fourier mode analysis of layers in shallow shell deformations abstract we investigate here the length scales of the boundary or interior layer effects in shell deformation quantitative information on the layers is obtained by considering two simplified shallow shell models corresponding to the classical three field love novozhilov koiter lnk respectively five field reissner naghdi rn shell models we start by analysing the layers as functions of the thickness of the shell while keeping the other geometric parameters fixed having found the four limit fourier modes we complete the analysis investigating systematically the layers length scales under more general assumptions particularly when also the wave parameter is variable scaling properly the energy expressions as indicated by the layer mode analysis shell deformation energies characteristic to shell layers are found these show how the layer is effectively seen by the finite element solver and can be useful in the analysis of numerical locking effects in the fem approximation of shell layers

confidence interval construction for proportion difference in small sample paired studies paired dichotomous data may arise in clinical trials such as pre post test comparison studies and equivalence trials reporting parameter estimates e g odds ratio rate difference and rate ratio along with their associated confidence interval estimates becomes a necessity in many medical journals various asymptotic confidence interval estimators have long been developed for differences in correlated binary proportions nevertheless the performance of these asymptotic methods may have poor coverage properties in small samples in this article we investigate several alternative confidence interval estimators for the difference between binomial proportions based on small sample paired data specifically we consider exact and approximate unconditional confidence intervals for rate difference via inverting a score test the exact unconditional confidence interval guarantees the coverage probability and it is recommended if strict control of coverage probability is required however the exact method tends to be overly conservative and computationally demanding our empirical results show that the approximate unconditional score confidence interval estimators based on inverting the score test demonstrate reasonably good coverage properties even in small sample designs and yet they are relatively easy to implement computationally we illustrate the methods using real examples from a pain management study and a cancer study

equivalence test and confidence interval for the difference in proportions for the paired sample design summary this paper considers a model for the di erence of two proportions in a paired or matched design of clinical trials case control studies and also sensitivity comparison studies of two laboratory tests this model includes a parameter indicating both interpatient variability of response probabilities and their correlation under the proposed model we derive a one sided test for equivalence based upon the e cient score equivalence is defined here as not more than 100 per cent inferior mcnemar s test for significance is shown to be a special case of the proposed test further a score based confidence interval for the di erence of two proportions is derived one of the features of these methods is applicability to the 2 2 table with o diagonal zero cells all the mcnemar type tests and confidence intervals published so far cannot apply to such data a monte carlo simulation study shows that the proposed test has empirical significance levels closer to the nominal a level than the other tests recently proposed and further that the proposed confidence interval has better empirical coverage probability than those of the four published methods 1998 john wiley sons ltd

coupling of two and three dimensional composite shell elements in linear and non linear applications abstract a numerical model for the non linear analysis of laminates is presented the developed element is based on piecewise polynomial interpolation in thickness direction although the total number of degrees of freedom is comparable to a discretization with 3d brick elements this approach provides several advantages e g a simple mesh generation due to a 2d type data structure and a better bending behavior the developed isoparametric quadrilateral finite element allows prediction of the complete stress state furthermore a transition element is presented which is used to couple the developed element with 5 parameter shell elements several linear and non linear examples are presented to illustrate the performance of the developed numerical model

updated lagrangian formulation of a flat triangular element for thin laminated shells an updated lagrangian formulation of a three node flat triangular shell element is presented for geometrically nonlinear analysis of laminated plates and shells the flat shell element is obtained by combining the discrete kirchhoff theory plate bending element and a membrane element that is similar to the allman element but a derivative of the linear strain triangular element results are presented for large rotation static response analysis of a cantilever beam under end moment cylindrical shell under pinching and stretching loads a hemispherical shell under pinching and stretching loads and a ring plate under a line load for dynamic response analysis of a cylindrical panel and for thermal postbuckling analysis of an imperfect square plate and a cylindrical panel to estimate the accuracy of the present formulation in predicting the nonlinear response of large flexible structures static analysis of an apex loaded circular arch is performed the arch is a building block of a large inflatable structure the results are in good agreement with those available in the existing literature and those obtained using the commercial finite element software abaqus demonstrating the accuracy of the present formulation he two most widely adopted approaches in the finite element analysis of shells are use of curved shell elements based on a suitable shell theory and approximation of the curved structure by an assemblage of flat shell elements in which the membranebending coupling is brought about as a result of material anisotropy and transformation of the element stiffness matrices computed in a local coordinate system to the global coordinate system prior to assembly the curved shell elements can be computationally very expensive especially in the case of nonlinear analysis because of the complexity of the formulation and the need to compute the curvature information flat shell elements are more attractive because of their simplicity and the ease with which they can be built from alreadyexisting familiar membrane and plate bending elements though a large number of elements are required to accurately model curved structures the analysis is computational ly less expensive because of extremely simple formulation updated lagrangian formulations have been predominantly used in the flat shell formulations available in the existing literature in an updated lagrangian formulation all of the variables are referred to a known configuration the reference configuration which is updated continuously during the deformation process if the rigid body modes are removed from the total or incremental displacements the resulting deformational translations and rotations are very small and hence a linearized incremental formulation1 can be used in a linearized incremental formulation the stresses are computed using linear strain displacement relations the tangent stiffness matrix contains only the linear stiffness matrix and the initial stress matrix the stiffness matrices resulting from the nonlinear terms in the strain displacement relations are neglected resulting in very economical analysis if the rigid body modes are not removed all nonlinear terms in the strain displacement relations will have to be considered for computing the stresses and the tangent stiffness matrix a three node flat triangular shell element was introduced by argyris et al 2 for nonlinear elastic stability problems this formula

numerical analysis of complex instability behaviour using incremental iterative strategies the paper describes how quasi static conservative instability problems can be analysed in a multi parametric space using generalised path following procedures for augmented equilibrium problems

nonlinear free vibrations of composite plates abstract the evolution of the natural mode method nmm for finite element analysis of complex composite structures continues in the present study by applying its principles and formulating the kinematically consistent matrix of a model three node multilayered triangular element both translational and rotational inertia are included in the mass matrix which is conceived using kinematical and geometrical arguments consistent with the assumed natural rigid body and straining modes of the element linear eigenfrequencies are validated with experimental and finite element solutions subsequently the large amplitude nonlinear undamped free vibration of composite plates is investigated a computational scheme is conceived whereby the structure is initially displaced by conducting a full geometrically nonlinear static analysis and subsequently set to transient nonlinear free oscillations by removing the static loading in this regard we discuss the two structured eulerian convective computational schemes employed namely the ariban scheme accumulation of rigid body and natural modes for static nonlinear analysis and the cubic hermitian scheme cuherm for large displacement transient deformation numerical examples demonstrate the efficiency of the formulation and the potential of the natural mode method to deal vigorously with intricate nonlinear time dependent phenomena as well as its potential to provide answers for larger and more complex structures the study also indicates the efficiency and tailoring flexibility offered by advanced composite structural systems

analysis of a bilinear finite element for shallow shells i approximation of inextensional deformations we consider a bilinear reduced strain finite element formulation for a shallow shell model of reissner naghdi type the formulation is closely related to the facet models used in engineering practice we estimate the error of this scheme when approximating an inextensional displacement field we make the strong assumptions that the domain and the finite element mesh are rectangular and that the boundary conditions are periodic and the mesh uniform in one of the coordinate directions we prove then that for sufficiently smooth fields the convergence rate in the energy norm is of optimal order uniformly with respect to the shell thickness in case of elliptic shell geometry the error bound is furthermore quasioptimal whereas in parabolic and hyperbolic geometries slightly enhanced smoothness is required except for the degenerate cases where the characteristic lines are parallel with the mesh lines the error bound is shown to be sharp

an optimal control approach to an inverse nonlinear elastic shell problem applied to car windscreen design a numerical procedure to optimise the sag bending process for car windscreens is proposed in particular a simplified elastic model with geometric nonlinearities is considered the optimisation approach is based on the numerical resolution of an optimal control problem in nonlinear elasticity the objective of the optimisation is to match a desired shape by controlling the temperature distribution and minimising a quadratic functional also we define and analyse the finite element approximation of the optimality system and a gradient method for the solution of the resulting discrete variational inequality finally numerical experiments for the simulation of the simplified model are discussed

singularities in shell theory anisotropic error estimates and numerical simulations in this paper we show the efficiency of anisotropic adaptive meshes in the computation of very thin shell problems including boundary and internal layers phenomena in a first part we present general results concerning the structure of the singularities appearing inside these layers which depends on the geometrical nature of the shell then we establish error estimates which reveal the performance and the efficiency of using anisotropic and adapted meshes inside the layers finally we present numerical computations using an adaptive and anisotropic mesh procedure the chosen examples for drastically different geometries exhibit the variety of situations that can be encountered and show the efficiency of anisotropic adaptive meshes for this kind of problems

locking and boundary layer in hierarchical models for thin elastic structures in the analysis of plate and shell like structures using the finite element method we may encounter difficulties owing to locking and boundary layer effects which lead to numerical simulations with a large error there have been considerable advances in finding out the causes and remedies of locking however a posteriori detection of this phenomenon in the numerical results without comparing with other reference data is another issue with a great importance here one simple but reliable detection method is introduced on the other hand boundary layer is a non smooth singular part in the solution of the singularly perturbed boundary value problems and restricted within very thin region in the neighborhood of boundaries if this rapidly varying behavior could not have been captured enough approximated solution greatly deviates from the exact solution in this study a guideline for the optimal mesh design is provided together with mathematical analysis of this effect

application of an automatic hp adaptive finite element method for thin walled structures the paper investigates the possibility of solving beam and thin walled structures with an automatic hp adaptive finite element method for three dimensional linear elasticity this technique generates sequences of meshes with nonuniform distribution of element sizes h and their spectral orders p to minimize the interpolation error for the hypothetical exact solution with constant number of degrees of freedom the intent of using hp method for beam and thin walled structures is that it should automatically create fe meshes with adequate distribution of the approximation orders to prevent the numerical locking phenomenon and to provide accurate solutions the method also reduces the human work spent on building the numerical model to generation of the description of the geometry we discuss energy based and goal oriented versions of hp adaptivity the paper presents a broad spectrum of examples of engineering applications

on the membrane locking of h p finite elements in a cylindrical shell problem we study the performance of high order h p finite clement schemes in approximating the nearly inexlensional deformation state of a thin cylindrical shell roof with both ends free severe locking is demonstrated for both quadratic and cubic elements and even for higher order if the grid is not aligned with the axis of the cylinder carefully designed selective reduced integration is shown to improve the accuracy of the finite element approximation at low and moderately high orders however so far this technique seems to work well only on aligned grids

nonlinear dynamic analysis of shells with the triangular element tric abstract tric is a facet triangular shell element which is based on the natural mode method it has been shown that the tric shell element satisfies the individual element test and in the framework of the nonconsistent formulation the convergence requirements are fulfilled while it has been proved to be very efficient in linear and nonlinear static problems moreover another major advantage in the formulation of this element is the incorporation of the transverse shear deformations in a way that defies the shear locking phenomenon in this work the derivation of the consistent and lumped mass matrices of the tric element is presented so that it can be used in linear and nonlinear dynamic problems both translational and rotational inertia are included in the consistent mass matrix which is conceived using kinematical and geometrical arguments consistent with the assumed natural rigid body and straining modes of the element all the kinematical and geometrical arguments that are invoked for the derivation of the consistent mass matrix are briefly presented moreover two formulations of the lumped mass matrix of tric are derived the first formulation is based entirely on geometrical considerations whereas the second is based on lumping the consistent mass matrix of tric finally the element s robustness and accuracy will be shown by applying it to properly selected benchmark examples of nonlinear shell dynamics while its computational efficiency will be demonstrated by comparing the cpu performance of the element with the other available shell elements

a reduced constaint hp finite element method for shell problems we propose and analyze an hp finite element method for the nagdhi shell model based on rectangular elements we show that for the bending dominated case assuming sufficient smoothness on the solution the method is locking free in terms of both h and p as the thickness of the shell tends to zero our results are established under the assumption that the geometrical coefficients appearing in the model are piecewise polynomial functions

asymptotic analysis of linearly elastic shells iii justification of koiter s shell equations we consider as in part i a family of linearly elastic shells of thickness 2 all having the same middle surfaces r3 where r2 is a bounded and connected open set with a lipschitz continuous boundary and l3 r3 the shells are clamped on a portion of their lateral face whose middle line is 0 where 0 is any portion of withlength 0 0 we make an essential geometrical assumption on the middle surfaces and on the set 0 which states that the space of inextensional displacements begin gathered v f omega eta eta i in h 1 omega times h 1 omega times h 2 omega hfill eta i partial v eta 3 0 on gamma 0 gamma alpha beta eta 0 in omega hfill end gathered where gamma alpha beta are the components of the linearized change is metric tensor ofs contains non zero functions this assumption is satisfied in particular ifs is a portion of cylinder and 0 is contained in a generatrix ofs

a locking free finite element method for naghdi shells abstract in this paper a locking free method using mixed finite elements is introduced to approximate the solution of naghdi shell problems with small parameter t the thickness of the shell the approach of arnold and brezzi 1997 is employed with some important changes instead of proving the discrete inf sup condition for arbitrary geometric coefficients which does not seem possible we prove a weaker stability condition for smooth enough geometrically dependent coefficients which is sufficient for deducing the optimal error estimate as long as h 2 t is uniformly bounded for extremely small t we can relax this condition either using a larger bubble space or stabilizing the problem by replacing t2 by t2 h4 in either case an optimal error estimate still holds

a priori error estimations of hp finite element approximations for hierarchical models of plate and shell like structures a priori error estimates of hp finite element approximations for hierarchical models of the thin elastic plate and shell like structures are derived the error in the approximations of a hierarchical model consists of the modelling error due to assumptions on displacement or stress fields and the finite element approximation error of discretizations of such a model also non uniformity with respect to the thickness owing to numerical locking is included in the present error estimates numerical results are given supporting the theoretical results

the optimal convergence rate of the p version of the finite element method optimal error estimates for the p version of the finite element method in two dimensions are proven for the case when u in h k omega or u has singularities induced by the corners of the domain the case of nonhomogenous essential boundary conditions is also analyzed

mixed interpolated elements for reissner mindlin plates dcpartement de mathtmatiyue l nit ersitt 1 aral quthec canado summary we present in this paper a procedure to establish reissner mindlin plate bending elements the procedure is based on the idea to combine known resuits on the approximation of stokes problems with known results on the approximation of elliptic problems the proposed elements satisfy the mathematical conditions of stability and convergence and some of them promise to provide efficient elements for practical solutions

shell deformation states and the finite element method a benchmark study of cylindrical shells abstract we demonstrate some of the basic mathematical characteristics of shell deformation states and shell models from the point of view of finite element approximation as benchmark cases we analyze in detail three simple cylindrical shell problems these problems are seemingly similar but turn out to be quite different we 1 compute the exact displacement and strain fields in the model problems both numerically and symbolically using two variants of classical shell models 2 for comparison compute numerically the displacements and strains corresponding to certain higher order dimension reduction models derived from the energy principle 3 demonstrate the dissimilarity of the three benchmark problems as to their asymptotic behaviour in the limit of zero thickness and 4 show both theoretically and experimentally how this diversity is reflected in the accuracy of standard finite element approximations of both low and high order

thermomechanical response of solids at high strains natural approach abstract the paper develops in pursuance of 4 the theoretical framework appertaining to coupled thermomechanical deformations of solids subject to large as well as inelastic deformations the essential feature of the analysis is a consistent natural formulation which encompasses also all thermodynamic aspects on the other hand it must be admitted that current concepts on mechanical constitutive assumptions 5 6 are not sufficiently sophisticated to permit a precise generalisation for the purpose of incorporating thermomechanical effects and delivering a fully compatible theory of the coupled problem uniqueness and bifurcation of the solutions as well as stable postcritical deformation paths are also considered in this account furthermore algorithms for the solution of the nonlinear algebraic equations representing the discretised problem and in particular quasi newton techniques are discussed the paper concludes with a number of applications of technical relevance

scale resolution locking and high order finite element modelling of shells abstract we demonstrate both by theory and experiment the benefits of using standard finite elements of relatively high degree in shell problems the difficulty of shell problems lies in their asymptotic diversity at zero thickness and in the multiple scale character of the deformation field when the thickness is small due to these characteristics standard finite elements of low degree often resolve the length scales of practical shell deformation very poorly unless extremely fine meshes are used however with standard finite elements of sufficiently high degree say cubic or quartic at least the quality of numerical scale resolution improves remarkably we show by simple error analysis that this effect is not problem specific but rather robust among the diversity of shell problems as numerical test cases we analyze two challenging problems in cylindrical shell geometry

locking free finite element methods for shells we propose a new family of finite element methods for the naghdi shell model one method associated with each nonnegative integer k the methods are based on a nonstandard mixed formulation and the kth method employs triangular lagrange finite elements of degree k 2 augmented by bubble functions of degree k 3 for both the displacement and rotation variables and discontinuous piecewise polynomials of degree k for the shear and membrane stresses this method can be implemented in terms of the displacement and rotation variables alone as the minimization of an altered energy functional over the space mentioned the alteration consists of the introduction of a weighted local projection into part but not all of the shear and membrane energy terms of the usual naghdi energy the relative error in the method measured in a norm which combines the h i norm of the displacement and ro tation fields and an appropriate norm of the shear and membrane stress fields converges to zero with order k 1 uniformly with respect to the shell thickness for smooth solutions at least under the assumption that certain geometrical coefficients in the nagdhi model are replaced by piecewise constants

confidence intervals for a difference between proportions based on paired data we construct several explicit asymptotic two sided confidence intervals cis for the difference between two correlated proportions using the method of variance of estimates recovery mover the basic idea is to recover variance estimates required for the proportion difference from the confidence limits for single proportions the ci estimators for a single proportion which are incorporated with the mover include the agresti coull the wilson and the jeffreys cis our simulation results show that the mover type cis based on the continuity corrected coefficient and the tango score ci perform satisfactory in small sample designs and spare data structures we illustrate the proposed cis with several real examples copyright 2009 john wiley sons ltd

semi analytical finite elements in the higher order theory of beams abstract the paper presents semi analytical finite elements leading to the development of a higher order theory for beams an analysis of existing beam theories reveals their semi analytical character the semi analytical finite element sfe method proposed assumes the cross section of a solid beam to be an assemblage of certain semi analytical elements the sfe method is based on independent approximations of three dimensional fields of displacements and stresses the method reflects the multi level nature of beams where conventional finite elements are transferred to the level of beam equations for heuristic considerations a mathematical formulation of the linear theory of a solid beam involves the equations of compatibility equilibrium and constitutive relationships i e the elastic law as well as static and kinematic boundary conditions compatibility conditions are derived directly by using finite element approximations while equilibrium equations constitutive equations and boundary conditions may be derived by applying stationarity of a modified hellinger reissner functional this derivation may be also defined by straightforward application of a generalised virtual work formulation the equations of a beam are formulated in terms of generalised variables integral resultants of stresses and strains as well as of nodal displacements the definition of generalised variables is assigned to the nodes of the finite element mesh bending warping and other higher order deformation modes are described automatically finally the set of governing equations includes mixed algebraic differential operators their explicit expressions depend on one of the element types isoparametric subparametric or superparametric the versatility of sfe is demonstrated in practical applications involving well known solutions the classical euler bernoulli and timoshenko theories are derived using a single one dimensional element the beams with a thin walled cross section are described as an assemblage of semi analytical elements on the basis of a higher order theory the conventional semi analytically based finite elements sabfe are derived their basic relations are also presented some numerical examples of the applications to thin walled beams illustrate the basic features possible extensions of sfe to dynamics geometric non linearity and shells are briefly discussed

confidence intervals for the mean of a variable taking the values 0 1 and 2 the problem of setting a confidence interval for the mean of a variable on 0 1 2 arises in three contexts paired organ procedure rates estimation of gene frequency and three point likert scales an effective approach to its estimation may be based on a good interval for a paired difference of proportions four good methods due to newcombe and tango are shown to have much better performance than more naive methods over regions of the parameter space corresponding to the above applications

unconditional exact tests for equivalence or noninferiority for paired binary endpoints problems of establishing equivalence or noninferiority between two medical diagnostic procedures involve comparisons of the response rates between correlated proportions when the sample size is small the asymptotic tests may not be reliable this article proposes an unconditional exact test procedure to assess equivalence or noninferiority two statistics a sample based test statistic and a restricted maximum likelihood estimation rmle based test statistic to define the rejection region of the exact test are considered we show the p value of the proposed unconditional exact tests can be attained at the boundary point of the null hypothesis assessment of equivalence is often based on a comparison of the confidence limits with the equivalence limits we also derive the unconditional exact confidence intervals on the difference of the two proportion means for the two test statistics a typical data set of comparing two diagnostic procedures is analyzed using the proposed unconditional exact and asymptotic methods the p value from the unconditional exact tests is generally larger than the p value from the asymptotic tests in other words an exact confidence interval is generally wider than the confidence interval obtained from an asymptotic test

spline approximation of thin shell dynamics abstract a spline based method for approximating thin shell dynamics is presented here while the method is developed in the context of the donnell mushtari thin shell equations it can be easily extended to the byrne flugge lur ye equations or other models for shells of revolution as warranted by applications the primary requirements for the method include accuracy flexibility and efficiency in smart material applications to accomplish this the method was designed to be flexible with regard to boundary conditions material nonhomogeneities due to sensors and actuators and inputs from smart material actuators such as piezoceramic patches the accuracy of the method was also of primary concern both to guarantee full resolution of structural dynamics and to facilitate the development of pde based controllers which ultimately require real time implementation several numerical examples provide initial evidence demonstrating the efficacy of the method

adaptive hpq finite element methods of hierarchical models for plate and shell like structures abstract a four step adaptive strategy for hpq finite element approximations of hierarchical models of the thin plate and shell like structures is derived based on a priori and a posteriori error estimations this strategy controls three parameters the model level q the mesh size h and the approximation order p so as to produce quasi optimal hierarchical models and finite element meshes numerical results are given supporting the theoretical results

an analysis of finite element locking in a parameter dependent model problem we consider the bilinear finite element approximation of smooth solutions to a simple parameter dependent elliptic model problem the problem of highly anisotropic heat conduction we show that under favorable circumstances that depend on both the finite element mesh and on the type of boundary conditions the effect of parametric locking of the standard fem can be reduced by a simple variational crime in our analysis we split the error in two orthogonal components the approximation error and the consistency error and obtain different bounds for these separate components also some numerical results are shown

a uniformly accurate finite element method for the reissner mindlin plate a simple finite element method for the reissner mindlin plate model in the prim itive variables is presented and analyzed the method uses nonconforming linear finite elements for the transverse displacement and conforming linear finite elements enriched by bubbles for the rotation with the computation of the element stiffness matrix modified by the inclusion of a simple elementwise averaging it is proved that the method converges with optimal order uniformly with respect to thickness

dual mixed p and hp finite elements for elastic membrane problems a complementary energy based dimensionally reduced plate model using a two field dual mixed variational principle of non symmetric stresses and rotations is derived both the membrane and bending equilibrium equations expressed in terms of non symmetric mid surface stress components are satisfied a priori introducing first order stress functions it is pointed out that i the membrane shear and bending energies of the plate written in terms of first order stress functions are decoupled ii although unmodified 3 d constitutive equations are applied the energy parts do not contain the 1 1 2 term for isotropic linearly elastic materials these facts mean that the finite element formulation based on the present plate model should be free from shear locking when the thickness tends to zero and free from incompressibility locking when the poisson ratio converges to 0 5 irrespective of low order h or higher order p elements are used curvilinear dual mixed hp finite elements with higher order stress approximation and continuous surface tractions are developed and presented for the membrane 2 d elasticity problem in this case the formulation requires the approximation of three independent variables two components of a first order stress function vector and a scalar rotation numerical performance of three quadrilateral dual mixed elements is presented and compared to displacement based hp finite elements when the poisson ratio converges to the incompressible limit of 0 5 the numerical results show that as expected the dual mixed elements developed in this paper are free from locking in the energy norm as well as in the stress computations for both h and p extensions copyright 2001 john wiley sons ltd

a multilayer composite triangular element for steady state conduction convection radiation heat transfer in complex shells abstract our latest study presents the theoretical formulation and computer implementation of a three node six degrees of freedom multilayer flat triangular element intended for the study of the temperature fields in complex multilayer composite shells inherent in the formulation in this first introductory and self consistent systematic study are the three modes of heat transfer namely conduction convection and radiation the latter introducing in our theoretical model strong nonlinear effects in the present discourse all nonlinear terms are strictly due to radiation the material properties are assumed independent of temperature but this in no way restricts the generality of the basic theory the formulation is based on a first order thermal lamination theory which assumes a linear through the thickness temperature variation the following features are uniquely implemented in the computer model 1 1 exact integration of all matrices including the highly nonlinear radiation matrix 2 2 exact integration of all derivative jacobian matrices for efficient nonlinear analysis 3 3 geometrical generality achieved by an arbitrarily oriented inexpensive flat shell element 4 4 compatibility with structural elements 5 5 computational efficiency and simplicity a predictor corrector scheme in the form of the newton raphson method is adopted for the solution of the stead state nonlinear problem numerical examples ranging from simple panels to complex anisotropic shells substantiate the theoretical formulation and show the potential of the present laminated triangular element in the computer simulation of temperature effects in complex geometries

analytical and computational assessment of locking in the hp finite element method locking is the phenomenon by which the numerical approximation of parameter dependent problems deteriorates for values of the parameter close to a limiting value in this paper we give a definition of locking and develop precise computable and analytic ways to quantify it using the example of nearly incompressible elasticity we show by means of computational and theoretical results the difference between the h version and php version in combatting locking our results establish the superiority of high order elements both h p and hp when the standard variational form is used we also discuss other issues such as curved elements mixed methods and locking phenomena for problems over anisotropic materials and over thin domains

improved confidence intervals for the difference between binomial proportions based on paired data by robert g newcombe statistics in medicine 17 2635 2650 1998

explanation and elimination of shear locking and membrane locking with field consistence approach abstract in this paper in the context of beam elements shear locking and membrane locking are explained and cured in a unified way with a field consistence approach in the view of field consistence approach when transverse displacements are coupled with section rotations in euler lagrangian equations and low order interpolations are adopted shear locking will occur similarly when in plane displacements are coupled with section rotations in euler lagrangian equations and low order interpolations are used membrane locking will happen the beam elements derived by field consistence approach are not only free of shear locking and membrane locking but also highly efficient compared with their isoparametric counterparts although theoretically the internal forces generalized strains in mixed variational principles can vary independently they are neither independent to each other nor independent of displacement fields from the point of view of the field consistence approach

the problem of selecting the shape functions for a p type finite element abstract the paper addresses the question of the optimal selection of the shape functions for p type finite elements and discusses the effectivity of the conjugate gradient and multilevel iteration method for solving the corresponding linear system the selection of the shape functions is of major importance for the performance of the solver based on iterative methods neither the theory nor practice of the optimal selection of the shape functions is available yet we have seen that the condensation approach which has obvious advantages from the point of parallel computations is a very effective tool for keeping the condition number under the control and is especially advantageous for the conjugate gradient method

exact one sided confidence limits for the difference between two correlated proportions we construct exact and optimal one sided upper and lower confidence bounds for the difference between two probabilities based on matched binary pairs using well established optimality theory of buehler starting with five different approximate lower and upper limits we adjust them to have coverage probability exactly equal to the desired nominal level and then compare the resulting exact limits by their mean size exact limits based on the signed root likelihood ratio statistic are preferred and recommended for practical use

analysis of the ratio of marginal probabilities in a matched pair setting statistical methods for testing and interval estimation of the ratio of marginal probabilities in the matched pair setting are considered in this paper we are especially interested in the situation where the null value is not one as in one sided equivalence trials we propose a fieller type statistic based on constrained maximum likelihood cml estimation of nuisance parameters for a series of examples the significance level of the cml test is satisfactorily close to the nominal level while a wald type test is anticonservative for reasonable sample sizes we present formulae for approximate power and sample size for the cml and wald tests the matched design is seen to have a clear advantage over the unmatched design in terms of asymptotic efficiency when the two responses of the pair are highly positively correlated we recommend the cml method over the wald method especially for small or moderate sample sizes

the p and hp finite element method for problems on thin domains abstract the p and hp versions of the finite element method allow the user to change the polynomial degree to increase accuracy we survey these methods and show how this flexibility can be exploited to counter four difficulties that occur in the approximation of problems over thin domains such as plates beams and shells these difficulties are 1 control of modeling error 2 approximation of corner singularities 3 resolution of boundary layers and 4 control of locking our guidelines enable the efficient resolution of these difficulties when a p hp code is available

sample size determination for establishing equivalence noninferiority via ratio of two proportions in matched pair design summary in this article we propose approximate sample size formulas for establishing equivalence or noninferiority of two treatments in match pairs design using the ratio of two proportions as the equivalence measure we derive sample size formulas based on a score statistic for two types of analyses hypothesis testing and confidence interval estimation depending on the purpose of a study these formulas can be used to provide a sample size estimate that guarantees a prespecified power of a hypothesis test at a certain significance level or controls the width of a confidence interval with a certain confidence level our empirical results confirm that these score methods are reliable in terms of true size coverage probability and skewness a liver scan detection study is used to illustrate the proposed methods

approximate interval estimation of the ratio of binomial parameters a review and corrections for skewness various methods for finding confidence intervals for the ratio of binomial parameters are reviewed and evaluated numerically it is found that the method based on likelihood scores koopman 1984 biometrics 40 513 517 miettinen and nurminen 1985 statistics in medicine 4 213 226 performs best in achieving the nominal confidence coefficient but it may distribute the tail probabilities quite disparately using general theory of bartlett 1953 biometrika 40 306 317 1955 biometrika 42 201 203 we correct this method for asymptotic skewness following gart 1985 biometrika 72 673 677 we extend this correction to the case of estimating the common ratio in a series of two by two tables computing algorithms are given and applied to numerical examples parallel methods for the odds ratio and the ratio of poisson parameters are noted

the first locking free plane elastic finite element historia mathematica abstract we consider a two parameter family of conforming bilinear quadrilateral finite element formulations for plane elastic problems with homogeneous isotropic material the approach taken earlier by belytschko et al is based on numerical strain reductions and stabilization and may be viewed as an extension reformulation of the classical turner rectangle of 1956 we present the full theory of this approach in the energy norm framework the analysis is based on splitting the error in two orthogonal components the approximation error and the equilibrium or consistency error the theory covers the full parametric dependence of the plane elastic problem emphasizing in particular the case of beam like bodies with arbitrarily small aspect ratios the theory shows that depending on the mesh the stabilized reduced strain formulation is capable of avoiding some or even all the parametric locking effects characteristic to 2d elastic problems we analyze first these locking effects in the context of standard bilinear fem

the problem of membrane locking in finite element analysis of cylindrical shells we analyse the problem of membrane locking in h p finite element models of a thin hemicylindrical shell roof loaded by a smoothly varying normal pressure distribution we show that in the standard finite element method locking occurs especially at low values ofp and when the finite element grid is not aligned with the axis of the cylinder a general strategy of avoiding locking by using modified bilinear forms is introduced and a special implementation of this strategy on aligned rectangular grids is considered

analysis of some low order finite element schemes for mindlin reissner and kirchhoff plates we set up a framework for analyzing mixed finite element methods for the plate problem using a mesh dependent energy norm which applies both to the kirchhoff and to the mindlin reissner formulation of the problem the analysis techniques are applied to some low order finite element schemes where three degrees of freedom are associated to each vertex of a triangulation of the domain the schemes proceed from the mindlin reissner formulation with modified shear energy

linear and geometrically nonlinear bending of isotropic and multilayered composite plates by the natural mode method abstract in the present study we apply the natural mode method and formulate an appropriate linear and geometrically nonlinear theory which is implemented on a model three node multilayered triangular facet element which incorporates the effect of transverse shear deformation and is intended for the nonlinear analysis of large and complex isotropic and composite structures in this context we discuss the derivation of the elastic and geometrical elemental stiffnesses which are based on appropriate kinematic as well as physical idealizations which constitute basic elements of the method of intelligent physical lumping subsequently we present the ariban scheme accumulation of the rigid body and natural modes for geometrically nonlinear analysis it is emphasized that both the triangular facet element and the nonlinear algorithm are developed for the analysis of large and complex structures for which higher order formal finite elements cannot provide answers inexpensivelly in addition the structure of the algorithm and its matrix language are ideally suited for modern parallel computers we conclude our study with numerical examples for isotropic and composite plates all the numerical experiments show the accuracy and potential of the developed methodology for extensive structural engineering computations

a four node plate bending element based on mindlin reissner plate theory and a mixed interpolation this communication discusses a 4 node plate bending element for linear elastic analysis which is obtained as a special case from a general nonlinear continuum mechanics based 4 node shell element formulation the formulation of the plate element is presented and the results of various example solutions are given that yield insight into the predictive capability of the plate and shell element

simple improved confidence intervals for comparing matched proportions for binary matched pairs data this article discusses interval estimation of the difference of probabilities and an odds ratio for comparing success probabilities we present simple improvements of the commonly used wald confidence intervals for these parameters the improvement of the interval for the difference of probabilities is to add two observations to each sample before applying it the improvement for estimating an odds ratio transforms a confidence interval for a single proportion

free vibration analysis of multilayered composite plates and shells with the natural approach abstract natural curved triangular shell element natcop developed in 1 is employed to vibration mode analysis of multilayered composite plates and shells the shells can be either symmetric or unsymmetric the spectral transformation lanczos method with selective or full orthogonalization is used to solve the eigenvalue problem of a pencil k m proper shifting of the eigenvalues is essential for the success of this method certain problems associated with the shift are discussed several numerical examples including symmetric and unsymmetric composite plates and unsymmetric composite conical shells are tested and show that element natcop is also efficient and reliable for free vibration analysis

rotation free bernstein bezier elements for thin plates and shells development and validation abstract a new finite element procedure for thin plates and shells is presented it combines a geometrically non linear rotation free kirchhoff love formulation with triangular and quadrilateral bernstein bezier elements and c 1 and g 1 inter element continuity conditions as well as boundary conditions for clamping and for symmetry the formulation is free from transverse shear locking and relies on a high polynomial degree to mitigate membrane locking bernstein bezier elements are as opposed to nurbs suitable for arbitrary triangulations unlike with hermite elements no stress concentrations occur if the boundary is partially clamped and the formulation can be potentially extended to stiffened plates and shells and to step wise changes of thickness and material properties the convergence behaviour is demonstrated and the computational efficiency is compared with that of c reissner mindlin elements on several numerical examples

analysis of a bilinear finite element for shallow shells ii consistency error we consider a bilinear reduced strain finite element of the mitc family for a shallow reissner naghdi type shell we estimate the consistency error of the element in both membrane and bending dominated states of deformation we prove that in the membrane dominated case under severe assumptions on the domain the finite element mesh and the regularity of the solution an error bound o h t 1h1 s can be obtained if the contribution of transverse shear is neglected here t is the thickness of the shell h the mesh spacing and s a smoothness parameter in the bending dominated case the uniformly optimal bound o h is achievable but requires that membrane and transverse shear strains are of order o t2 as t 0 in this case we also show that under sufficient regularity assumptions the asymptotic consistency error has the bound o h

locking and robustness in the finite element method for circular arch problem in this paper we discuss locking and robustness of the finite element method for a model circular arch problem it is shown that in the primal variable i e the standard displacement formulation the p version is free from locking and uniformly robust with order p k and hence exhibits optimal rate of convergence on the other hand the h version shows locking of order h 2 and is uniformly robust with order h p 2 for p 2 which explains the fact that the quadratic element for some circular arch problems suffers from locking for thin arches in computational experience if mixed method is used both the h version and the p version are free from locking furthermore the mixed method even converges uniformly with an optimal rate for the stress

on locking and robustness in the finite element method a numerical scheme for the approximation of a parameter dependent problem is said to exhibit locking if the accuracy of the approximations deteriorates as the parameter tends to a limiting value a robust numerical scheme for the problem is one that is essentially uniformly convergent for all values of the parameter precise mathematical definitions for these terms are developed their quantitative characterization is given and some general theorems involving locking and robustness are proven a model problem involving heat transfer is analyzed in detail using this mathematical framework and various related computational results are described applications to some different problems involving locking are presented

co rotational flat facet triangular elements for shell instability analyses abstract this paper investigates the formulation of co rotational flat facet triangular elements for the numerical analysis of instability phenomena in shell structures the elements have three nodes with six degrees of freedom at each node the term co rotational relates here to the provision of a local system that continuously rotates and translates with the element following mainly nour omid and rankin b nour omid and c c rankin finite rotation analysis and consistent linearization using projectors comput methods appl mech engrg 93 1991 353 384 the definition of an element resorts to a change of variables from the local frame to the global one this is done through the use of a projector matrix which relates the variations of the local displacements to the variations of the global ones by extracting the rigid body modes from the latter the main difference from the original formulation lies in the parameterization of 3d finite rotations in contrast to the paper by nour omid and rankin a parameterization based on the rotational vector is here adopted and thus an additional change of variables has to be performed as a result the rotational variables become additive and the necessity of a special updating procedure is avoided the main feature of the adopted formulation is its independence of the local assumptions used to derive the internal forces and tangent stiffness in local coordinates for a certain class of elements i e elements with the same number of nodes and degrees of freedom the main co rotational framework is the same using this property three types of local formulations are considered a set of carefully chosen test problems is used in order to assess the performances of the three element types

invariant hermitian finite elements for thin kirchhoff rods i the linear plane case abstract the objective of this work is to develop finite elements for the simulation of thin kirchhoff rods that is rods where the influence of transverse shear strain can be neglected leading to governing equations that require c 1 continuous finite element interpolations we start in this paper with the formulation of new finite elements for the infinitesimal plane deformations of otherwise generally curved rods addressing in particular the lack of invariance observed in related traditional treatments of plane arches by non invariance we mean that the classical rigid body modes of translations and infinitesimal rotations of the underlying structural theory lead to non zero strains in the element an effect sometimes referred to as self straining this phenomenon occurs in curved configurations of the elements and in the infinitesimal setting of interest in this paper it results in the elements stiffness matrix not to exhibit the correct zero energy modes associated with these physical rigid body motions as a consequence the basic equilibrium relations of balance of forces and moments are not satisfied for the associated nodal forces and moments in non invariant finite elements in this context we propose a new framework for the formulation of c 1 continuous finite elements based on hermitian shape functions that do lead to the satisfaction of this fundamental invariance property accounting fully for the rod s curvature and associated kirchhoff s kinematics in contrast to common straight framework element approximations based on the simplified euler bernoulli beam kinematics the formulation relies crucially on a consistent treatment of the kinematics and the assumed interpolation of the rods geometry an additional assumed strain treatment is considered to avoid limitations of membrane locking complete rigorous analyses and several numerical simulations are presented to prove and illustrate the properties and performance of the newly proposed finite element methods