nonlinear analysis of reissner plates on an elastic foundation by the bem the fundamental solutions and the boundary element method for obtaining numerical solutions of nonlinear reissner plates on an elastic foundation are presented in the paper the derivation of the fundamental solutions is mainly based on two of hu s functions and the resolution method of differential operator an incremental form of the boundary integral equations is suggested to achieve linearization of the original nonlinear equations the plate may be moderately thick or sandwich plates with or without elastic foundation finally three examples are considered to illustrate the correctness and accuracy of the proposed method

conjugate progector preconditioning for the solution of contact problems we present a new algorithm for numerical solution of contactproblems without friction the method is based on enhancing conjugate projector preconditioning into the standard conjugate gradient method for the solution of quadratic programming problems with inequality constraints we show that the algorithm is correct and discuss the efficiency of the algorithm the relation of the algorithm to the domain decomposition methods is also explained the paper is supplied with numerical experiment

multi speed solitary waves for the klein gordon schrodinger system with cubic interaction abstract considered in this report is the existence of multi speed solitary waves of a klein gordon schrodinger system with cubic interaction these solutions behave at large time as a couple of single solitary waves at different speeds this type of solutions has been investigated for nonlinear schrodinger system in 15 27 it is obtained by solving the system backward in time around a sequence of approximate multi speed solitary waves and showing convergence to a solution with the desired property the new ingredients of the proof are coercivity of the hessian of the action around each component of the multi speed solitary waves energy estimate and finite speed of propagation

strongly interacting bumps for the schrodinger newton equations we study concentrated bound states of the schrodinger newton equations h2 e x u 0 0 x r3 u 12 2 0 x r3 x 0 u x 0 as x moroz et al an analytical approach to the schrodinger newton equations nonlinearity 12 201 1999 proved the existence and uniqueness of ground states of u 0 0 x r3 u 12 2 0 x r3 x 0 u x 0 as x we first prove that the linearized operator around the unique ground state radial solution 0 u0 with 0 r ae r r 1 o 1 as r x u0 r b r 1 o 1 as r x for some a b 0 has a kernel whose dimension is exactly 3 corresponding to the translational modes using this result we further show that if for some positive integer k the points pi r3 i 1 2 k with pi pj for i j are all local minimum or local maximum or nondegenerate critical points of e p then for h small enough there exist solutions of the schrodinger newton equations with k bumps which concentrate at pi we also prove that given a local maximum point p0 of e p the

nonoscillation and oscillation of second order half linear differential equations abstract we study the oscillation problems for the second order half linear differential equation p t x q t x 0 where u u r 1 u with r 0 1 p and q are locally integrable on r p 0 q 0 a e on r and 0 p 1 r t d t we establish new criteria for this equation to be nonoscillatory and oscillatory respectively when p 1 our results are complete extensions of work by huang c huang oscillation and nonoscillation for second order linear differential equations j math anal appl 210 1997 712 723 and by wong j s w wong remarks on a paper of c huang j math anal appl 291 2004 180 188 on linear equations to the half linear case for all r 0 these results provide corrections to the wrongly established results in j jiang oscillation and nonoscillation for second order quasilinear differential equations math sci res hot line 4 6 2000 39 47 on nonoscillation when 0 r 1 and on oscillation when r 1 the approach in this paper can also be used to fully extend elbert s criteria on linear equations to half linear equations which will cover and improve a partial extension by yang x yang oscillation nonoscillation criteria for quasilinear differential equations j math anal appl 298 2004 363 373

oscillation and nonoscillation for second order linear differential equations abstract new oscillation and nonoscillation theorems are obtained for the second order linear differential equation u p t u 0 where p t c 0 and p t 0 conditions only about the integrals of p t on every interval 2 n t 0 2 n 1 t 0 n 1 2 for some fixed t 0 0 are used in the results

boundary element solution for half plane problems abstract the complete fundamental solution due to unit point loads within the half plane is presented together with its application to the boundary element method this solution procedure has proved to be highly accurate and computationally more efficient than the analogue implementation of kelvin fundamental solution for problems concerning the half plane expressions for stresses at internal points are also presented and the application of the formulation to some classical problems is included

a parallel finite element contact impact algorithm for non linear explicit transient analysis part i the search algorithm and contact mechanics a contact algorithm has been developed and implemented in a non linear dynamic explicit finite element program to analyse the response of three dimensional shell structures the contact search algorithm accounts for initial contact sliding and release through the use of a parametric representation of the motion of points located on the surface of the structure combined with a contact surface representation which approximates the actual surface by means of triangular search planes the mechanics of contact is handled by taking advantage of the fact that an explicit time integration scheme results in very small displacements during a time step the amount of overlap of the discrete representation of the surfaces which occurs at contact is taken as a measure of the approach of the surfaces hence experimental data which relates approach to normal contact pressure can be used to determine the contact pressure applied to the finite element model of the surface as contact evolves the friction model also incorporates experimental data on the dependence of the coefficient of friction on both the relative sliding velocity and on the relative tangential displacement between surfaces in contact observed in friction tests the parallel implementation of this contact algorithm and its performance on a 128 processor distributed memory multiprocessor computer is discussed in part ii of this paper

stability theory of solitary waves in the presence of symmetry ii abstract consider an abstract hamiltonian system which is invariant under a group of operators we continue to study the effect of the group invariance on the stability of solitary waves applications are given to bound states and traveling wave solutions of nonlinear wave equations

a finite element method for elasto plastic structures and contact problems by parametric quadratic programming in this paper the stiffness matrix of a contact element is introduced by means of a penalty function expression of the contact pressure and frictional force the contact condition and the flow rule are expressed by the same form as in a non associated plastic flow problem a unified pqp parametric quadratic programming model related to contact problems as well as to elasto plastic structures is constructed a series of pqp formulae for contact problems and elastic plastic structures is derived in the text and some numerical examples are illustrated as well

solution of large displacement contact problems with friction using newton s method for generalized equations this work is concerned with the formulation and numerical realization of large displacement contact problems with friction a restricted class of contact problems is treated where the deformation of one of the contacting bodies is prescribed the formulation utilizes a particular convected co ordinate chart to define firstly tangential components for all potential contact points and secondly the notion of incremental tangential displacement by writing the discretized problem as a generalized equation in the sense of robinson it is made clear how newton s method may be extended to this kind of non differentiable problems the proposed algorithm is verified by several numerical examples

a direct constraint trefftz fem for analysing elastic contact problems summary a direct constraint technique based on the hybrid trefftz finite element method is first presented to solve elastic contact problems without friction for efficiency static condensation is employed to condense a large model down to a smaller one which involves nodes within the potential contact surfaces only this model can remarkably reduce computational time and effort subsequently the contact interface equation is constructed by introducing the contact conditions of compatibility and equilibrium based on the formulation developed a general solution strategy which is applicable to the well known three classical situations receding conforming and advancing is developed finally three typical examples related to the three situations mentioned are provided to verify the reliability and applicability of the approach copyright 2005 john wiley sons ltd

remarks on a paper of c huang we prove oscillation and nonoscillation theorems for the second order linear differential equation e y q t y 0 where q t 0 and locally integrable on t these results are extensions of earlier results of huang j math anal appl 210 1997 712 723 furthermore we show that the oscillation criterion established for eq e can be extended to the delayed differential equation y q t y t 0 where t t and limt t

oscillation and non oscillation for second order linear difference equations abstract we prove new oscillation and non oscillation theorems for the second order linear difference equation 2xn 1 pnxn 0 where p n n 1 is a real sequence with pn 0 these results are extensions of earlier results of zhang and zhou comput math appl 39 2000 1 7

a perturbed lagrangian formulation for the finite element solution of contact problems making use of a perturbed lagrangian formulation a finite element procedure for contact problems is developed for the general case in which node to node contact no longer holds the proposed procedure leads naturally to a discretization of the contact interface into contact segments within the context of a bilinear interpolation for the displacement field a mixed finite element approximation is introduced by assuming discont naous contact pressure constant on the contact segment because of this piece wise constant approximation the gap function enters into the formulation in an average sense instead of through a point wise definition numerical examples are presented that illustrate the performance of the proposed procedure current finite element formulations for contact problems based on either the classical lagrange parameter procedure l 3 12 203 or the penalty function method 4 6 11 are characterized by a point wise enforcement of the contact constraint condition in the sense that penetration of the bodies is established on a nodal basis moreover in this methods the recovery of the contact pressure over the element from the contact nodal forces generally requires an additional procedure within the framework of classical lagrange multiplier methods the contact condition is exactly satisfied by transforming the constrained problem into an unconstrained one with the introduction of additional variables lagrange multipliers these extra variables add computational effort to the solution process which often requires special procedures to handle the presence of zero diagonal terms penalty methods on the other hand enable one to transform the constrained problem into an unconstrained one without introducing additional variables the constraint condition is now satisfied only approximately for finite values of the penalty parameter the main difhculty associated with these methods however lies in the poor conditioning of the problem as the penalty is increased to more accurately enforce the constraint condition this is a well understood phenomenon particularly in the context of the incompressible and nearly incompressible problem in solid and fluid mechanics e g see l 22 25 for a review recently augmented lagrangian procedures have been proposed as a promising way to partially overcome these difficulties and regularize the penalty formulation e g see the survey in 7 8 within the framework of zinearited e u c it is possible to restrict the finite element formulation of contact problems by assuming that node to node contact occurs this is in fact the case often considered in the literature l 2 4 6 12 20 211 in the general context of fully

nonoscillation and oscillation of second order half linear difference equations this paper considers the oscillation problem for the second order half linear difference equation xn 1 r 1 xn 1 qn xn r 1xn 0 where qn n 0 is a nonnegative sequence and r 0 we establish new criteria for this equation to be nonoscillatory and oscillatory respectively when r 1 our results are complete extensions of work by zhang and zhou oscillation and nonoscillation for second order linear difference equations comp math appl 39 2000 1 7 and reduce to the results in y g sun oscillation and nonoscillation for second order linear difference equations appl math comput 170 2005 1095 1103 when r 0 our results generalize and complement sun s results in y g sun oscillation and nonoscillation for half linear second order difference equations indian j pure appl math 35 2004 133 142

stability of standing waves for the klein gordon schrodinger system abstract we study the orbital stability of standing wave solutions for the klein gordon schrodinger system in three space dimensions it is proved that the standing wave is stable if the frequency is sufficiently large

variational principles fe and mpt for analysis of non linear impact contact problems this paper presents an analysis of the impact contact problems between elasto plastic bodies without friction three pairs of extended variational complementary functionals for the impact contact problems are presented and constitute the theoretical foundations of the ensuing numerical analysis a general condition of non interpenetration is suggested for general cases of two elastoplastic solids in contact in fact the extended variational principles are equivalent to a stationarity of the potential energy with constraints on displacements which may be reduced to a particular case of the mathematical programming techniques mpt the present analysis is limited to a two dimensional time dependent case where both geometrical and material non linearities are considered with the incremental form of the functional ii2 an eight node plane element is used to derive to finite element fe formulation in the problem the resulting equations are solved by an extended wilson scheme and the lamker method to verify the suitability of the method two numerical examples are calculated and the results are compared with the corresponding experimental ones the comparison demonstrates that the present model is capable of modelling the non linear impact contact problems

oscillation and nonoscillation for second order linear difference equations new oscillation and nonoscillation theorems are obtained for the second order linear difference equation 2xn 1 pnxn 0 where if pn n 1 is a real sequence with pn 0