bluuebunny/crossref_metadata_2025_split huggingface dataset:
Numerical simulation of mechanical systems using methods for differential‐algebraic equations
Authors: Anantharaman Martin , Hiller Manfred 
Published: November 2005

AbstractA 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

AbstractAn 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

AbstractIn 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

AbstractFor 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

AbstractSome 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

AbstractWeak 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

AbstractA 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

AbstractQuasi‐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

AbstractA 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

AbstractA 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

AbstractThe 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

AbstractA 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

AbstractA 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

AbstractThe 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

AbstractNumerical 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

AbstractA 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

AbstractA 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

AbstractThe 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

AbstractIn 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

AbstractAn 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

AbstractA 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

AbstractIt 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

AbstractIn 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

AbstractIn 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.