an element free galerkin approach for rigidflexible coupling dynamics in 2d state based on an improved element free galerkin efg method and the geometric nonlinear elastic theory an element free numerical approach for rigidflexible coupling dynamics of a rotating hubbeam system is implemented using the hamilton principle the coupled nonlinear integral differential governing equations are derived in which the dynamic stiffening effect is expressed by the longitudinal shrinking of the beam induced by the transverse displacement by the efg method where the global interpolating moving least squares imls and generalized moving least squares igmls were used for discretizing the longitudinal and transverse deformation variables respectively the spatially element free discretized dynamic equations of the system are obtained and the newmark scheme was selected as the time integration method for the numerical computation the superiority of the global interpolating property makes the ease for imposing both displacement and derivative boundary conditions the transverse bending vibration and structural dynamics of the flexible beam in non inertial system are analyzed in the numerical simulations and influence parameters of the efg method are also fully discussed simulation results verify the feasibility of the improved efg approach for rigidflexible coupling dynamics

non linear substructure approach for dynamic analysis of rigid flexible multibody systems abstract this paper presents a substructure synthesis method ssm for non linear analysis of multibody systems the detailed derivation of the equation of motion which takes into account the geometric non linear effects of large rotation undergoing small strain elastic deformation is presented using the substructure synthesis approach the equation of motion of the systems can be simplified for rigid and flexible substructures for the flexible substructure the equation of motion is condensed through the boundary conditions at the interface between the flexible and rigid substructures as a result equations of motion for multi flexible body systems including the geometric non linear effects of large rotation are derived to demonstrate the applicability and accuracy of the proposed approach an example of a two link manipulator was chosen for this presentation the results using the linear and non linear models are presented to highlight the effects of geometric non linearities

a globally uniformly convergent finite element method for a singularly perturbed elliptic problem in two dimensions we analyze a new galerkin finite element method for numerically solving a linear convection dominated convection diffusion problem in two dimensions the method is shown to be convergent uniformly in the perturbation parameter of order h1 2 in a global energy norm which is stronger than the l2 norm this order is optimal in this norm for our choice of trial functions

a comparison of second order epiderivatives calculus and optimality conditions abstract the first order theory of generalized derivatives is now well developed significant progress toward a second order theory has also been made two types of second order directional derivatives appear to be particularly promising for applications to optimization parabolic epiderivatives which are well suited for necessary optimality conditions and satisfy standard calculus rules for a large class of functions and the second order epiderivatives of rockafellar which lead to general sufficient optimality conditions that are close to being necessary in this paper the properties of these two types of epiderivatives are surveyed and contrasted special results for c1 1 functions are examined in detail

on some relations between chaney s generalizedsecond order directional derivative and that of ben tal andzowe for a locally lipschitz real valued function f on bbb r n and x u in bbb r n our main result implies that if x is in clarke s subdifferential partial f x coming from the direction u in chaney s sense such that x u equals the directional derivative f x u then chaney s second order directional derivative f x x u when it exists coincides with the value at x of the conjugate function of the ben tal zowe second order directional derivative provided that this value is finite

graded mesh difference schemes for singularly perturbed two point boundary value problems etude de l approximation numerique des operateurs differentiels sans points de retournement par des schemas aux differences finies compacts analyse de la stabilite

optimality conditions for non finite valued convex composite functions burke 1987 has recently developed second order necessary and sufficient conditions for convex composite optimization in the case where the convex function is finite valued in this note we present a technique for reducing the infinite valued case to the finite valued one we then use this technique to extend the results in burke 1987 to the case in which the convex function may take infinite values we conclude by comparing these results with those established by rockafellar 1989 for the piecewise linear quadratic case

second order moderate derivatives f x f x it is the purpose of the present paper to introduce a notion of second order generalized derivative for arbitrary finite functions which retains the preceding properties in particular which coincides with the usual second order derivative when it exists and enjoys useful calculus rules our proposal is close to the proposal of 3 cf also 4 the variant we use is similar in spirit to the first order variant of the clarke circa derivatives introduced in l 21 here however the concept of fan plays a key role as in 3 51 let us note that the absence of built in upper semicontinuity is intimately linked with the accuracy of the concept under added assumptions of semicontinuity one recovers the notions of 3 51 our results can be found in 6

necessary and sufficient optimality conditions for a class of nonsmooth minimization problems the purpose of this paper is to derive in a unified way second order necessary and sufficient optimality criteria for four types of nonsmooth minimization problems thediscrete minimax problem thediscrete l1 approximation the minimization of theexact penalty function and the minimization of theclassical exterior penalty function our results correct and supplement conditions obtained by various authors in recent papers

comparison of a higher order method and the simple upwind and non monotone methods for singularly perturbed boundary value problems in this paper we will present a new scheme for discretization of singularly perturbed boundary value problems based on finite difference methods this method is a combination of simple upwind scheme and central difference method on a special non uniform mesh shishkin mesh for the space discretization numerical results show that the convergence of method is uniform with respect to singular perturbation parameter and has a higher order of convergence

convexity and generalized second order derivatives for locally lipschitz functions abstract we define the generalized second order directional derivatives by means of the clarke generalized gradient for locally lipschitz functions then we give characterization of convexity and state a new sufficient optimality condition

second order necessary conditions for optimality in nonsmooth nonlinear programming the notion of a second order directional derivative introduced by ben tal and zowe and a generalization of this notion by penot are used to state new second order necessary optimality conditions for a nonsmooth nonlinear programming problem with a finite number of inequality and equality constraints

some applications of variational inequalities in nonsmooth analysis abstract in this paper we apply some results on variational inequalities to the clarke generalized gradient and the generalized second order directional derivative f x u v and obtain some variational inequalities of them

on second order conditions in unconstrained optimization the main purpose of this paper is to establish the second order nonsmooth sufficient unconstrained optimality condition for so called l stable at some point functions and in this way to generalize some previous results in this direction we provide the comparisons with other results by examples

uniform high order difference schemes for a singularly perturbed two point boundary value problem on construit une famille de schemas aux differences finies uniformement precis pour le probleme du type eu a x u b x u f x on donne une analyse complete de l erreur de discretisation basee sur les resultats de stabilite on presente des essais numeriques

on generalized second order derivatives and taylor expansions in nonsmooth optimization a representation of cominetti and correa s generalized second order directional derivative siam j control optim 28 1990 pp 789 809 is given and then applied to obtain a taylor theorem type result a conjecture in siam j control optim 28 1990 pp 789 809 concerning functions of the form max 1 leq i leq n g i x is proved under a strengthened assumption but not true otherwise

optimal error estimate using mesh equidistribution technique for singularly perturbed system of reaction diffusion boundary value problems in this article we study the problem of determining an appropriate grading of meshes for a system of coupled singularly perturbed reaction diffusion problems having diffusion parameters with different magnitudes the central difference scheme is used to discretize the problem on adaptively generated mesh where the mesh equation is derived using an equidistribution principle an a priori monitor function is obtained from the error estimate a suitable a posteriori analogue of this monitor function is also derived for the mesh construction which will lead to an optimal second order parameter uniform convergence we present the results of numerical experiments for linear and semilinear reaction diffusion systems to support the effectiveness of our preferred monitor function obtained from theoretical analysis

numerical methods for time dependent convection diffusion equations abstract we examine a singularly perturbed linear parabolic initial boundary value problem in one space variable various finite difference schemes are derived for this problem using a semidiscrete petrov galerkin finite element method these schemes do not have a cell reynolds number restriction and are shown to be first order accurate uniformly in the perturbation parameter numerical results are also presented

a generalized second order derivative in nonsmooth optimization in this work a new notion of generalized second order directional derivative and generalized hessian for nonsmooth real valued functions is studied the general properties of these mathematical objects are investigated together with some calculus rules that may facilitate their practical computation two applications of these derivatives in optimization theory are considered first to obtaining necessary and sufficient second order optimality conditions for problems with or without constraints and second to extending the newton method for the minimization of a mathcal c 1 1 function

a brief survey on numerical methods for solving singularly perturbed problems in the present paper a brief survey on computational techniques for the different classes of singularly perturbed problems is given this survey is a continuation of work performed earlier by the first author and contains the literature of the work done by the researchers during the years 2000 2009 however some older important relevant papers are also included in this survey we also mentioned those papers which are not surveyed in the previous survey papers by the first author of this paper see appl math comput 30 1989 223 259 130 2002 457 510 134 2003 371 429 for details thus this survey paper contains a surprisingly large amount of literature on singularly perturbed problems and indeed can serve as an introduction to some of the ideas and methods for the singular perturbation problems

geometric non linear substructuring for dynamics of flexible mechanical systems a substructure synthesis formulation is presented that permits use of established flexible multibody dynamic analysis computer codes to account for structural geometric non linear effects large relative displacement is permitted between points within bodies that undergo small strain elastic deformation components are divided into substructures on each of which the theory of linear elasticity relative to a body reference frame is adequate to describe deformation and its coupling with system motion normal vibration and static correction deformation modes are used to account for elastic deformation within each substructure compatibility conditions are derived and imposed as constraint equations at boundary points between substructures system equations of motion that include geometric non linear effects of large rotation in terms of generalized co ordinates of a reference frame for each substructure and a set of deformation modes that are defined within the substructure are assembled the method is implemented in an industry standard flexible multibody dynamics code with minimal modification use of the formulation is illustrated on the classical problem of a spinning beam with geometric stiffening and on a space structure that experiences large deformation

inadequacy of first order upwind difference schemes for some recirculating flows spurious numerical solutions of problems with closed sub characteristics by upwind difference schemes in particular problems of recirculating incompressible flow at high reynolds numbers are proved to be due to the anisotropy of the artificial viscosity numerical examples are presented to show that even very simple problems including basic problems in fluid dynamics are not approximated well by schemes with anisotropic artificial viscosity regardless of numerical parameters 1991 academic press inc numerical methods for solving incompressible fluid flow equations are frequently tested on problems of recirculating flow quite often results obtained by different methods differ from each other significantly reliable experimental data is usually difficult to obtain and discrepancies between numerical two dimensional solutions and experimental data may be the result of the influence of walls in the experiments the problems in solving recirculating incompressible flows at high reynolds numbers are well known several researchers have pointed out that some of the methods employed to obtain stable discretization e g upwind differencing may lead to spurious results such results have been attributed to excessive artificial viscosity in the numerical scheme to multiple solutions of the non linear set of algebraic equations that is obtained from the numerical scheme and to poor resolution by grids that are too coarse 2 4 51 but spurious results occur even when none of these reasons are valid indeed a single linear partial differential equation may exhibit such behavior when the sub characteristics are closed this is true even when the mesh size is small enough to easily resolve the solution and truncation errors are genuinely small everywhere and even when the differential solution does not depend on the

calculus rules on a new set valued second order derivative for convex functions etant donnee une fonction convexe f qui a ete construite a partir d autres fonctions f i dont les differentielles secondes sont aisees a determiner on cherche a exprimer les differentielles secondes de f en fonction des 2 f i

uniform fourth order difference scheme for a singular perturbation problem the numerical solution of a nonlinear singularly perturbed two point boundary value problem is studied the developed method is based on hermitian approximation of the second derivative on special discretization mesh numerical examples which demonstrate the effectiveness of the method are presented

an inertia capacitance beam substructure formulation based on the bond graph method with application to rotating beams in this paper a novel inertia capacitance ic beam substructure formulation based on the ic field presentation from the bond graph method is developed the ic beam provides a modular systematic and graphical approach to beam modeling these features allow the modeler to focus more on the modeling and less on the mathematics as such the ic beam is proposed as an alternative to the many existing types of beam models available in the literature the ic beam is formulated in the center of mass body fixed coordinate system allowing for easy interfacing in a multibody system setting this floating frame approach is also computationally cheap elastic deformations in the ic beam are assumed to be small and described by modal superposition the formulation couples rigid body and elastic deformations in a nonlinear fashion the formulation is also compact and efficient detailed derivations for a two dimensional planar ic beam with bending modes are presented a modal acceleration method based on the decoupling of bending modes is proposed for use in the ic beam the rotating beam spin up maneuver problem is solved the karnopp margolis method is applied to ensure complete integral causality for an efficient numerical system geometric substructuring technique is applied to model large deflections the ic beam is shown to be capable of solving the rotating beam problem accurately and efficiently

generalized hessian for c 1 1 functions in infinite dimensional normed spaces the subject of this paper is the systematic study of second order notions concerning differentiable functions with lipschitz derivative the results and notions are motivated by recent papers of cominetti correa and hiriart urruty the first goal of this paper is the comparison of several known second order directional derivatives the second goal is the introduction of a generalized hessian which is a set of certain symmetric bilinear forms the relation of this generalized hessian to other existing second order derivatives is also described