.

By way of example, the analysis techniques are applied to the volume integrals which arise in continuum, inelastic problems.
Some recent trends and developments in finite element analysis for incompressible thermal flows
Authors: Ramaswamy B. , Jue T. C.
Published: November 2005

A numerical procedure for solving the time‐dependent, incompressible Navier–Stokes and energy equations is presented. The present method is based on a set of finite element equations of the primitive variable formulation, and a time‐splitting procedure which has unique features in its formulation as well as in its evaluation from the viewpoint of efficiency and accuracy. The applicability of the proposed formulation was verified by computations and comparison with known results.
A new unconditionally stable fractional step method for non‐linear coupled thermomechanical problems
Authors: Armero F. , Simo J. C.
Published: November 2005

A new class of time‐stepping algorithms for strongly coupled thermomechanical problems is presented which retains the computational convenience of traditional staggered algorithms without upsetting the unconditional stability property characteristic of fully implicit (monolithic) schemes.

This class of methods was first introduced by the authors (in the general context of thermoplasticity) in the USCM held at Chicago, July 1991, and in the IUTAM symposium held at Hannover, Germany, September 1991

The proposed schemes are fractional step methods associated with a two phase operator split of the full non‐linear system of thermoelasticity into an adiabatic elastodynamics phase, followed by a heat conduction phase at fixed configuration. This operator split is shown to inherit the contractivity property of the full problem of evolution, thus leading to unconditionally B‐stable product formula algorithms. In sharp contrast with this stability result, traditional staggered algorithms based on an isothermal mechanical phase followed by a heat conduction phase with an effective heat source are shown to lead, at best, to conditionally stable schemes. It is further shown that the actual implementation of these two classes of schemes is essentially identical. The numerical simulations presented include both dynamic and quasi‐static problems and are shown to closely replicate the stability estimates and non‐linear stability results derived for these two classes of staggered schemes.
A finite element model for the simulations of mould filling in metal casting and the associated heat transfer
Authors: Usmani A. S. , Cross J. T. , Lewis R. W.
Published: November 2005

The flow associated with the pouring of molten metal into moulds has been modelled based upon certain simplfying assumptions. A finite element based Navier‐Stokes equation solver has been used to analyse the flow. The velocities obtained from the Navier‐Stokes equation solver are used to advect a pseudo‐concentration function for modelling the free fluid front. A simple problem with a known analytical solution is solved first to test the model. Subsequently, several more examples of varied geometrical configuration are modelled to demonstrate the applicability of the proposed model. The Taylor‐Galerkin method has been used to model the heat transfer during filling due to its advection dominated nature.
Numerical simulation of forming processes using a coupled fluid flow and heat transfer model
Authors: Reddy M. P. , Reddy J. N.
Published: November 2005

Numerical simulation of forming processes is studied using the Navier‐Stokes equations and the energy equation governing viscous, incompressible fluids. A review of various important aspects of forming processes is also reviewed for completeness. A penalty finite element model of the equations is developed. The finite element model is used to study the effectiveness of various constitutive models developed for metal forming and polymer processing. The element‐by‐element (EBE) data structure with efficient iterative solution methods is used to solve the large systems of equations that arise in the analysis of complex 3‐D problems. Numerical results for problems representative of various forming processes (e.g. extrusion and solidification) are presented.
An alternative approach to shape design sensitivity analysis
Authors: Zhao Zhiye , Adey R. A.
Published: November 2005

A novel method is presented in this paper for calculating shape design sensitivity, which is based on the finite difference method (FDM). By analysing the numerical procedure of the FDM, the perturbation of the geometry is replaced by a perturbation load which can be calculated once the stress field of the initial problem and the design boundary perturbation are known. The final shape design sensitivity is obtained by solving the perturbation problem which has the same geometry and the kinematical boundary condition as the initial problem, but under the perturbation loads. Therefore the new method does not require the calculation of the matrices of the perturbed structure, and is independent of the perturbation step. A numerical implementation of the finite difference load method (FDLM) is described in which the boundary element method is used to evaluate the structural response. The numerical examples demonstrate that this new method for shape design sensitivity analysis is very accurate.
Theory and finite element formulation of rubberlike membrane shells using principal stretches
Authors: Gruttmann F. , Taylor R. L.
Published: November 2005

A theory of rubberlike membrane shells undergoing large elastic deformations is derived. The stresses are deduced from Ogden's material law, which is formulated in terms of the principal values of the right stretch tensor. Incompressibility is fulfilled exactly using the plane stress constraint. Furthermore, a finite element formulation of the membrane theory is given. The use of the tangential stiffness matrix, derived analytically, provides a quadratically convergent solution process. Several numerical examples show the robustness of the developed finite element.
Localized collapse of shells of revolution using a local‐global strategy
Authors: Ravichandran R. V. , Gould P. L. , Sridharan S.
Published: November 2005

The mode of collapse in many metallic shells is, oftentimes, one of localized collapse, wherein severe plastic deformation and high displacement gradients are localized within some region. The combined material and geometric non‐linearity emanating from this local region is the predominant cause of instability in shells of revolution. In such a situation a local‐global strategy is very useful for an efficient analysis. This strategy consists of employing two dimensional degenerated isoparametric shell elements with non‐linear capability in a well defined 'local' zone where all the non‐linearities are expected to be localized and which also contains some form of local deviation from axisymmetry such as a circumferential imperfection, cutouts, cracks, etc. Linear elastic ring type elements are employed in the remaining axisymmetric zone and the two zones are linked through a transformation between the degrees of freedom involved. The solution of the non‐linear problem is achieved by appropriate condensation procedures to reduce the number of active degrees of freedom and the load incrementation is achieved by the well known 'arc length' iterative procedure. Numerical exampies are presented to demonstrate that this strategy is very efficient and accurate for problems with well defined non‐linear local zones. The capability of this strategy for treating problems with local material discontinuities such as cracks, cutouts, etc. as an efficient alternative to a complete two dimensional discretization is pointed out.
An efficient method for the two‐dimensional elastostatic boundary element method
Authors: Yokoyama Masaaki , Zaita Tomohiro
Published: November 2005

In order to obtain accurate results and to reduce computation time, we have proposed in this paper a new strategic method, where quadratic elements are used at the corner points and linear elements at the points off the corner points. A computer program using this method has been developed and applied to several problems of various shapes. The usefulness of this method was illustrated by the application results.
Finite element asymptotic analysis of slender elastic structures: A simple approach
Authors: Casciaro R. , Salerno G. , Lanzo A. D.
Published: November 2005

An asymptotic method directly derived from Koiter's theory and suitable for the solution of elastic buckling problems and its natural adaptation to a numerical solution by means of a finite element technique are presented here. The order of the extrapolation of the equilibrium equations has been intentionally kept very low because attention has been entirely devoted to all those features (theoretical definitions, eigenproblem numerical techniques, suitable FEM implementation) which make such an approach competitive with respect to the classic step‐by‐step methods. For plane frames and 3D pin‐jointed trusses, the performances of the algorithm (numerical accuracy and computational cost) are compared with those of Riks' are‐length method.
Hybrid trefftz plane elasticity elements with p ‐method capabilities
Authors: Jirousek J. , Venkatesh A.
Published: November 2005

A family of p‐method plane elasticity elements is derived based on the hybrid Trefftz formulation.1 Exact solutions of the Lamé‐Navier equations are used for the intra‐element displacement field together with an independent displacement frame function field along the element boundary. The final unknowns are the parameters of the frame function field consisting of the usual degrees of freedom at corner nodes and an optional number of hierarchic degrees of freedom associated with the mid‐side nodes. Since the element matrices do not involve integration over the element area, the elements have a polygonal contour with an optional number of curved sides. The quadrilateral element has the same external appearance as the conventional p‐method plane elasticity element.2,3 But unlike in the conventional p‐method approach, suitable special‐purpose Trefftz functions are generally used to handle the singularity and/or stress concentration problems rather than a local mesh refinement. The practical efficiency of the new elements is assessed through a series of examples.
On the limits of finite element perfectability
Authors: Macneal Richard H.
Published: November 2005

It has been shown2 that a four‐noded membrane element of trapezoidal shape must either lock or fail constant strain patch tests. That result is generalized here to establish similar limitations for all finite elements. A modal analysis is used to show that essential coupling exists between low modes whose displacement states can be exactly represented by an element's basis functions and higher modes whose displacement states cannot be so represented. Such coupling can be avoided only when an element has particular shapes. In all other cases the element designer is faced with the choice of patch test failure in a low mode or locking in a higher mode. Several examples are described.
Three‐dimensional 8‐node and 20‐node refined hybrid isoparametric elements
Authors: Chen Wanji , Cheung Y. K.
Published: November 2005

In this paper a new hybrid variational principle with independent variables of strain, stress and displacement and with a weaker constraint condition of interelement continuity is proposed. Based on this functional, a general formulation of a refined hybrid isoparametric element method has been established by the orthogonal approach.

The present formulation is a rational approach to be adopted for deriving high‐performance three‐dimensional hybrid isoparametric elements even up to the higher‐order 20‐node element.

Several numerical examples are presented to show that the present elements RGH8(8‐node) and RGH20(20‐node) have high accuracy, excellent computational efficiency and less sensitivity to mesh distortion.
Projection methods in flexible multibody dynamics. Part II: Dynamics and recursive projection methods
Authors: Wehage R. A. , Shabana A. A. , Hwang Y. L.
Published: November 2005

In Part I of this paper the kinematic relationships between the absolute, elastic and joint accelerations are developed. In this paper, these kinematic equations are used with the generalized Newton‐Euler equations and the relationship between the actual and generalized reaction forces to develop a recursive projection algorithm for the dynamic analysis of open‐loop mechanical systems consisting of a set of interconnected rigid and deformable bodies. Optimal matrix permutation, partitioning and projection methods are used to eliminate the elastic accelerations while maintaining the inertia coupling between the rigid body motion and the elastic deformation. Recursive projection methods are then applied in order to project the inertia of the leaf bodies onto their parent bodies. This leads to an optimal symbolic factorization which recursively yields the absolute and joint accelerations, and the joint reaction forces. The method presented in this paper avoids the use of Newton‐Raphson algorithms in the numerical solution of the constrained dynamic equations of open‐loop kinematic chains since the joint accelerations are readily available from the solution of the resulting reduced system of equations. Furthermore, the method requires only the inversion or decomposition of relatively small matrices and the numerical integration of a minimum number of co‐ordinates. Open‐loop multibody robotic manipulator systems are used to compare the results and efficiency of the recursive methods with that of the augmented formulations that employ Newton‐Raphson algorithms.
An automatic adaptive refinement finite element procedure for 2D elastostatic analysis
Authors: Lee C. K. , Lo S. H.
Published: November 2005

An automatic adaptive refinement procedure for finite element analysis is presented. The procedure is applied to two‐dimensional elastostatic problems to obtain solutions of prescribed accuracy. Through the combined use of new mesh generator using contour developed by Lo1 and the concept of strain energy concentration, high‐quality graded finite element meshes are generated. The whole process is fully automatic and no user intervention is required during the successive cycles of the mesh refinements. The Zienkiewicz and Zhu2 error estimator is found to be effective and has been adopted for the present implementation. In the numerical examples tested, the error estimator gives an accurate error norm estimation and the effectivity index of the estimator converges to a value close to unity.
The modelling of aerodynamic flows by solution of the euler equations on mixed polyhedral grids
Authors: Peace A. J. , Shaw J. A.
Published: November 2005

In this paper, an algorithm for obtaining solutions to the compressible Euler equations on mixed polyhedral grids is described. These grids, which are, in general, composed of hexahedral, pentahedral and tetrahedral elements, are used in the modelling of aerodynamic flows over complex three‐dimensional geometries. The hexahedra are grouped into regular blocks, while the other elements are part of irregular grid regions, giving rise to the term “hybrid grid approach”. The interconnection of the grid elements is defined by an efficient data structure, which supplies the required information to drive the Euler algorithm. In fact, cell‐vertex and cell‐centre spatial discretization variants of this algorithm are detailed, along with an explicit time‐marching scheme for obtaining steady‐state solutions. Results on two geometrically simple configurations provide an evaluation of these solution techniques, whilst the focus on a third, complex configuration, demonstrates the potential of the method in addressing the flow over general aircraft geometries.
Direct polycondensations of N,N′‐(4,4′‐oxydiphthaloyl)‐bis‐L‐leucine diacid by use of tosyl chloride in the presence of N,N‐dimethylformamide
Authors: Mallakpour Shadpour , Kowsari Elaheh
Published: November 2005

4,4′‐Oxydiphthalic anhydride (1) was reacted with L‐leucine (2) in acetic acid and the resulting N,N′‐(4,4′‐oxydiphthaloyl)‐bis‐L‐leucine diacid (4) was obtained in high yield. The direct polycondensation reaction of this diacid with several aromatic diols such as bisphenol A (5a), phenolphthalein (5b), hydroquinone (5c), 4,4′‐dihydroxydiphenyl sulfide (5d), 4,6‐dihydroxypyrimidine (5e) and 4,4′‐dihydroxydiphenyl sulfone (5f) 2,4′‐dihydroxyacetophenone (5g) and 2,6‐dihydroxytoluene (5h) was carried out in a system of tosyl chloride (TsCl), pyridine and N,N‐dimethylformamide (DMF). The reactions with TsCl were significantly promoted by controlling alcoholysis with diols in the presence of the catalytic amounts of DMF to give a series of optically active poly(ester‐imide)s (PEI)s with good yield and moderate inherent viscosity ranging 0.36–0.78 dL/g. The polycondensation reactions were significantly affected by the amounts of DMF, the molar concentration of monomers, TsCl and pyridine, aging time, temperature and the reaction time. All of the above polymers were fully characterized by 1H‐NMR, FT‐IR, elemental analysis and specific rotation. Some structural characterization and physical properties of these optically active PEIs are reported. Copyright © 2005 John Wiley & Sons, Ltd.
How ischaemic preconditioning protects small liver grafts
Authors: Franco‐Gou R , Roselló‐Catafau J , Casillas‐Ramirez A , Massip‐Salcedo M , Rimola A , Calvo N , Bartrons R , Peralta C
Published: November 2005

Interleukin‐1 (IL‐1) and transforming growth factor‐β (TGFβ) are key inhibitors of hepatocyte proliferation after hepatectomy. IL‐1 inhibition by heat shock proteins (HSPs) has been reported in inflammatory processes. A recent study indicated the benefits of ischaemic preconditioning in reduced‐size orthotopic liver transplantation (ROLT). The present study examined: (a) the effect of ischaemic preconditioning on IL‐1 and TGFβ in ROLT; (b) whether preconditioning protects small liver grafts through HSP induction; and (c) whether the potential benefits of preconditioning on HSP is related to IL‐1 inhibition. Our results, obtained with an IL‐1 receptor antagonist, indicated the injurious effects of IL‐1 in ischaemia‐reperfusion (I/R) injury and established a relationship between IL‐1 and growth factors. Thus, IL‐1 reduced hepatocyte growth factor (HGF) and promoted TGFβ release, thus contributing to the impaired liver regeneration associated with ROLT. Preconditioning inhibited IL‐1 through nitric oxide (NO), thereby protecting against the injurious effects of IL‐1. In addition, by another pathway independent of NO, preconditioning induced HSP70 and haem‐oxygenase‐1 (HO‐1). HO‐1 protected against I/R injury and liver regeneration, whereas the benefits resulting from HSP70 were mainly related to hepatocyte proliferation. These results suggest a mechanism that explains the effectiveness of preconditioning in ROLT. They suggest, too, that other strategies, in addition to preconditioning, that modulate IL‐1 and/or HSPs could be considered in clinical situations requiring liver regeneration such as small liver grafts. Copyright © 2005 Pathological Society of Great Britain and Ireland. Published by John Wiley & Sons, Ltd.
Synthesis and optical and electrochemical properties of new π‐conjugated 1,3,5‐triazine‐containing polymers
Authors: Ren Shijie , Fang Qiang , Yu Feng , Bu Dongsheng
Published: November 2005

Two new π‐conjugated polymers containing 1,3,5‐triazine units in the main chain, Pa and Pb, are reported. Pa and Pb (R = H and OCH3, respectively) showed blue photoluminescence emissions with quantum yields of more than 50% in toluene. In the solid state, Pa and Pb showed photoluminescence maximum emission peaks at 479 and 475 nm, respectively. Electrochemically, Pa and Pb showed good stability and reversibility under repeated electrochemical reduction. The polymers had glass‐transition temperatures higher than 90 °C and had 5 wt % loss temperatures higher than 400 °C. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 6554–6561, 2005
Novel fluorinated stabilizers for ring‐opening polymerization in supercritical carbon dioxide
Authors: Bratton Daniel , Brown Malcolm , Howdle Steven M.
Published: November 2005

Ring‐opening polymerization (ROP) in supercritical carbon dioxide (scCO2) has been the subject of much recent interest, although few publications describe the development of stabilizers to produce biodegradable particles of poly(L‐lactide) (PLLA) and polyglycolide (PGA). Here we describe the synthesis of a series of novel fluorinated diblock copolymers by the acid‐catalyzed esterification of well‐defined blocks of polycaprolactone (PCL) with Krytox 157FSL, a carboxylic acid terminated perfluoropolyether. These diblock copolymers were then tested as stabilizers in the ROP of glycolide and L‐lactide, or a mixture of the two, in scCO2, and this resulted in the corresponding homopolymers or random copolymers. In the absence of stabilizers, only aggregated solids were formed. When the reaction was repeated with a stabilizer, PGA and PLLA were obtained as discrete microparticles. The stabilizer efficiency increased as the length of the polymer‐philic PCL block increased. One optimized stabilizer worked at loadings as low as 3% (w/w) with respect to the monomer, demonstrating these to be extremely effective stabilizers. It was found that to produce microparticles with this process, the product polymers must be semicrystalline; amorphous polymers, such as poly(lactide‐co‐glycolide), are plasticized by scCO2 and yield only aggregated solids rather than discrete particles. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 6573–6585, 2005
Preparation of a reflective‐type electrochromic device based on monodisperse, micrometer‐size‐range polymeric microspheres and viologen pendants
Authors: Ryu Jee‐Hyun , Shin Dong‐Oh , Suh Kyung‐Do
Published: November 2005

A reflective electrochromic device (ECD) based on polymeric microspheres was proposed, and its feasibility for a display was investigated. The viologen moiety was introduced onto the surface of chloro‐functionalized polymeric microspheres via refluxing in toluene. The existence of the viologen pendants was confirmed with X‐ray photoelectron spectroscopy, and their redox reactions were examined with cyclic voltammetry. The ECD had an inherent white background without an applied potential because the micrometer size range of the substrate particles scattered the light, whereas a deep violet color appeared when 3.0 V was applied to the cell. This color change could have been caused by the reduction of viologen pendants on the surface of the polymeric microspheres. The reflectance values of the ECD were observed with a spectrophotometer, and the response times and cyclic stability of the ECD, depending on the potential, were also examined. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 6562–6572, 2005
Cooperativity of conventional and unconventional hydrogen bonds involving imidazole
Authors: Kar Tapas , Scheiner Steve
Published: November 2005

Correlated ab initio calculations are used to investigate the cooperativity of H‐bonds between imidazole and a pair of water molecules. H‐bonds comprise not only the conventional NH … O and OH … N types, but also CH … O and OH … φ (wherein a proton is donated to the delocalized π cloud lying above the aromatic ring). Conventional and OH … φ H‐bonds obey the normal principles of cooperativity, wherein these bonds are strengthened when a central molecule serves simultaneously as both proton donor and acceptor. In contrast, CH … O bonds do not appear to be amenable to such positive cooperativity. When placed in a polarizable medium, all H‐bonds weaken as the dielectric constant of the solvent grows. The qualitative aspects of the cooperativity are not affected by the medium, although some weakening is observed. Calculations also consider the effects of cooperativity on other aspects of the complexes, including the intermolecular distance, the effect on the covalent X‐H bond length, and IR and NMR spectral data. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006