embeddings of submanifolds and normal bundles this paper studies the embeddings of a complex submanifold s inside a complex manifold m in particular we are interested in comparing the embedding of s in m with the embedding of s as the zero section in the total space of the normal bundle ns of s in m we explicitly describe some cohomological classes allowing to measure the difference between the two embeddings in the spirit of the work by grauert griffiths and camacho movasati and sad we are also able to explain the geometrical meaning of the separate vanishing of these classes our results hold for any codimension but even for curves in a surface we generalize previous results due to laufert and camacho movasati and sad

error estimation and adaptive meshing in strongly nonlinear dynamic problems we present work aimed at developing a general framework for mesh adaption in strongly nonlinear possibly dynamic problems we begin by showing that the solutions of the incremental boundary value problem for a wide class of materials including nonlinear elastic materials compressible newtonian fluids and viscoplastic solids obey a minimum principle provided that the constitutive updates are formulated appropriately this minimum principle can be taken as a basis for asymptotic error estimation in particular we chose to monitor the error of a lower order projection of the finite element solution the optimal mesh size distribution then follows from a posteriori error indicators which are purely local i e can be computed element by element we demonstrate the robustness and versatility of the computational framework with the aid of convergence studies and selected examples of application

topological invariants and equidesingularization for holomorphic vector fields on etudie l invariance du nombre de milnor et ses applications on demontre un theoreme d equidesingularisation

on shear deformable beam theories the frequency and normal mode equations of the homogeneous orthotropic bickford beam abstract this paper provides a step forwards the construction and documentation of the frequency equations and the characteristic functions of a general three degrees of freedom theory that describes the plane motion of shear deformable elastic beams the governing equations of this shear deformable beam theory g3dofbt involve a general shape function of the transverse beam co ordinate parameter the a posteriori choice of which specifies the distribution of the transverse shear strain or stress along the beam thickness different choices of this shape function produce as particular cases the corresponding governing equations of different beam theories these include the differential equations of the euler bernoulli beam theory as well as the corresponding equations of the shear deformable theories due to timoshenko and bickford other examples can also be found by considering the shear deformable beam theories produced as one dimensional versions of relevant refined plate theories since corresponding developments of the timoshenko beam theory are already available in the literature the bickford theory is considered as the pilot beam theory in this study the frequency equations the characteristic functions and the orthogonality conditions of this theory which assumes a through thickness parabolic distribution of the transverse shear strain or stress are constructed analytically for all the classical sets of boundary conditions applied at the beam ends some preliminary numerical results are also presented and discussed for beams having both their ends simply supported or clamped

polynomial versus trigonometric expansions for nonlinear vibrations of circular cylindrical shells with different boundary conditions abstract large amplitude geometrically nonlinear forced vibrations of circular cylindrical shells with different boundary conditions are investigated the sanders koiter nonlinear shell theory which includes in plane inertia is used to calculate the elastic strain energy the shell displacements longitudinal circumferential and radial are expanded by means of a double mixed series harmonic functions for the circumferential variable and three different formulations for the longitudinal variable these three different formulations are a chebyshev orthogonal polynomials b power polynomials and c trigonometric functions the same formulation is applied to study different boundary conditions results are presented for simply supported and clamped shells the analysis is performed in two steps first a liner analysis is performed to identify natural modes which are then used in the nonlinear analysis as generalized coordinates the lagrangian approach is applied to obtain a system of nonlinear ordinary differential equations different expansions involving from 14 to 34 generalized coordinates associated with natural modes of both simply supported and clamped clamped shells are used to study the convergence of the solution the nonlinear equations of motion are studied by using arclength continuation method and bifurcation analysis numerical responses obtained in the spectral neighborhood of the lowest natural frequency are compared with results available in literature

ritz type dynamic analysis of cross ply laminated circular cylinders subjected to different boundary conditions this paper extends the applicability of the ritz type method presented in a previous publication 1 towards an advanced study of the influence of the edge boundary conditions on the vibration characteristics of complete cross ply laminated cylindrical shells the analysis is based on a combination of the ritz method with appropriate complete bases of orthonormal polynomials and its subsequent application on the energy functional of the love type version of a unified shear deformable shell theory as a result two different kinds of shear deformable love type shell theories are employed including versions that either fulfil or violate the continuity of the interlaminar stresses through the shell thickness apart from the study of the physical problem itself several features related to the theoretical model as well as to the analytical procedure are further addressed and investigated as far as the modelling is concerned particular emphasis is given to the version of the parabolic shear deformable shell theory that considers continuity of interlaminar stresses moreover the relation of this version of the theory as well as its performance with respect to the corresponding older version that violates this continuity requirement 8 is further investigated it is concluded that the accurate modelling of the interlaminar stress distribution may become a serious issue for further investigation as it already is for the stress analysis of laminated composite structural elements

darboux integrating factors inverse problems abstract we discuss planar polynomial vector fields with prescribed darboux integrating factors in a nondegenerate affine geometric setting we establish a reduction principle which transfers the problem to polynomial solutions of certain meromorphic linear systems and show that the space of vector fields with a given integrating factor modulo a subspace of explicitly known standard vector fields has finite dimension for several classes of examples we determine this space explicitly

a general vibration model of angle ply laminated plates that accounts for the continuity of interlaminar stresses abstract this paper presents the generalisation of a well documented two dimensional shear deformable laminated shell theory compos struct 25 1993 165 that based on a fixed number of unknown variables was initially proposed for laminates made of specially orthotropic layers only the theory is here specialised for laminated plates but is able to encompass monoclinic layers in a general multilayered configuration moreover it is able to account for the interlaminar continuity of both displacements and transverse shear stresses higher order effects as shear deformation and rotary inertia are naturally included into the formulation in order to obtain the relevant governing differential equations both hamilton s variational principle and a recently proposed vectorial approach compos engng 3 1993 3 have been independently used the effectiveness of the present model is tested numerically by comparing its results with exact three dimensional elasticity results obtained under the particular condition that the plates vibrate in cylindrical bending

extendable cohomologies for complex analytic varieties we introduce a cohomology called extendable cohomology for abstract complex singular varieties based on suitable differential forms beside a study of the general properties of such a cohomology we show that given a complex vector bundle one can compute its topological chern classes using the extendable chern classes defined via a chern weil type theory we also prove that the localizations of the extendable chern classes represent the localizations of the respective topological chern classes thus obtaining an abstract residue theorem for compact singular complex analytic varieties as an application of our theory we prove a camacho sad type index theorem for holomorphic foliations of singular complex varieties

mesh motion techniques for the ale formulation in 3d large deformation problems efficient mesh motion techniques are a key issue to achieve satisfactory results in the arbitrary lagrangian eulerian ale finite element formulation when simulating large deformation problems such as metal forming in the updated lagrangian ul formulation mesh and material movement are attached and an excessive mesh distortion usually appears by uncoupling mesh movement from material movement the ale formulation can relocate the mesh to avoid distortion to facilitate the calculation process the ale operator is split into two steps at each analysis time step ul step where deformation due to loading is calculated without convective terms and eulerian step where mesh motion is applied in this work mesh motion is performed by new nodal relocation methods developed for eight node hexahedral elements which can move internal and boundary nodes improving and concentrating the mesh in critical zones after mesh motion data is transferred from the ul mesh to the relocated mesh using an expansion of stresses in a taylor s series two numerical applications are presented comparing results of ul and ale formulation with results found in the literature copyright 2004 john wiley sons ltd

adaptive mesh refinement in strain localization problems an adaptive meshing method tailored to problems of strain localization is given the adaption strategy consists of equi distributing the variation of the velocity field over the elements of the mesh a heuristic justification for the use of variations as indicators is advanced and possible connections with interpolation error bounds are discussed meshes are constructed by delaunay triangulation it is shown how the hu washizu principle determines a consistent transfer operator for the state variables examples of application are given which demonstrate the versatility of the method

singular element construction using a mapping technique conformal mapping regularizes in the new plane the singular stress field around the crack tip so conventional finite elements can be used in the transformed plane the inverse mapping of the above elements gives another class of mapped elements the crack tip mapped element is a singular element thus using various elements the parent elements in the mapped plane we obtain an infinity of singular elements the product elements these singular elements are introduced naturally and have no defect as many other singular elements have

a method of grid optimization for finite element methods a computationally useful criterion for grid optimization is derived based on a measure of the interpolation error associated with the finite element model the result is intended to be used to improve the quality of finite element solutions by changing the location of the nodes within a fixed number of degrees of freedom examples of the application of the criterion are provided the finite element method has become an important tool of engineering analysis and design much of the popularity of the method is due to the freedom that it allows in the construction of the discretized model it has long been realized however that this freedom must be carefully exercised since the quality of the finite element solution greatly depends on how the discretization is performed several methods have been proposed to improve the discretized model in an iterative manner one such method is presented in this paper a natural way of improving the quality of finite element solutions is to increase the number of degrees of freedom the process is normally performed after an initial solution is already available several schemes have been devised to introduce the new degrees of freedom in a selective manner in order to produce the greatest possible improvement of the previous solution this calls for the definition of criteria to identify the regions of the domain where the finite element approximation is poorer the new degrees of freedom are added in these regions by either increasing the order of polynomial approximation inside elements the so called p method or by subdivision of elements or h method the process is continued until a specified accuracy is achieved the quality of the finite element solution may be improved also by optimizing the disposition of the nodes analysts often rely on their experience to construct grids that make an efficient use of the available degrees of freedom it is also possible to improve the quality of existing meshes iteratively using predefined guidelines for the redistribution of the nodes this paper considers the development of such guidelines

on the rates of convergence of the finite element method abstract the rate of convergence of the finite element method is a function of the strategy by which the number of degrees of freedom are increased alternative strategies are examined in the light of recent theoretical results and computational experience author

vibration studies of cross ply laminated shear deformable circular cylinders on the basis of orthogonal polynomials abstract this paper deals with a study of the free vibration characteristics of transverse shear deformable cross ply laminated circular cylindrical shells on the basis of the ritz method the analysis is based on the energy functional of the love type version of the unified shell theory presented in reference 28 as a result several kinds of shear deformable love type shell theories are employed along with their classical counterpart the theoretical formulation is given in a general form but the variational approach is finally applied in conjunction with a complete functional basis made of the appropriate admissible orthogonal polynomials the method is currently capable of treating cross ply laminated circular cylindrical shells subjected to any set of variationally consistent edge boundary conditions in this paper particular emphasis is given to the free vibrations of shells having one or both of their edges free of external tractions the efficiency of the proposed method is exhibited by comparing corresponding results with certain experimental data as well as with the very few existing relevant analytical results obtained elsewhere on the basis of an alternative mathematical method the state space concept apart from the specific value of the present dynamic investigation the analysis is further considered as a successful test towards its extension for the study of corresponding problems in which the state space concept cannot be applied directly

vibrations of circular cylindrical shells theory and experiments in the present paper a method for analysing linear and nonlinear vibrations of circular cylindrical shells having different boundary conditions is presented the method is based on the sanders koiter theory displacement fields are expanded in a mixed double series based on harmonic functions and chebyshev polynomials simply supported and clamped clamped boundary conditions are analysed as well as connections with rigid bodies in the latter case experiments are carried out comparisons with experiments and finite element analyses show that the technique is computationally efficient and accurate in modelling linear vibrations of shells with different boundary conditions an application to large amplitude of vibration shows that the technique is effective also in the case of nonlinear vibration comparisons with the literature confirm the accuracy of the approach the method proposed is a general framework suitable for analysing vibration of circular cylindrical shells both in the case of linear and nonlinear vibrations r 2007 elsevier ltd all rights reserved

mesh smoothing using a posteriori error estimates we develop a simple mesh smoothing algorithm for adaptively improving finite element triangulations the algorithm makes use of a posteriori error estimates which are now widely used in finite element calculations in this paper we derive the method present some numerical illustrations and give a brief analysis of the issue of uniqueness

grid optimization for the boundary element method the quality of solution obtained using the boundary element method bem is dependent on how the boundary is discretized this is particularly true in domains of complex geometry a rule for grid optimization for the bem is derived on the bases of an asymptotic measure of the boundary element error that preserves the number of elements degrees of freedom three example problems are provided to show the advantages of grid optimization in terms of accuracy and cost

validation of a posteriori error estimators by numerical approach abstract a numerical methodology which determines the quality or robustness of a posteriori error estimators is described the methodology accounts precisely for the factors which affect the quality of error estimators for finite element solutions of linear elliptic problems namely the local geometry of the grid and the structure of the solution the methodology can be employed to check the robustness of any estimator for the complex grids which are used in engineering computations

the influence of boundary conditions and transverse shear on the vibration of angle ply laminated plates circular cylinders and cylindrical panels abstract this paper investigates the influence of the edge boundary conditions on the vibration characteristics of transverse shear deformable composite plates closed cylindrical shells and open cylindrical panels having an arbitrary angle ply lay up the shell model employed for this purpose is equivalent to the unified shear deformable love type theory introduced in refs 6 7 whereas the analysis is based on the ritz method following some recent relevant developments 1 5 in which the method was applied successfully in connection with vibration problems of shear deformable cross ply laminates the ritz method is employed in conjunction with complete functional bases formed by appropriate orthonormal polynomials the present vibration study is based on angle ply laminates having different combinations of simply supported clamped and free edge boundaries apart from the convergence tests performed and the new results presented the success of the present analysis is verified through comparisons with the corresponding results based on classical plate and shell theories as well as through comparisons with corresponding numerical and experimental results that are available in the literature

application of theorem of minimum potential energy to a complex structure part i two dimensional analysis a cylindrical shell with a non circular cross section consisting of flat sides and circular arc corners is analyzed using the theorem of minimum potential energy the three dimensional analysis builds on previous two dimensional work the potential energy expression for the structure is developed including first order transverse shear deformation effects all unknown displacements are represented by power series and the potential energy expression is rewritten in terms of the summation convention for the power series the variation of the potential energy expression is taken leading to a linear system of equations that is solved for the unknown power series coefficients with the displacements determined stresses are calculated for a composite sandwich construction an examination of both short shells less than twice the boundary layer length and long shells more than twice the boundary layer length is made the mpe method with power series is found to predict behavior well for short shells but not for long shells

three dimensional adaptive meshing by subdivision and edge collapse in finite deformation dynamic plasticity problems with application to adiabatic shear banding this paper is concerned with the development of a general framework for adaptive mesh refinement and coarsening in three dimensional finite deformation dynamic plasticity problems mesh adaption is driven by a posteriori global error bounds derived on the basis of a variational formulation of the incremental problem the particular mesh refinement strategy adopted is based on rivara s longest edge propagation path lepp bisection algorithm our strategy for mesh coarsening or unrefinement is based on the elimination of elements by edge collapse the convergence characteristics of the method in the presence of strong elastic singularities are tested numerically an application to the three dimensional simulation of adiabatic shear bands in dynamically loaded tantalum is also presented which demonstrates the robustness and versatility of the method copyright c 2001 john wiley sons ltd

some improvements of the finite element solution for one dimensional problems new algorithms which improve the finite element solution on a fixed mesh of the domain are developed for this objective functions which depend on a positive parameter to be determined are proposed these functions lead to criteria which combine in several ways the residual of the solution the approximation in the euclidean norm of the value of the solution at the nodes and the approximations in the energy and hk norms some aspects of optimality are studied and finally numerical results are given

an adaptive h r boundary element algorithm for the laplace equation in this paper the combination of the h method mesh refinement and the r method mesh redistribution is employed to solve the laplace equation using the boundary element procedure the key in this approach is to derive on upper bound for the residual associated with the boundary element solution and minimize this bound with respect to an unknown grading function the latter part is achieved by employing techniques of the calculus of variations

adaptive s method for linear elastostatics abstract a methodology has been developed to simultaneously treat phenomena at several scales the key features of the method are i a detailed error diagnosis which identifies critical regions and ii a feedback procedure which overlays portions of the finite element mesh where unacceptable errors have been identified by local finite element mesh es and then subsequently improves the quality of the solution in the global and local response until the desired level of accuracy is achieved the method can be routinely used as a global local method and or as an adaptive technique which provides a measure of reliability of global and local computations numerical experiments for problems in homogeneous and heterogeneous laminated composites media are presented to validate the present formulation

a model study of the quality of a posteriori error estimators for linear elliptic problems error estimation in the interior of patchwise uniform grids of triangles abstract this paper is the first in a series in which we discuss computational methodologies for checking the quality of a posteriori error estimators for finite element approximations of linear elliptic problems in this first part we study the asymptotic properties of error estimators in the interior of patchwise uniform grids of triangles a completely numerical methodology for the analysis of the quality of estimators is presented results from the application of the methodology to the study of the quality of several well known error estimators are reported in subsequent papers we shall discuss methods to study the properties of estimators for meshes of quadrilaterals non uniform grids at boundaries grid interfaces and near singular points

on an h type mesh refinement strategy based on minimization of interpolation errors abstract an adaptive finite element method is proposed which involves an automatic mesh refinement in areas of the mesh where local errors are determined to exceed a pre assigned limit the estimation of local errors is based on interpolation error bounds and extraction formulas for highly accurate estimates of second derivatives applications to several two dimensional model problems are discussed the results indicate that the method can be very effective for both regular problems and problems with strong singularities

error indicators for adaptive mesh refinement in the boundary element method a new approach in this paper a new approach to the development of a posteriori error indicators for the direct boundary element method bem is presented it takes advantage of a unique opportunity offered by the collocation bem that is the possibility of obtaining more than one numerical solution from a given boundary element mesh unlike other approaches the error indicator introduced in the present paper does not require any explicit evaluation of the residual of the approximate solution in order to test the capability of the proposed error indicators to actually control a selective mesh refinement process an h adaptive refinement strategy is also described together with the criteria for refinement and for the termination of the adaptive process full details on the whole numerical implementation for two dimensional problems are provided in particular there is described a direct method for the numerical evaluation of cauchy principal value integrals numerical examples show that pointwise convergence is always obtained in a few steps and the final meshes look nearly as if they were designed by an expert analyst

goal oriented r adaptivity based on variational arguments in the physical and material spaces abstract the error in a local quantity of interest depends on the error in the corresponding dual solution or generalized green s function this fact is used in dual weighted based goal oriented error estimation techniques and h or p adaptive algorithms this contribution is concerned with a novel approach for goal oriented r adaptivity based on energy minimization principles for the primal and the dual problems the minimization of the energy of the primal problem as well as the minimization of the energy of the dual problem with respect to a design function lead to the primal and dual material residuals respectively these residuals are error indicators for the discretization error on the current mesh we propose a goal oriented mesh optimization algorithm which ends in an optimized mesh with respect to a chosen quantity of interest by means of selected computational examples we demonstrate the capability of the proposed framework

on optimal triangular meshes for minimizing the gradient error construction of optimal triangular meshes for controlling the errors in gradient estimation for piecewise linear interpolation of data functions in the plane is discussed using an appropriate linear coordinate transformation rigorously optimal meshes for controlling the error in quadratic data functions are constructed it is shown that the transformation can be generated as a curvilinear coordinate transformation for anyc data function with nonsingular hessian matrix using this transformation a construction of nearly optimal meshes for general data functions is described and the error equilibration properties of these meshes discussed in particular it is shown that equilibration of errors is not a sufficient condition for optimality a comparison of meshes generated under several different criteria is made and their equilibrating properties illustrated

multi level finite element solution algorithms based on multiplicative and additive correction procedures owing to the failure of the finite element analyst to employ a properly refined computational model the accuracy of preliminary finite element computations is often low thus it is useful to introduce a computational procedure for improving the results obtained from a preliminary finite element solution such a procedure is presented in this paper in this procedure the solution error components are decomposed into two parts one of the error components is assumed to have a long period variation the other component is assumed to have a short period variation multiplicative and additive correction procedures are introduced to iteratively eliminate the two error components the multiplicative and additive correction procedures are implemented using multi level solution techniques

liouvillian integration and bernoulli foliations analytic foliations in the 2 dimensional complex projective space with algebraic invariant curves are studied when the holonomy groups of these curves are solvable it is shown that such a condition leads to the existence of a liouville type first integral and under generic extra conditions it is proven that these foliations can be defined by bernoulli equations

an exact solution for free vibration of cross ply laminated composite cylindrical shells with elastic restraint ends abstract in this paper a new exact solution based on the classical shell theory cst for free vibration of cross ply laminated composite cylindrical shells with elastic restraint ends is proposed the present exact solution can be summed up in the following steps firstly the displacement functions are constructed by the governing differential equations with the exact closed form solutions then the artificial spring technology is introduced to simulate the general boundary conditions of the two end edges of shell thirdly the equation for natural frequencies is obtained by means of the method of reverberation ray matrix mrrm lastly the vibration results are presented by the modified golden section search mgss algorithm by comparing the present method with published papers the accuracy of present method is verified on the basis of that some new exact nature frequencies and mode shapes of the cross ply laminated composite cylindrical shells with various classical boundary conditions and elastic restraints are performed and they can be served as the benchmark data for the future

an adaptive finite element method for linear elliptic problems on propose une methode adaptative d elements finis basee sur une estimation d erreur optimale de norme maxima pour les problemes elliptiques lineaires