three dimensional vibrations of thick circular and annular plates abstract the ritz method is applied in a three dimensional 3 d analysis to obtain accurate frequencies for thick circular and annular plates the method is formulated in a manner which allows one to have any combination of free or fixed plate boundaries admissible functions for the three displacement components are chosen as trigonometric functions in the circumferential co ordinate and algebraic polynomials in the radial and axial co ordinates upper bound convergence of the non dimensional frequencies to at least four significant figures is demonstrated comparisons of results are made with ones obtained by others using 2 d mindlin thick plate theory and with other 3 d solutions extensive and accurate four significant figure frequencies are presented for completely free circular plates having thickness to diameter ratios of 0 2 0 3 0 4 and 0 5 for poisson s ratios 0 0 3 and 0 499 frequencies are also given for thick annular plates having a thickness to outer diameter of 0 2 inside to outside diameter ratios of 0 1 0 5 and 0 9 and 0 3 all 3 d modes are included in the analyses e g flexural thickness shear in plane stretching and torsional the circular and annular plate frequency data given is exact to at least four digits thus being benchmark data against which results from 2 d thick plate theories or other approximate methods e g finite elements may be compared

imposing dirichlet boundary conditions in the extended finite element method this paper is devoted to the imposition of dirichlet type conditions within the extended finite element method x fem this method allows one to easily model surfaces of discontinuity or domain boundaries on a mesh not necessarily conforming to these surfaces imposing neumann boundary conditions on boundaries running through the elements is straightforward and does preserve the optimal rate of convergence of the background mesh observed numerically in earlier papers on the contrary much less work has been devoted to dirichlet boundary conditions for the x fem or the limiting case of stiff boundary conditions in this paper we introduce a strategy to impose dirichlet boundary conditions while preserving the optimal rate of convergence the key aspect is the construction of the correct lagrange multiplier space on the boundary as an application we suggest to use this new approach to impose precisely zero pressure on the moving resin front in resin transfer moulding rtm process while avoiding remeshing the case of inner conditions is also discussed as well as two important practical cases material interfaces and phase transformation front capturing copyright 2006 john wiley sons ltd

level set topology optimization of structural problems with interface cohesion summary this paper presents a finite element topology optimization framework for the design of two phase structural systems considering contact and cohesion phenomena along the interface the geometry of the material interface is described by an explicit level set method and the structural response is predicted by the extended finite element method in this work the interface condition is described by a bilinear cohesive zone model on the basis of the traction separation constitutive relation the non penetration condition in the presence of compressive interface forces is enforced by a stabilized lagrange multiplier method the mechanical model assumes a linear elastic isotropic material infinitesimal strain theory and a quasi static response the optimization problem is solved by a nonlinear programming method and the design sensitivities are computed by the adjoint method the performance of the presented method is evaluated by 2d and 3d numerical examples the results obtained from topology optimization reveal distinct design characteristics for the various interface phenomena considered in addition 3d examples demonstrate optimal geometries that cannot be fully captured by reduced dimensionality the optimization framework presented is limited to two phase structural systems where the material interface is coincident in the undeformed configuration and to structural responses that remain valid considering small strain kinematics copyright 2017 john wiley sons ltd

three dimensional vibration analysis of circular and annular plates via the chebyshev ritz method abstract a three dimensional free vibration analysis of circular and annular plates is presented via the chebyshev ritz method the solution procedure is based on the linear small strain three dimensional elasticity theory selecting chebyshev polynomials which can be expressed in terms of cosine functions as the admissible functions a convenient governing eigenvalue equation can be derived through the ritz method according to the geometric properties of circular and annular plates the vibration is divided into three distinct categories axisymmetric vibration torsional vibration and circumferential vibration each vibration category can be further subdivided into the antisymmetric and symmetric ones in the thickness direction convergence and comparison study demonstrated the high accuracy and efficiency of the present method the present approach shows a distinct advantage over some other ritz solutions in that stable numerical operation can be guaranteed even when a large number of admissible functions is employed therefore not only lower order but also higher order eigenfrequencies can be obtained by using sufficient terms of the chebyshev polynomials finally some valuable results for annular plates with one or both edges clamped are given and discussed in detail

a comparison study between the modified decomposition method and the traditional methods for solving nonlinear integral equations in this paper we conduct a comparative study between the modified decomposition method and two of the traditional methods for analytic treatment of nonlinear integral and integro differential equations the proper implementation of the modified method can dramatically minimize the size of work if compared to existing traditional techniques the analysis is accompanied by examples that demonstrate the comparison and show the pertinent features of the modified technique

variational iteration method for autonomous ordinary differential systems in this paper a new iteration technique is proposed to solve autonomous ordinary differential systems in this method general lagrange multipliers are introduced to construct correction functionals for the systems the multipliers in the functionals can be identified by the variational theory the initial approximations can be freely chosen with possible unknown constants which can be determined by imposing the boundary initial conditions some examples are given the results reveal that the method is very effective and convenient

computing eigenelements of boundary value problems with fractional derivatives variational iteration method has been successfully implemented to handle linear and nonlinear differential equations the main property of the method is its flexibility and ability to solve nonlinear equations accurately and conveniently in this paper first a general framework of the variational iteration method is presented for analytic treatment of differential equations of fractional order where the fractional derivatives are described in caputo sense second the new framework is used to compute approximate eigenvalues and the corresponding eigenfunctions for boundary value problems with fractional derivatives numerical examples are tested to show the pertinent features of this method this approach provides a new way to investigate eigenvalue problems with fractional order derivatives

solving the fifth order caudrey dodd gibbon cdg equation using the exp function method abstract in this work the exp function method is applied to search for a generalized solitary solution of the fifth order caudrey dodd gibbon cdg equation the obtained result includes naturally those in open literature as special cases the work highlights the significant features of the exp function method

three dimensional vibration analysis of cantilevered and completely free isosceles triangular plates the free vibration of cantilevered and completely free isosceles triangular plates based on exact three dimensional elasticity theory is investigated the actual plate domain is first mapped onto a basic cubic domain then the ritz method is applied to derive the eigenfrequency equation from the strain energy and the kinetic energy of the plate a set of chebyshev polynomial series multiplied by a boundary function chosen to satisfy the essential geometry boundary conditions of the plate is developed as the admissible functions of each displacement component the convergence and comparison studies show that rather accurate results can be obtained by using this approach the effects of thickness to width ratio and apex angle on eigenfrequencies of the plates are studied in detail sets of valuable results are presented which may serve as the benchmark values for future numerical techniques in thick plate vibration analysis data for the completely free isosceles triangular plates are presented for the first time

3 d free vibration analysis of annular plates on pasternak elastic foundation via p ritz method in this study a three dimensional 3 d free vibration analysis of thick annular plates resting on elastic foundation with different combinations of free soft simply supported hard simply supported and clamped boundary conditions at the inner and outer edges of the annular plate is presented on the basis of the polynomials ritz method the elastic foundation is considered as a pasternak model with adding a shear layer to the winkler model the analysis procedure is based on the linear small strain and 3 d elasticity theory in this analysis method a set of orthogonal polynomial series in cylindrical polar coordinate is used to extract eigenvalue equation yielding the natural frequencies and mode shapes for the annular plates the accuracy of these results is verified by appropriate convergence studies and checked with the available literature finite element method fem analysis and the mindlin theory furthermore the effect of the foundation stiffness parameters thickness radius ratio inner outer radius ratio and different combinations of boundary conditions on the ill conditioning of the mass matrix as well as on the vibration behavior of the annular plates is investigated finally the validity and the range of applicability of the results obtained on the basis of the mindlin and classical plate theories for a thin and moderately thick annular plate with different values of the winkler foundation stiffness are graphically presented through comparing them with those obtained by the present 3 d p ritz solution

a review of the decomposition method in applied mathematics abstract the decomposition method can be an effective procedure for analytical solution of a wide class of dynamical systems without linearization or weak nonlinearity assumptions closure approximations perturbation theory or restrictive assumptions on stochasticitiy

exact closed form frequency equations for thick circular plates using a third order shear deformation theory abstract this paper presents for the first time exact closed form frequency equations and transverse displacement for thick circular plates with free soft simply supported hard simply supported and clamped boundary conditions based on reddy s third order shear deformation theory hamiltonian and minimum potential energy principles are used to extract the equations of dynamic equilibrium and natural boundary conditions of the plate the new formulation is verified by comparing the results with their counterparts reported in open literature natural frequencies of circular plates with different boundary conditions are tabulated in dimensionless form for various values of thickness radius ratios the results presented on the basis of exact closed form frequency equations are expected to serve as reliable benchmarks

three dimensional vibration analysis of a torus with circular cross section the free vibration characteristics of a torus with a circular cross section are studied by using the three dimensional small strain elasticity theory a set of three dimensional orthogonal coordinates system comprising the polar coordinate r at each circular cross section and the circumferential coordinate around the ring is developed each of the displacement components ur and w in the r and directions respectively is taken as a product of the chebyshev polynomials in the r direction and the trigonometric functions in the and directions eigenfrequencies and vibration mode shapes have been obtained via a three dimensional displacement based extremum energy principle upper bound convergence of the first seven eigenfrequencies accurate to at least six significant figures is obtained by using only a few terms of the admissible functions the eigenfrequency responses due to variation of the ratio of the radius of the ring centroidal axis to the cross sectional radius are investig

the variational iteration method an efficient scheme for handling fractional partial differential equations in fluid mechanics variational iteration method has been used to handle linear and nonlinear differential equations the main property of the method lies in its flexibility and ability to solve nonlinear equations accurately and conveniently in this work a general framework of the variational iteration method is presented for analytical treatment of fractional partial differential equations in fluid mechanics the fractional derivatives are described in the caputo sense numerical illustrations that include the fractional wave equation fractional burgers equation fractional kdv equation fractional klein gordon equation and fractional boussinesq like equation are investigated to show the pertinent features of the technique comparison of the results obtained by the variational iteration method with those obtained by adomian decomposition method reveals that the first method is very effective and convenient the basic idea described in this paper is expected to be further employed to solve other similar linear and nonlinear problems in fractional calculus

axisymmetric straining modes in the vibration of circular plates axisymmetric straining modes which are different from the axisymmetric flexural modes of vibrating circular plates and cannot be revealed by conventional plate theory based approaches are investigated in the present study mode shapes of an example problem with clamped and four different simply supported boundary conditions are presented to show what straining modes may look like the straining modes are classified into three types and a criterion is set up to predict the appearance of straining modes some observations about straining modes are obtained and discussions are made results for different poisson ratios are also shown

the variational iteration method for rational solutions for kdv k 2 2 burgers and cubic boussinesq equations in this work the reliable variational iteration method is used to determine rational solutions for the kdv the k 2 2 the burgers and the cubic boussinesq equations the study highlights the efficiency of the method and its dependence on the lagrange multiplier rational solutions are obtained directly in a straightforward manner

blending in the extended finite element method by discontinuous galerkin and assumed strain methods summary in the extended finite element method xfem errors are caused by parasitic terms in the approximation space of the blending elements at the edge of the enriched subdomain a discontinuous galerkin dg formulation is developed which circumvents this source of error a patch based version of the dg formulation is developed which decomposes the domain into enriched and unenriched subdomains continuity between patches is enforced with an internal penalty method an element based form is also developed where each element is considered a patch the patch based dg is shown to have similar accuracy to the element based dg for a given discretization but requires significantly fewer degrees of freedom the method is applied to material interfaces cracks and dislocation problems for the dislocations a contour integral form of the internal forces that only requires integration over the patch boundaries is developed a previously developed assumed strain as method is also developed further and compared with the dg method for weak discontinuities and linear elastic cracks the dg method is shown to be significantly more accurate than the standard xfem for a given element size and to converge optimally even where the standard xfem does not the accuracy of the dg method is similar to that of the as method but requires less application specific coding copyright q 2007 john wiley sons ltd

a bubble stabilized finite element method for dirichlet constraints on embedded interfaces we examine a bubble stabilized finite element method for enforcing dirichlet constraints on embedded interfaces by embedded we refer to problems of general interest wherein the geometry of the interface is assumed independent of some underlying bulk mesh as such the robust imposition of dirichlet constraints using a lagrange multiplier field is not trivial to focus issues we consider a simple one sided problem that is representative of a wide class of evolving interface problems the bulk field is decomposed into coarse and fine scales giving rise to coarse scale and fine scale one sided sub problems the fine scale solution is approximated with bubble functions permitting static condensation and giving rise to a stabilized form bearing strong analogy with a classical method importantly the method is simple to implement readily extends to multiple dimensions obviates the need to specify any free stabilization parameters and can lead to a symmetric positive definite system of equations the performance of the method is then examined through several numerical examples the accuracy of the lagrange multiplier is compared to results obtained using a local version of the domain integral method the variational multiscale approach proposed herein is shown to both stabilize the lagrange multiplier and improve the accuracy of the post processed fluxes copyright 2006 john wiley sons ltd

high order x fem and levelsets for complex microstructures uncoupling geometry and approximation in this contribution a strategy is proposed for uncoupling geometrical description and approximation with the x fem the strategy is based on an uniform coarse mesh that defines a high order approximation of the mechanical fields and an adapted mesh that defines the geometrical features by means of levelsets the connection between the geometry and the approximation is obtained by sharing the quadtree trees of the two meshes numerical examples involving level set based parts convergence studies mechanical computations and numerical homogenization show good promise for this approach

alternative state space formulations for magnetoelectric thermoelasticity with transverse isotropy and the application to bending analysis of nonhomogeneous plates abstract by introducing two displacement functions and two stress functions the governing equations of the linear theory of magneto electro thermo elasticity with transverse isotropy are simplified on selecting certain physical quantities as the basic unknowns two new state equations are established each of them is order reduced when compared with the one reported recently in literature leading to a higher numerical efficiency the material inhomogeneity along the axis of symmetry z direction can be taken into account and an approximate laminate model is employed to facilitate deriving analytical solutions the validity of new formulations is examined by considering a laminated magneto electro elastic rectangular plate and good agreement is obtained with existent results a plate with a functionally graded property is then analyzed the effect of magnetoelectric coupling in a batio3 cofe2o4 composite predicted from the micromechanics simulation is studied quantitatively

variational iteration method for solving burger s and coupled burger s equations by means of variational iteration method the solutions of burger s equation and coupled burger s equations are exactly obtained comparison with the adomian decomposition method is made showing that the former is more effective than the later in this paper he s variational iteration method is introduced to overcome the difficulty arising in calculating adomian polynomials

the variational iteration method a reliable analytic tool for solving linear and nonlinear wave equations in this work he s variational iteration method vim is used for analytic treatment of the linear and the nonlinear wave equations in bounded and unbounded domains wave like equations are also investigated the method is capable of reducing the size of calculation and easily overcomes the difficulty of the perturbation technique or adomian polynomials the study highlights the power of the vim method

three dimensional vibration analysis of thick rectangular plates using chebyshev polynomial and ritz method this paper describes a method for free vibration analysis of rectangular plates with any thicknesses which range from thin moderately thick to very thick plates it utilises admissible functions comprising the chebyshev polynomials multiplied by a boundary function the analysis is based on a linear small strain three dimensional elasticity theory the proposed technique yields very accurate natural frequencies and mode shapes of rectangular plates with arbitrary boundary conditions a very simple and general programme has been compiled for the purpose for a plate with geometric symmetry the vibration modes can be classified into symmetric and antisymmetric ones in that direction in such a case the computational cost can be greatly reduced while maintaining the same level of accuracy convergence studies and comparison have been carried out taking square plates with four simply supported edges as examples it is shown that the present method enables rapid convergence stable numerical operation and very high computational accuracy parametric investigations on the vibration behaviour of rectangular plates with four clamped edges have also been performed in detail with respect to different thickness side ratios aspect ratios and poissons ratios these results may serve as benchmark solutions for validating approximate two dimensional theories and new computational techniques in future 2002 elsevier science ltd all rights reserved

a new method for solving singular initial value problems in the second order ordinary differential equations singular initial value problems linear and nonlinear homogeneous and nonhomogeneous are investigated by using adomian decomposition method the solutions are constructed in the form of a convergent series a new general formula is established the approach is illustrated with few examples

a corrected xfem approximation without problems in blending elements the extended finite element method xfem enables local enrichments of approximation spaces standard finite elements are used in the major part of the domain and enriched elements are employed where special solution properties such as discontinuities and singularities shall be captured in elements that blend the enriched areas with the rest of the domain problems arise in general these blending elements often require a special treatment in order to avoid a decrease in the overall convergence rate a modification of the xfem approximation is proposed in this work the enrichment functions are modified such that they are zero in the standard elements unchanged in the elements with all their nodes being enriched and varying continuously in the blending elements all nodes in the blending elements are enriched the modified enrichment function can be reproduced exactly everywhere in the domain and no problems arise in the blending elements the corrected xfem is applied to problems in linear elasticity and optimal convergence rates are achieved copyright 2007 john wiley sons ltd

determination of the size of the representative volume element for random composites statistical and numerical approach the representative volume element rve plays a central role in the mechanics and physics of random heterogeneous materials with a view to predicting their effective properties a quantitative definition of its size is proposed in this work a rve size can be associated with a given precision of the estimation of the wanted overall property and the number of realizations of a given volume v of microstructure that one is able to consider it is shown to depend on the investigated morphological or physical property the contrast in the properties of the constituents and their volume fractions the methodology is applied to a specific random microstructure namely a two phase three dimensional voronoi mosaic finite element simulations of volumes of different sizes are performed in the case of linear elasticity and thermal conductivity the volumes are subjected to homogeneous strain stress or periodic boundary conditions the effective properties can be determined for large volumes and a small number of realizations conversely smaller volumes can be used providing that a sufficient number of realizations are considered a bias in the estimation of the effective properties is observed for too small volumes for all types of boundary conditions the variance of computed apparent properties for each volume size is used to define the precision of the estimation the key notion of integral range is introduced to relate this error estimation and the definition of the rve size for given wanted precision and number of realizations one is able to provide a minimal volume size for the computation of effective properties the results can also be used to predict the minimal number of realizations that must be considered for a given volume size in order to estimate the effective property for a given precision the rve sizes found for elastic and thermal properties but also for a geometrical property like volume fraction are compared

numerical steady state and hopf bifurcation analysis on the diffusive nicholson s blowflies equation1research partially supported by natural sciences and engineering research council of canada 1 for the dirichlet boundary value problem of the diffusive nicholson s blowflies equation it was shown in ref 17 that in a certain range of the parameter space there is a unique positive steady state solution in this paper we propose a scheme to compute this steady state numerically in addition we describe an iterative procedure to locate the critical values of the delay where a hopf bifurcation of time periodic solutions takes place near the steady state some numerical simulations of both schemes are given

free vibration studies of simply supported non homogeneous functionally graded magneto electro elastic finite cylindrical shells in this article free vibration studies on functionally graded materials fgm magneto electro elastic cylindrical shells have been carried out a series solution is assumed in circumferential and axial direction such that the three dimensional character of the solution is preserved the finite element model is derived based on constitutive equation of magneto electro elastic material accounting for coupling between elasticity electric and magnetic effect frequency behavior with the variation of power law index is analyzed and explained on the basis of constitutive material one of the aims of the study is to evaluate the influence of magnetic and piezoelectric effect on the structural frequency in addition influence of length to radius ratio and radius to thickness ratio on the frequency behaviour of such shells have been attempted

vibration analysis of functionally graded annular plates with mixed boundary conditions in thermal environment abstract the free vibration analysis of functionally graded annular plates with mixed boundary conditions in thermal environment is carried out by the 3d elasticity theory and the chebyshev ritz method the material properties are assumed to be temperature dependent and graded in the thickness direction the mixed boundary conditions which include upper and lower surfaces partially fixed inner side partially fixed and outer side partially fixed are considered respectively the accuracy of the present approach for solving the free vibration of the plates with different boundary conditions is validated by comparing the present numerical results with the results available the effects of the different mixed boundary conditions the temperature rise the material graded index and the geometrical parameters on the eigen frequencies are studied

three dimensional elasticity solutions for free vibrations of circular plates a polynomials ritz analysis this paper presents accurate three dimensional elasticity solutions for free vibration of circular plates the derivation of a linear frequency equation based on an exact three dimensional small strain linearly elastic principle is detailed the solution to this problem is made possible by using the ritz method with a set of orthogonal polynomial series to approximate the spatial displacements of the circular plate in cylindrical polar coordinates the perturbation of frequency responses due to the variations of boundary conditions and thickness is investigated first known frequency parameters and three dimensional deformed mode shapes are presented in vivid graphical forms the accuracy of these results are verified by appropriate convergence studies and when possible are checked with existing solutions

a computational approach to handle complex microstructure geometries in multiscale analysis of components there is usually a need to solve microstructures with complex geometries in this paper we use the extended finite element method x fem to solve scales involving complex geometries the x fem allows one to use meshes not necessarily matching the physical surface of the problem while retaining the accuracy of the classical finite element approach for material interfaces this is achieved by introducing a new enrichment strategy although the mesh does not need to conform to the physical surfaces it needs to be fine enough to capture the geometry of these surfaces a simple algorithm is described to adaptively refine the mesh to meet this geometrical requirement numerical experiments on the periodic homogenization of two phase complex cells demonstrate the accuracy and simplicity of the x fem c 2003 elsevier b v all rights reserved

on free vibration of non homogeneous transversely isotropic magneto electro elastic plates two independent state equations are established for transversely isotropic magneto electro elastic media by introducing proper stress and displacement functions the free vibration problem of simply supported rectangular plates with general inhomogeneous functionally graded material properties along the thickness direction is then considered an approximate laminate model is employed to transform the state equations with variable coefficients to the ones with constant coefficients two different classes of vibrations are found in particular the frequency of the first class is only related to the elastic property of the plate while that of the second class is affected by the couplings among the elastic electric and magnetic fields numerical results are presented and some important issues are discussed

on strategies for enforcing interfacial constraints and evaluating jump conditions with the extended finite element method we consider a problem stemming from recent models of phase transitions in stimulus responsive hydrogels wherein a sharp interface separates swelled and collapsed phases extended finite element methods that approximate the local solution with an enriched basis such that the mesh need not explicitly fit the interface geometry are emphasized attention is focused on the weak enforcement of the normal configurational force balance and various options for evaluating the jump in the normal component of the solute flux at the interface we show that as the reciprocal interfacial mobility vanishes it plays the role of a penalty parameter enforcing a pure dirichlet constraint eventually triggering oscillations in the interfacial velocity we also examine alternative formulations employing a lagrange multiplier to enforce this constraint it is shown that the most convenient choice of basis for the lagrange multiplier results in oscillations in the multiplier field and a decrease in accuracy and rate of convergence in local error norms suggesting a lack of stability in the discrete formulation under such conditions neither the direct evaluation of the gradient of the approximation at the phase interface nor the interpretation of the lagrange multiplier field provide a robust means to obtain the jump in the normal component of solute flux fortunately the adaptation and use of local domain integral methodologies considerably improves the flux evaluations several example problems are presented to compare and contrast the various techniques and methods

exact solution of the heat equation with boundary condition of the fourth kind by he s variational iteration method in this paper solutions of the heat equation with the boundary condition of the fourth kind are presented the proposed solution is based on he s variational iteration method after the application of which the exact solution of the problem is obtained

rapid analysis of variable stiffness beams and plates legendre polynomial triple product formulation copyright 2017 john wiley sons ltd numerical integration techniques are commonly employed to formulate the system matrices encountered in the analysis of variable stiffness beams and plates using a ritz based approach computing these integrals accurately is often computationally costly herein a novel alternative is presented the recursive analytical polynomial integral definition rapid formulation the rapid formulation offers a significant improvement in the speed of analysis achieved by reducing the number of numerical integrations that are performed by an order of magnitude a common legendre polynomial basis is employed for both trial functions and stiffness load variations leading to a common form for the integrals encountered the legendre polynomial basis possesses algebraic recursion relations that allow these integrals to be reformulated as triple products with known analytical solutions defined compactly using the wigner 3j coefficient the satisfaction of boundary conditions calculation of derivatives and transformation to other bases is achieved through combinations of matrix multiplication with each matrix representing a unique boundary condition or physical effect therefore permitting application of the rapid approach to a variety of problems indicative performance studies demonstrate the advantage of the rapid formulation when compared to direct analysis using matlab s integral and integral2 copyright 2017 john wiley sons ltd

the variational iteration method for cauchy problems in this paper the variational iteration method is used to solve the cauchy problem some examples are given to elucidate the solution procedure and reliability of the obtained results the variational iteration algorithm leads to exact solutions in the present study

modeling holes and inclusions by level sets in the extended finite element method a methodology to model arbitrary holes and material interfaces inclusions without meshing the internal boundaries is proposed the numerical method couples the level set method s osher j a sethian j comput phys 79 1 1988 12 to the extended finite element method x fem n moes j dolbow t belytschko int j numer methods engrg 46 1 1999 131 in the x fem the finite element approximation is enriched by additional functions through the notion of partition of unity the level set method is used for representing the location of holes and material interfaces and in addition the level set function is used to develop the local enrichment for material interfaces numerical examples in two dimensional linear elastostatics are presented to demonstrate the accuracy and potential of the new technique

arbitrary branched and intersecting cracks with the extended finite element method summary extensions of a new technique for the nite element modelling of cracks with multiple branches multiple holes and cracks emanating from holes are presented this extended nite element method x fem allows the representation of crack discontinuities and voids independently of the mesh a standard displacementbased approximation is enriched by incorporating discontinuous elds through a partition of unity method a methodology that constructs the enriched approximation based on the interaction of the discontinuous geometric features with the mesh is developed computation of the stress intensity factors sif in dierent examples involving branched and intersecting cracks as well as cracks emanating from holes are presented to demonstrate the accuracy and the robustness of the proposed technique copyright 2000 john wiley sons ltd

extended finite element method for three dimensional crack modelling an extended finite element method x fem for three dimensional crack modelling is described a discontinuous function and the two dimensional asymptotic crack tip displacement fields are added to the finite element approximation to account for the crack using the notion of partition of unity this enables the domain to be modelled by finite elements with no explicit meshing of the crack surfaces computational geometry issues associated with the representation of the crack and the enrichment of the finite element approximation are discussed stress intensity factors sifs for planar three dimensional cracks are presented which are found to be in good agreement with benchmark solutions copyright 2000 john wiley sons ltd

elasticity solutions for free vibrations of annular plates from three dimensional analysis abstract this article examines the vibrational characteristics of annular plates by using the three dimensional elasticity theory it aims to raise the quality of the investigation beyond that provided by the two dimensional plate theories by resorting to a full three dimensional analysis a polynomials ritz model based on sets of orthogonally generated polynomial functions to approximate the spatial displacements of the plates in cylindrical polar coordinates is presented the model is then used to extract the full vibration spectrum of natural frequencies and mode shapes the vibration responses due to the variations of boundary conditions and thickness are investigated frequency parameters and three dimensional deformed mode shapes are presented in vivid graphical forms the accuracy of the method is validated through appropriate convergence and comparison studies

natural vibration of circular and annular thin plates by hamiltonian approach abstract the present paper deals with the natural vibration of thin circular and annular plates using hamiltonian approach it is based on the conservation principle of mixed energy and is constructed in a new symplectic space a set of hamiltonian dual equations with derivatives with respect to the radial coordinate on one side of the equations and to the angular coordinate on the other side are obtained by using the variational principle of mixed energy the separation of variables is employed to solve hamiltonian dual equations of eigenvalue problem analytical frequency equations are obtained based on different cases of boundary conditions the natural frequencies are the roots of the frequency equations and corresponding mode functions are in terms of the dual variables q1 r three basic edge constraint cases for circular plates and nine edge constraint cases for annular plates are calculated and the results are compared well with existing ones

a higher order shear deformation theory for the vibration of thick plates abstract several first order shear deformation theories for thick plates have been formulated during the past half century e g by reissner hencky mindlin and ambartsumyan the mindlin theory has been widely used for vibration analysis it is well known that consideration of shear flexibility corrects the flexural frequencies by reducing them however it has been found that first order shear deformation theories result in over correction in the present work a higher order theory is presented which provides additional freedom to the displacements through the plate thickness and essentially eliminates the over correction a complete theory is developed including energy functionals equations of motion and boundary conditions comparisons of frequencies arising from classical thin plate theory mindlin theory and the present theory are made for completely free rectangular plates of moderate and large thickness completely free boundaries rather than simply supported ones are chosen because they are more consistent with physical models in the theories used

a comparison between the variational iteration method and adomian decomposition method in this paper we present a comparative study between the variational iteration method and adomian decomposition method the study outlines the significant features of the two methods the analysis will be illustrated by investigating the homogeneous and the nonhomogeneous advection problems

uncertainty quantification in homogenization of heterogeneous microstructures modeled by xfem an extended finite element method xfem coupled with a monte carlo approach is proposed to quantify the uncertainty in the homogenized effective elastic properties of multiphase materials the methodology allows for an arbitrary number aspect ratio location and orientation of elliptic inclusions within a matrix without the need for fine meshes in the vicinity of tightly packed inclusions and especially without the need to remesh for every different generated realization of the microstructure moreover the number of degrees of freedom in the enriched elements is dynamically reallocated for each monte carlo sample run based on the given volume fraction the main advantage of the proposed xfem based methodology is a major reduction in the computational effort in extensive monte carlo simulations compared with the standard fem approach monte carlo and xfem appear to work extremely efficiently together the monte carlo approach allows for the modeling of the size aspect ratios orientations and spatial distribution of the elliptical inclusions as random variables with any prescribed probability distributions numerical results are presented and the uncertainty of the homogenized elastic properties is discussed copyright 2011 john wiley sons ltd

a high order generalized fem for through the thickness branched cracks this paper presents high order implementations of a generalized finite element method for through the thickness three dimensional branched cracks this approach can accurately represent discontinuities such as triple joints in polycrystalline materials and branched cracks independently of the background finite element mesh representative problems are investigated to illustrate the accuracy of the method in combination with various discretizations and refinement strategies the combination of local refinement at crack fronts and high order continuous and discontinuous enrichments proves to be an excellent combination which can deliver convergence rates close to that of problems with smooth solutions copyright 2007 john wiley sons ltd

variational iteration method some recent results and new interpretations this paper is an elementary introduction to the concepts of variational iteration method first the main concepts in variational iteration method such as general lagrange multiplier restricted variation correction functional are explained heuristically subsequently the solution procedure is systematically addressed in particular for nonlinear oscillators particular attention is paid throughout the paper to give an intuitive grasp for the method the main motivation is to put things together in a convenient form for later reference and systematic use

necessary conditions for the appearance of noise terms in decomposition solutions series in this paper the phenomena of the noise terms that appear in the components of the series solution introduced by adomian and rach 1 will be examined extensively the phenomena is useful in demonstrating a fast convergence of the exact solution however the condition set by adomian and rach 1 in that these noise terms appear for every nonhomogeneous equation is not always true and the nonhomogeneity condition is not sufficient another necessary condition will be established in this study to ensure the appearance of noise terms in specific cases several differential and integral equations will be tested to confirm the newly developed condition

analytical approximations and pade approximants for volterra s population model in this paper an analytic approximation for volterra s model for population growth of a species in a closed system is presented the nonlinear integro differential model includes an integral term that characterizes accumulated toxicity on the species in addition to the terms of the logistic equation the series solution method and the decomposition method are implemented independently to the model and to a related ode the pade approximants that often show superior performance over series approximations are effectively used in the analysis to capture the essential behavior of the population u t of identical individuals

closed form solution for free vibration of piezoelectric coupled annular plates using levinson plate theory abstract free vibration analysis of annular moderately thick plates integrated with piezoelectric layers is investigated in this study for different combinations of soft simply supported hard simply supported and clamped boundary conditions at the inner and outer edges of the annular plate on the basis of the levinson plate theory lpt the distribution of electric potential along the thickness direction in the piezoelectric layer is assumed as a sinusoidal function so that the maxwell static electricity equation is approximately satisfied the differential equations of motion are solved analytically for various boundary conditions of the plate in this study the closed form solution for characteristic equations displacement components of the plate and electric potential are derived for the first time in the literature to demonstrate the accuracy of the present solution comparison studies is first carried out with the available data in the literature and then natural frequencies of the piezoelectric coupled annular plate are presented for different thickness radius ratios inner outer radius ratios thickness of piezoelectric material of piezoelectric and boundary conditions present analytical model provides design reference for piezoelectric material application such as sensors actuators and ultrasonic motors

buckling and vibration of polar orthotropic circular plate resting on winkler foundation buckling and vibrational behavior of polar orthotropic circular plates of linearly varying thickness is presented on the basis of classical plate theory the plate is resting on winkler type foundation an approximate solution has been obtained by ritz method which employs basis functions based upon static deflection of polar orthotropic plates the effect of elastic foundation and that of orthotropy on the natural frequency of plate has been illustrated for different values of taper parameter flexibility parameter in plane force and nodal diameter the critical buckling load for clamped and simply supported plates have been obtained a comparison of results with those available in literature has been presented

vibration of electro elastic versus magneto elastic circular annular plates using the chebyshev ritz method abstract the aim of this paper is to analyze three dimensional free vibration of magneto elastic electro elastic circular annular plates with different boundary conditions using the chebyshev ritz method in which a set of duplicate chebyshev polynomial series multiplied by the boundary function satisfying the boundary conditions are chosen as the trial functions of the displacement components the electric potential and the magnetic potential convergence of the method is checked using various chebyshev polynomial terms the effect of geometrical parameters and material properties of magneto elastic electro elastic circular annular plates on the eigenfrequencies of free vibration is considered

a multiple level set approach to prevent numerical artefacts in complex microstructures with nearby inclusions within xfem in this paper we highlight that when the extended finite element method xfem is employed to model a microstructure in which inclusions are involved and the distance between two inclusions is small enough to be comparable with the mesh size three numerical artefacts are induced significantly affecting the convergence and accuracy of the numerical solution to the problem with such a microstructure these artefacts are a an artificial percolation of nearby inclusions b an artificial distortion of phase domains c an enrichment deficiency we propose to improve the xfem levelset method so as to avoid these artefacts the new technique leading to this improvement uses one level set function for each inclusion and adds additional enrichment in an element whose support is cut by several interfaces a local description of the multiple level sets is provided to avoid the storage of all level set functions a simple integration rule is employed for numerical quadrature in elements cut by several interfaces we show that the artefacts mentioned hereinbefore are circumvented in this framework the performances of the method are demonstrated through benchmarks and examples applied to the homogenization of concrete materials in 2d and 3d cases

a new algorithm for calculating adomian polynomials for nonlinear operators in this paper a reliable technique for calculating adomian polynomials for nonlinear operators will be developed the new algorithm offers a promising approach for calculating adomian polynomials for all forms of nonlinearity the algorithm will be illustrated by studying suitable forms of nonlinearity a nonlinear evolution model will be investigated

a stable lagrange multiplier space for stiff interface conditions within the extended finite element method this paper introduces a new algorithm to define a stable lagrange multiplier space to impose stiff interface conditions within the context of the extended finite element method in contrast to earlier approaches we do not work with an interior penalty formulation as e g for nitsche techniques but impose the constraints weakly in terms of lagrange multipliers roughly speaking a stable and optimal discrete lagrange multiplier space has to satisfy two criteria a best approximation property and a uniform inf sup condition owing to the fact that the interface does not match the edges of the mesh the choice of a good discrete lagrange multiplier space is not trivial here we propose a new algorithm for the local construction of the lagrange multiplier space and show that a uniform inf sup condition is satisfied a counterexample is also presented i e the inf sup constant depends on the mesh size and degenerates as it tends to zero numerical results in two dimensional confirm the theoretical ones copyright

approximate analytical solution for seepage flow with fractional derivatives in porous media abstract in this paper a new and more exact model for seepage flow in porous media with fractional derivatives has been proposed which has modified the well known darcy law and overcome the continuity assumption of seepage flow a new kind of analytical method of nonlinear problem called the variational iteration method is described and used to give approximate solutions of the problem the results show that the proposed iteration method requiring no linearization or small perturbation is very effective and convenient

the variational iteration method for analytic treatment for linear and nonlinear odes in this work the variational iteration method vim is used for analytic treatment of the linear and nonlinear ordinary differential equations homogeneous or inhomogeneous the method is capable of reducing the size of calculations and handles both linear and nonlinear equations homogeneous or inhomogeneous in a direct manner however for concrete problems a huge number of iterations are needed for a reasonable level of accuracy

computational nonlinear stochastic homogenization using a nonconcurrent multiscale approach for hyperelastic heterogeneous microstructures analysis this paper is devoted to the computational nonlinear stochastic homogenization of a hyperelastic heterogeneous microstructure using a non concurrent multiscale approach the geometry of the microstructure is random since the non concurrent multiscale approach is based on the use of a tensorial decomposition which is then submitted to the curse of dimensionality we perform an analysis with respect to the stochastic dimension the technique uses a database describing the strain energy density function potential in both the macroscopic cauchy green strain space and the geometrical random parameters domain each value of the potential is numerically computed by means of the finit element method on an elementary cell an interpolation scheme is finall introduced to obtain a continuous explicit form of the potential which by derivation allows to evaluate the macroscopic stress and elastic tangent tensors during the macroscopic structural computations two numerical examples are presented

effect of built in edges on 3 d vibrational characteristics of thick circular plates the vibrational characteristics of thick circular plates built into a rigid medium in the vicinity of the circumference are studied the analysis procedure is based on the exact small strain three dimensional linear elasticity theory in the analysis the plate is considered as comprising an inner circular disc with free upper and lower surfaces connected to an outer annulus that is built into the rigid medium the chebyshev polynomials multiplied by suitable boundary characteristic functions are selected as the admissible functions of the displacement functions and the three dimensional displacement fields in each part can be expressed accordingly through the ritz method the eigenvalue equations can be established for the inner disc and the outer annulus respectively utilizing the displacement continuity conditions at the interface between the two parts the eigenvalue equation for the whole plate is derived convergence and comparison studies demonstrate the correctness and accuracy of the present method the effect of structural parameters such as plate thickness built in length and the end condition on eigenfrequencies of circular plate is investigated in detail it is shown that with the increase of plate thickness the effect of the built in annulus on eigenfrequencies significantly increases therefore for a thick plate the flexibility of the built in part should be considered in the dynamic analysis