a note on the elastodynamic load transfer problem abstract this paper illustrates the solution of elastodynamic load transfer problems involving a cylindrical elastic bar partially embedded in a homogeneous isotropic elastic half space using a solution scheme based on a coupled variational boundary integral equation algorithm the present solution scheme has several advantages over conventional schemes based on the fictitious bar extended half space model when applied to solve elastodynamic load transfer problems the analysis ensures limiteddisplacement compatibility andtraction continuity along thetrue contact surface between the bar and the half space the solution scheme is based on an elastodynamic variational principle and utilizes appropriate green s function representations for the surrounding half space selected numerical results for torsional and axial impedances of the bar half space system are presented and these are compared with those obtained previously on the basis of the fictitious bar extended half space model in addition the bar displacement and the bar stress resultant profiles are presented for torsion and axial load transfer problems to portray the dependence of the load diffusion on the governing parameters of the bar half space system

a local error estimate of the method of multi scale asymptotic expansions for elliptic problems with rapidly oscillatory coefficients in this paper on basis of o a oleinik a s shamaev g a yosifian mathematical problems in elasticity and homogenization north holland amsterdam 1992 we present a local error estimate of the method of multi scale asymptotic expansions for second order elliptic problems with rapidly oscillatory coefficients

periodic solution to nonlinear differential equation at resonance abstract in this paper a class of nonlinear sturm liouville problems at resonance is discussed an extended form of a non variational version of a max min principle is applied to show that the equation possesses unique 2 periodic solution under a less restrictive condition this result extends what we have already known

a new approximate method for second order elliptic problems with rapidly oscillating coefficients based on the method of multiscale asymptotic expansions abstract in this paper we consider second order elliptic problems with rapidly oscillating coefficients on basis of o a oleinik a s shamaev g a yosifian mathematical problems in elasticity and homogenization north holland amsterdam 1992 wen ming he jun zhi cui a pointwise estimate on the 1 order approximation of g x 0 e ima j appl math 70 2005 241 269 we propose a new approximate method to solve these problems of course we present its error estimate

a mixed multiscale finite element method for elliptic problems with oscillating coefficients the recently introduced multiscale finite element method for solving elliptic equations with oscillating coefficients is designed to capture the large scale structure of the solutions without resolving all the fine scale structures motivated by the numerical simulation of flow transport in highly heterogeneous porous media we propose a mixed multiscale finite element method with an over sampling technique for solving second order elliptic equations with rapidly oscillating coefficients the multiscale finite element bases are constructed by locally solving neumann boundary value problems we provide a detailed convergence analysis of the method under the assumption that the oscillating coefficients are locally periodic while such a simplifying assumption is not required by our method it allows us to use homogenization theory to obtain the asymptotic structure of the solutions numerical experiments are carried out for flow transport in a porous medium with a random log normal relative permeability to demonstrate the efficiency and accuracy of the proposed method

convergence of a multiscale finite element method for elliptic problems with rapidly oscillating coefficients we propose a multiscale finite element method for solving second order elliptic equations with rapidly oscillating coefficients the main purpose is to design a numerical method which is capable of correctly capturing the large scale components of the solution on a coarse grid without accurately resolving all the small scale features in the solution this is accomplished by incorporating the local microstructures of the differential operator into the finite element base functions as a consequence the base functions are adapted to the local properties of the differential operator in this paper we provide a detailed convergence analysis of our method under the assumption that the oscillating coefficient is of two scales and is periodic in the fast scale while such a simplifying assumption is not required by our method it allows us to use homogenization theory to obtain a useful asymptotic solution structure the issue of boundary conditions for the base functions will be discussed our numerical experiments demonstrate convincingly that our multiscale method indeed converges to the correct solution independently of the small scale in the homogenization limit application of our method to problems with continuous scales is also considered

the hole filling method and multiscale algorithm for the heat transfer performance of periodic porous materials in this paper we consider the transient heat transfer problem with rapidly oscillating coefficients in periodic porous materials the hole filling method through filling all holes with a very compliant material is investigated and as the thermal conductivity parameters of the weak phase go to zero the proof of the limiting process is derived in detail then the multiscale analysis and computations based on the hole filling method for the associated multiphase problem in a domain without holes are proposed finally some numerical results are given which show a good agreement and verify the feasibility of the hole filling method a multiscale analysis and computation based on hole filling method is proposed transient heat transfer problem of periodic porous materials is considered proof of the limiting process as the parameters of the weak phase go to zero is derived some numerical results are given in detail to validate the multiscale method developed

convergence of a nonconforming multiscale finite element method the multiscale finite element method msfem t y hou x h wu and z cai math comp 1998 to appear t y hou and x h wu j comput phys 134 1997 pp 169 189 has been introduced to capture the large scale solutions of elliptic equations with highly oscillatory coefficients this is accomplished by constructing the multiscale base functions from the local solutions of the elliptic operator our previous study reveals that the leading order error in this approach is caused by the resonant sampling which leads to large error when the mesh size is close to the small scale of the continuous problem similar difficulty also arises in numerical upscaling methods an oversampling technique has been introduced to alleviate this difficulty t y hou and x h wu j comput phys 134 1997 pp 169 189 a consequence of the oversampling method is that the resulting finite element method is no longer conforming here we give a detailed analysis of the nonconforming error our analysis also reveals a new cell resonance error which is caused by the mismatch between the mesh size and the wavelength of the small scale we show that the cell resonance error is of lower order our numerical experiments demonstrate that the cell resonance error is generically small and is difficult to observe in practice

on the load transfer from a rigid cylindrical inclusion into an elastic half space abstract the present paper examines the problems related to the axial lateral and rotational loading of a rigid cylindrical inclusion which is embedded in bonded contact at the boundary of an isotropic elastic half space the rigid inclusion is modeled as a field of distributed forces which represent the normal and shear tractions that act on the inclusion elastic medium interface the intensities of these distributed tractions are determined by enforcing displacement compatibility conditions at discrete locations of the interface these compatibility conditions are derived from rigid body displacement modes appropriate for each loading the results derived from this numerical scheme are compared with equivalent results derived via analytical techniques which focus on the solution of the governing integral equation schemes and other approximate solution schemes the numerical results presented in the paper illustrate the manner in which the generalized stiffnesses of the embedded inclusion are influenced by its geometry and poisson s ratio of the half space region

analysis of the heterogeneous multiscale method for elliptic homogenization problems the heterogeneous multiscale method hmm is applied to various parabolic problems with multiscale coefficients these problems can be either linear or nonlinear optimal estimates are proved for the error between the hmm solution and the homogenized solution

periodic solutions for 2kth order ordinary differential equations with resonance in this paper a non variational version of a max min principle is extended and some unique existence results are obtained for the periodic boundary value problem of the higher order ordinary differential equations under a resonant condition

a torsion load transfer problem for a class of non homogeneous elastic solids abstract this paper is concerned with the axisymmetric torsion of a finite long cylindrical bar which is partially embedded in a non homogeneous transversely isotropic elastic layer underlaid by a rigid base the non homogeneity of the elastic layer is represented by both linear and non linear variations of shear moduli with depth the bar elastic layer system is decomposed to a real bar and an elastic layer with a cylindrical cavity identical to the embedded bar instead of adopting the conventional fictitious bar extended elastic medium decomposition the proposed decomposition allows the imposition of displacement compatibility and traction continuity along the true contact surface in the analysis a solution scheme based on a classical variational theorem is presented to analyse the load transfer problem the displacement and traction green s functions of the nonhomogeneous elastic layer are required in the analysis and these are derived explicitly using hankel integral transforms numerical results are presented to illustrate the effect of non homogeneity and transverse isotropy on the torque twist relationship at the top end of the bar and twist angle and torque transfer curves along the length of the bar

iterated two scale asymptotic method and numerical algorithm for the elastic structures of composite materials in this paper we shall discuss the elasto static problem of composite materials with two or more different length scales and shall present iterated two scale asymptotic expansion of the solution for considering problem the mathematical proofs of some convergence theorems will be given under some assumptions finally some numerical results are reported

on periodic solutions for even order differential equations abstract a class of sufficient conditions are obtained for the existence of a unique 2 periodic solution of even order differential equations employing an initial value problem

periodic solutions for 2kth boundary value problem with resonance abstract in this paper a non variational version of a max min principle is extended and some unique existence results for the periodic boundary value problem of the higher order nonconservative systems with resonance u 2 k t j 1 k a j u 2 j 1 t 1 k 1 g u t e t are obtained

on the periodic solution to the newtonian equation of motion on considere l equation du mouvement newtonienne d un systeme mecanique soumis a des forces internes conservatives et a des forces externes periodiques u t grad g u t p t ou p r r 11 est continue et de periode 2 et g a des derivees partielles d ordre 2 continues

existence and uniqueness results for periodic solution of nonlinear differential equations the existence and uniqueness of solutions for a class of 2nd order differential equations with periodic conditions are discussed

a note on global inversion theorems and applications to differential equations analysing the proof of plastock s theorem given by m and s rbdulescu 4 we prove that for 1 o s cx we may obtain estimates of the balls on which diffeomorphisms take place secondly we shall use these results to find estimates for the existence interval of the solution of cauchy s problem for differential equation these results will generalize a theorem of m and s radulescu 3 throughout this paper e f g will denote banach spaces

torsion of a long cylindrical elastic bar partially embedded in a layered elastic half space abstract this is a study of the axially symmetric torsion of a long elastic cylindrical bar which is embedded in a layered elastic half space the stress singularity factor at the embedded end of the bar is estimated by an existing method and its effects on the solution are investigated such effects are found to be not so significant especially for long bars and when the main concern is only on the torque twist angle relationship even for rather short bars the results given by this study agree well with those by an existing method which is more rigorous but restrictive only to the case of an infinitely rigid bar

on the existence of periodic solutions of periodically perturbed conservative systems consider the system of ordinary differential equations u t gh u t p t where p r r is a continuous function with period 2 and g r n r has a continuous second partial derivative it is important to determine sufficient conditions for the existence of a unique 2 periodic solution in this paper the above system is related to an initial value problem in terms of which a new set of sufficient conditions can be given

on the longitudinal harmonic motion of an elastic bar embedded in an elastic half space abstract the present study is concerned with the motion of a long cylindrical elastic bar which is partially embedded in a homogeneous elastic half space and subjected to a harmonic axial load initially green s functions corresponding to axisymmetric harmonic ring loads are derived and presented explicitly it is found that the direct extension of elastostatic solution schemes to solve elastodynamic problems may lead to erroneous solutions due to the inability of these algorithms to properly account for inertia effects some discrepancies in existing solutions with respect to the inertia component of the bar are shown an efficient solution scheme based on lagrange s equation of motion and a discretization technique is presented to solve the title problem numerical results are presented to illustrate the influence of bar flexibility mass density geometry and frequency of excitation on the axial impedance of the system

an application of a global inversion theorem to an existence and uniqueness theorem for a class of nonlinear systems of differential equations abstract in this paper a class of systems of nonlinear differential equations at resonance is considered with the use of a global inversion theorem which is an extended form of a non variational version of a max min principle we prove that this class of equations possesses a unique 2 periodic solution under a rather weaker condition for existence and uniqueness than those given in papers j chen w li periodic solution for 2 k th boundary value problem with resonance j math anal appl 314 2006 661 671 f cong periodic solutions for 2 k th order ordinary differential equations with nonresonance nonlinear anal 32 1998 787 793 f cong periodic solutions for second order differential equations appl math lett 18 2005 957 961 w li periodic solutions for 2 k th order ordinary differential equations with resonance j math anal appl 259 2001 157 167 w li h li a min max theorem and its applications to nonconservative systems int j math math sci 17 2003 1101 1110 w li z shen a constructive proof of existence and uniqueness of 2 periodic solution to duffing equation nonlinear anal 42 2000 1209 1220 this result extends the results known so far

two point boundary value problem of 2mth order differential equations an existence and uniqueness result for the boundary value problem x 2 m email protected k 1 ma kx 2 k 1 1 m 1f t x e t x j 0 x j p 0 j 0 1 m 1 is given

hybrid modelling of semi infinite media abstract an accurate and efficient hybrid formulation based on lagrange s equations of motion is presented to solve geometrically axisymmetric problems associated with layered semi infinite media under arbitrary loading a near field region containing all inhomogeneities is modelled using conventional finite elements the contribution of the exterior semi infinite domain to the equations of motion is represented by a surface integral defined over the finite element boundary the integrand of this integral involves a matrix relationship between harmonics of nodal displacements and tractions at the finite element boundary a boundary traction displacement relationship for the exterior domain is established in terms of traction and displacement green s functions for a uniform undisturbed half space the present formulation guarantees a symmetric stiffness matrix for the entire system therefore both direct and indirect versions of the boundary integral equation method can be used the accuracy of the hybrid modelling algorithm is confirmed by solving a few elastostatic and elastodynamic boundary value problems for which analytical solutions can be derived