a stabilized conforming nodal integration for galerkin mesh free methods domain integration by gauss quadrature in the galerkin mesh free methods adds considerable complexity to solution procedures direct nodal integration on the other hand leads to a numerical instability due to under integration and vanishing derivatives of shape functions at the nodes a strain smoothing stabilization for nodal integration is proposed to eliminate spatial instability in nodal integration for convergence an integration constraint ic is introduced as a necessary condition for a linear exactness in the mesh free galerkin approximation the gradient matrix of strain smoothing is shown to satisfy ic using a divergence theorem no numerical control parameter is involved in the proposed strain smoothing stabilization the numerical results show that the accuracy and convergent rates in the mesh free method with a direct nodal integration are improved considerably by the proposed stabilized conforming nodal integration method it is also demonstrated that the gauss integration method fails to meet ic in mesh free discretization for this reason the proposed method provides even better accuracy than gauss integration for galerkin mesh free method as presented in several numerical examples copyright 2001 john wiley sons ltd

3d structure recovery and unwarping of surfaces applicable to planes the deformation of applicable surfaces such as sheets of paper satisfies the differential geometric constraints of isometry lengths and areas are conserved and vanishing gaussian curvature we show that these constraints lead to a closed set of equations that allow recovery of the full geometric structure from a single image of the surface and knowledge of its undeformed shape we show that these partial differential equations can be reduced to the hopf equation that arises in non linear wave propagation and deformations of the paper can be interpreted in terms of the characteristics of this equation a new exact integration of these equations is developed that relates the 3 d structure of the applicable surface to an image the solution is tested by comparison with particular exact solutions we present results for both the forward and the inverse 3d structure recovery problem

reduced integration at superconvergent points in isogeometric analysis abstract we propose a new reduced integration rule for isogeometric analysis iga based on the concept of variational collocation it has been recently shown that if a discrete space is constructed by smooth and pointwise non negative basis functions there exists a set of points named cauchy galerkin cg points such that collocation performed at these points can reproduce the galerkin solution of various boundary value problems exactly since cg points are not known a priori estimates are necessary in practice and can be found based on superconvergence theory in this contribution we explore the use of estimated cg points i e superconvergent points as numerical quadrature points to obtain an efficient and stable reduced quadrature rule in iga we use the weighted residual formulation as basis for our new quadrature rule so that the proposed approach can be considered intermediate between the standard accurately integrated galerkin variational formulation and the direct evaluation of the strong form in collocation approaches the performance of the method is demonstrated by several examples for odd degrees of discretization we obtain spatial convergence rates and accuracy very close to those of accurately integrated standard galerkin with a quadrature rule of two points per parametric direction independently of the degree

nonlinear fourth order elliptic equations with nonlocal boundary conditions this paper is concerned with a class of fourth order nonlinear elliptic equations with nonlocal boundary conditions including a multi point boundary condition in a bounded domain of rn also considered is a second order elliptic equation with nonlocal boundary condition and the usual multi point boundary problem in ordinary differential equations the aim of the paper is to show the existence of maximal and minimal solutions the uniqueness of a positive solution and the method of construction for these solutions our approach to the above problems is by the method of upper and lower solutions and its associated monotone iterations the monotone iterative schemes can be developed into computational algorithms for numerical solutions of the problem by either the finite difference method or the finite element method

sign changing solutions for some fourth order nonlinear elliptic problems in this paper we consider the existence and multiplicity of sign changing solutions for some fourth order nonlinear elliptic problems and some existence and multiple are obtained the weak solutions are sought by means of sign changing critical theorems

a quadrature based superconvergent isogeometric frequency analysis with macro integration cells and quadratic splines abstract a quadrature based superconvergent isogeometric method is presented for efficient frequency analysis with macro integration cells and quadratic splines the present development particularly refers to the isogeometric analysis of scalar wave equations the single element two element and three element macro integration cells are proposed to develop a set of explicit superconvergent quadrature rules with a 6th order frequency accuracy in contrast to the 4th order frequency accuracy associated with the standard isogeometric formulation with consistent mass matrix the 1d quadrature rules with various macro integration cells are derived from the condition of exact integration of the higher order mass matrix as well as the stiffness matrix consequently 3 point 5 point and 7 point quadrature rules with identical precision are established for the single element two element and three element macro integration cells respectively by construction these quadrature rules exactly recover the isogeometric higher order mass matrix formulation with frequency superconvergence in 1d case the 2d and 3d superconvergent quadrature rules with versatile integration cells are directly constructed through the tensor product formulation of the 1d integration algorithms it is shown that the multidimensional isogeometric analysis employing the proposed quadrature rules for both mass and stiffness matrices does produce the frequency superconvergence simultaneously without the wave propagation direction dependence problem which needs special treatments for the multidimensional higher order mass matrix formulation the proposed approach is featured by its simplicity for numerical implementation and efficiency using macro integration cells numerical examples confirm the efficacy of the present methodology

optimal order isogeometric collocation at galerkin superconvergent points abstract in this paper we investigate numerically the order of convergence of an isogeometric collocation method that builds upon the least squares collocation method presented in anitescu et al 2015 and the variational collocation method presented in gomez and de lorenzis 2016 the focus is on smoothest b splines nurbs approximations i e having global c p 1 continuity for polynomial degree p within the framework of gomez and de lorenzis 2016 we select as collocation points a subset of those considered in anitescu et al 2015 which are related to the galerkin superconvergence theory with our choice that features local symmetry of the collocation stencil we improve the convergence behavior with respect to gomez and de lorenzis 2016 achieving optimal l 2 convergence for odd degree b splines nurbs approximations the same optimal order of convergence is seen in anitescu et al 2015 where however a least squares formulation is adopted further careful study is needed since the robustness of the method and its mathematical foundation are still unclear

optimal and reduced quadrature rules for tensor product and hierarchically refined splines in isogeometric analysis abstract we continue the study initiated in hughes et al 2010 in search of optimal quadrature rules for tensor product and hierarchically refined splines in isogeometric analysis these rules are optimal in the sense that there exists no other quadrature rule that can exactly integrate the elements of the given spline space with fewer quadrature points we extend the algorithm presented in hughes et al 2010 with an improved starting guess which combined with arbitrary precision arithmetic results in the practical computation of quadrature rules for univariate non uniform splines up to any precision explicit constructions are provided in sixteen digits of accuracy for some of the most commonly used uniform spline spaces defined by open knot vectors we study the efficacy of the proposed rules in the context of full and reduced quadrature applied to two and three dimensional diffusion reaction problems using tensor product and hierarchically refined splines and prove a theorem rigorously establishing the stability and accuracy of the reduced rules

computable upper and lower bounds on eigenfrequencies this paper is a revisit of the work ladeveze and pelle int j numer methods engrg 28 1989 where the goal here is to acquire guaranteed accurate and computable bounds of eigenfrequencies through post processing of conventional finite element results to this end a new theoretical quotient is introduced and thereafter a practical way to deal with the new quotient is developed where the constitutive relation error estimation featured with guaranteed bounding property acts as a key role academic numerical examples are performed to check the accuracy of the bounds

composition of a dewarped and enhanced document image from two view images in this paper we propose an algorithm to compose a geometrically dewarped and visually enhanced image from two document images taken by a digital camera at different angles unlike the conventional works that require special equipments or assumptions on the contents of books or complicated image acquisition steps we estimate the unfolded book or document surface from the corresponding points between two images for this purpose the surface and camera matrices are estimated using structure reconstruction 3 d projection analysis and random sample consensus based curve fitting with the cylindrical surface model because we do not need any assumption on the contents of books the proposed method can be applied not only to optical character recognition ocr but also to the high quality digitization of pictures in documents in addition to the dewarping for a structurally better image image mosaic is also performed for further improving the visual quality by finding better parts of images with less out of focus blur and or without specular reflections from either of views we compose a better image by stitching and blending them these processes are formulated as energy minimization problems that can be solved using a graph cut method experiments on many kinds of book or document images show that the proposed algorithm robustly works and yields visually pleasing results also the ocr rate of the resulting image is comparable to that of document images from a flatbed scanner

duality and unified analysis of discrete approximations in structural dynamics and wave propagation comparison of p method finite elements with k method nurbs we study the discretization behavior of classical finite element and nurbs approximations on problems of structural vibrations and wave propagation we find that on the basis of equal numbers of degrees of freedom and bandwidth nurbs have superior approximation properties in fact we observe that the high mode behavior of classical finite elements is divergent with the order of approximation a surprisingly negative result on the other hand nurbs offer almost spectral approximation properties and all modes converge with increasing order of approximation

reduced bezier element quadrature rules for quadratic and cubic splines in isogeometric analysis abstract we explore the use of various element based reduced quadrature strategies for bivariate and trivariate quadratic and cubic spline elements used in isogeometric analysis the rules studied encompass tensor product gauss and gauss lobatto rules and certain so called monomial rules that do no possess a tensor product structure the objective of the study is to determine quadrature strategies which enjoy the same accuracy and stability behavior as full gauss quadrature but with significantly fewer quadrature points several cases emerge that satisfy this objective and also demonstrate superior efficiency compared with standard c 0 continuous finite elements of the same order

geometric information criterion for model selection in building a 3 d model of the environment from image and sensor data one must fit to the data an appropriate class of models which can be regarded as a parametrized manifold or geometric model defined in the data space in this paper we present a statistical framework for detecting degeneracies of a geometric model by evaluating its predictive capability in terms of the expected residual and derive the geometric aic we show that it allows us to detect singularities in a structure from motion analysis without introducing any empirically adjustable thresholds we illustrate our approach by simulation examples we also discuss the application potential of this theory for a wide range of computer vision and robotics problems

stochastic isogeometric analysis of free vibration of functionally graded plates considering material randomness abstract the paper is to develop stochastic isogeometric analysis for the free vibration of functionally graded plates with spatially varying random material properties the isogeometric analysis method is employed in the new stochastic analysis scheme which is called stochastic isogeometric analysis siga the elastic modulus and mass density are modeled as homogeneous gaussian random fields along the plane of structure the governing equation of stochastic isogeometric analysis for free vibration of functionally graded plates is derived in conjunction with perturbation expansions to predict the first and second moments of eigenvalues in order to verify proposed method the brute force monte carlo simulation is employed the mean variance and cov coefficient of variation predicted by siga and those predicted by monte carlo simulation show good agreement the numerical examples demonstrate that the randomness of material properties affects significantly the structural responses of the functionally graded plates the correlation between elastic modulus and mass density is also observed to have significant effect on the response cov of eigenvalue

geometric and shading correction for images of printed materials using boundary a novel technique that uses boundary interpolation to correct geometric distortion and shading artifacts present in images of printed materials is presented unlike existing techniques our algorithm can simultaneously correct a variety of geometric distortions including skew fold distortion binder curl and combinations of these in addition the same interpolation framework can be used to estimate the intrinsic illumination component of the distorted image to correct shading artifacts we detail our algorithm for geometric and shading correction and demonstrate its usefulness on real world and synthetic data

an isogeometric collocation method using superconvergent points abstract we develop an iga collocation method modified by collocating at points other than the standard greville abscissae the method is related to orthogonal collocation used for solving differential equations and to the superconvergence theory therefore we refer to this method as super collocation iga sc by carefully choosing the collocation points it can be seen that the iga sc converges in the first derivative energy norms at rates similar to that of the galerkin solution this is different from the collocation at greville abscissae iga c where the convergence in energy norm for odd polynomial degrees is typically suboptimal the method is tested on 1d 2d and 3d numerical examples in which it is compared to iga c and galerkin s method iga g the comparison includes a detailed cost vs accuracy analysis which shows an improved efficiency of the proposed method in particular for odd polynomial degrees

modified integration rules for reducing dispersion error in finite element methods abstract this paper describes a simple but effective technique for reducing dispersion errors in finite element solutions of time harmonic wave propagation problems the method involves a simple shift of the integration points to locations away from conventional gauss or gauss lobatto integration points for bilinear rectangular elements such a shift results in fourth order accuracy with respect to dispersion error error in wavelength as opposed to the second order accuracy resulting from conventional integration numerical experiments involving distorted meshes indicate that the method has superior performance in comparison with other dispersion reducing finite elements

dispersion minimizing quadrature rules for c1 quadratic isogeometric analysis abstract we develop quadrature rules for the isogeometric analysis of wave propagation and structural vibrations that minimize the discrete dispersion error of the approximation the rules are optimal in the sense that they only require two quadrature points per element to minimize the dispersion error barto et al 2017 1 and they are equivalent to the optimized blending rules we recently described our approach further simplifies the numerical integration instead of blending two three point standard quadrature rules we construct directly a single two point quadrature rule that reduces the dispersion error to the same order for uniform meshes with periodic boundary conditions also we present a 2 5 point rule for both uniform and non uniform meshes with arbitrary boundary conditions consequently we reduce the computational cost by using the proposed quadrature rules various numerical examples demonstrate the performance of these quadrature rules

new concepts for finite element mass matrix formulations improved finite element formulations are presented for dynamic analysis the improvements are based on modifications of the finite element mass matrix and are of high importance since no additional computational effort is required compared with the necessary effort for the standard consistent mass matrix formulation formulations are presented for the one dimensional bar two dimensional membrane and the pure bending beam element free vibration analysis and forced vibration results are presented employing new mass matrices in general the frequency errors and stress errors are at least three times smaller than the corresponding consistent or lumped mass formulation errors accurate model data can be achieved for all the modes of relatively coarse meshes

studies of refinement and continuity in isogeometric structural analysis we investigate the effects of smoothness of basis functions on solution accuracy within the isogeometric analysis framework we consider two simple one dimensional structural eigenvalue problems and two static shell boundary value problems modeled with trivariate nurbs solids we also develop a local refinement strategy that we utilize in one of the shell analyses we find that increased smoothness that is the k method leads to a significant increase in accuracy for the problems of structural vibrations over the classical c0c0 continuous p method whereas a judicious insertion of c0c0 continuous surfaces about singularities in a mesh otherwise generated by the k method usually outperforms a mesh in which all basis functions attain their maximum level of smoothness we conclude that the potential for the k method is high but smoothness is an issue that is not well understood due to the historical dominance of c0c0 continuous finite elements and therefore further studies are warranted

optimal reduction of numerical dispersion for wave propagation problems part 2 application to 2 d isogeometric elements abstract based on the optimal coefficients of the stencil equation a numerical technique for the reduction of the numerical dispersion error has been suggested new isogeometric elements with the reduced numerical dispersion error for wave propagation problems in the 2 d case have been developed with the suggested approach by the minimization of the order of the dispersion error of the stencil equation the order of the dispersion error is improved from order 2 p the conventional isogeometric elements to order 4 p the isogeometric elements with reduced dispersion where p is the order of the polynomial approximations because all coefficients of the stencil equation are obtained from the minimization procedure the obtained accuracy is maximum possible the corresponding elemental mass and stiffness matrices of the isogeometric elements with reduced dispersion are calculated with help of the optimal coefficients of the stencil equation the analysis of the dispersion error of the isogeometric elements with the lumped mass matrix has also shown that independent of the procedures for the calculation of the lumped mass matrix the second order of the dispersion error cannot be improved with the conventional stiffness matrix however the dispersion error with the lumped mass matrix can be improved from the second order to order 2 p by the modification of the stiffness matrix the numerical examples confirm the computational efficiency of the isogeometric elements with reduced dispersion the numerical results obtained by the new and conventional isogeometric elements may include spurious oscillations due to the dispersion error these oscillations can be quantified and filtered by the two stage time integration technique developed recently the approach developed in the paper can be directly applied to other space discretization techniques with similar stencil equations

superconvergent isogeometric analysis of natural frequencies for elastic continua with quadratic splines abstract a superconvergent isogeometric formulation is presented to accurately analyze the natural frequencies for elastic continua this formulation is realized by a set of superconvergent quadrature rules which are designed for the numerical integration of isogeometric mass and stiffness matrices in order to obtain these quadrature rules a natural frequency error measure for elastic continua is systematically deduced using the quadratic basis functions where the mass and stiffness matrices are formulated by the assumed quadrature rules in contrast to the quadrature based superconvergent isogeometric formulation for the scalar valued wave equations it is shown that herein different quadrature rules are required for the mass and stiffness matrices to achieve the superconvergence of natural frequency computation for the vector valued elastic continuum problems consequently the superconvergent quadrature rules are established through optimizing the natural frequency accuracy it turns out that with these quadrature rules the accuracy of natural frequencies for elastic continua is improved by two orders compared with the standard isogeometric formulation employing the consistent mass matrix meanwhile it is found that the superconvergent quadrature rules involve the wave propagation angle and consequently simplified quadrature rules without the angle dependence are further proposed for straightforward practical applications numerical results reveal the superconvergence of the proposed method regarding the natural frequencies for elastic continua

dispersion optimized quadrature rules for isogeometric analysis modified inner products their dispersion properties and optimally blended schemes abstract this paper introduces optimally blended quadrature rules for isogeometric analysis and analyzes the numerical dispersion of the resulting discretizations to quantify the approximation errors when we modify the inner products we generalize the pythagorean eigenvalue theorem of strang and fix the proposed blended quadrature rules have advantages over alternative integration rules for isogeometric analysis on uniform and non uniform meshes as well as for different polynomial orders and continuity of the basis the optimally blended schemes improve the convergence rate of the method by two orders with respect to the fully integrated galerkin method the proposed technique increases the accuracy and robustness of isogeometric analysis for wave propagation problems

multiple solutions for some fourth order nonlinear elliptic variational inequalities abstract we consider the solvability for fourth order nonlinear elliptic variational inequalities some existence results are given by the variational methods

optimal reduction of numerical dispersion for wave propagation problems part 1 application to 1 d isogeometric elements abstract a numerical technique with the optimal coefficients of the stencil equation has been suggested based on this approach new high order isogeometric elements with the reduced dispersion error have been developed for wave propagation problems in the 1 d case by the modification of the mass and stiffness matrices the order of the dispersion error is improved from order 2 p the conventional elements to order 4 p the new elements where p is the order of the polynomial approximations it was shown that the new approach yields the maximum order of the dispersion error for the stencil equations related to the high order isogeometric elements the analysis of the dispersion error of the high order isogeometric elements with the lumped mass matrix has also shown that independent of the procedures for the calculation of the lumped mass matrix the second order of the dispersion error cannot be improved with the conventional stiffness matrix however the dispersion error for the lumped mass matrix can be improved from the second order to order 2 p by the modification of the stiffness matrix the numerical examples confirm the computational efficiency of the new high order isogeometric elements with reduced dispersion we have also showed that numerical results obtained by the new and conventional high order isogeometric elements may include spurious oscillations due to the dispersion error these oscillations can be quantified and filtered by the two stage time integration technique recently developed in our papers the approach developed in the paper can be directly applied to other space discretization techniques with similar stencil equations

novel higher order mass matrices for isogeometric structural vibration analysis abstract a set of novel higher order mass matrices are presented for isogeometric analysis of structural vibrations using nurbs the proposed method for the construction of higher order mass matrices contains two essential steps firstly based upon the standard consistent mass matrix a special reduced bandwidth mass matrix is designed this reduced bandwidth mass matrix meets the requirement of mass conservation while simultaneously preserves the same order of frequency accuracy as the corresponding consistent mass matrix subsequently a mixed mass matrix is formulated through a linear combination of the reduced bandwidth mass matrix and the consistent mass matrix the desired higher order mass matrix is then deduced from the mixed mass matrix by optimizing the linear combination parameter to achieve the most favorable order of accuracy both quadratic and cubic formulations are discussed in detail and it is shown that with regard to the vibration frequency the proposed higher order mass matrices have 6th and 8th orders of accuracy in contrast to the 4th and 6th orders of accuracy associated with the quadratic and cubic consistent mass matrices a generalization to two dimensional higher order mass matrix is further realized by the tensor product operation on the one dimensional reduced bandwidth and consistent mass matrices a series of benchmark examples congruously demonstrate that the proposed higher order mass matrices are capable of achieving the theoretically derived optimal accuracy orders for structural vibration analysis

existence of nontrivial solutions for fourth order asymptotically linear elliptic equations abstract in this paper we discuss the following fourth order semilinear elliptic problem 2 u c u f x u x u u 0 x where f x t is asymptotically linear with respect to t at infinity is a smooth bounded domain in r n and n 4 in this case f x t does not satisfy the following ambrosetti rabinowitz type condition see ambrosetti and rabinowitz 1973 9 for short which is called the ar condition that is for some 0 and m 0 0 f x t 0 t f x s d s 1 2 f x t t uniformly a e x and t m which is important in applying the mountain pass theorem by a variant version of the mountain pass theorem we obtain the existence of nontrivial solutions to the above problem under suitable assumptions of f x t which generalizes and improves the results in liu and wang 2007 12 and an and liu 2008 13

fast formation of isogeometric galerkin matrices by weighted quadrature abstract in this paper we propose an algorithm for the formation of matrices of isogeometric galerkin methods the algorithm is based on three ideas the first is that we perform the external loop over the rows of the matrix the second is that we calculate the row entries by weighted quadrature the third is that we exploit the local tensor product structure of the basis functions while all ingredients have a fundamental role for computational efficiency the major conceptual change of paradigm with respect to the standard implementation is the idea of using weighted quadrature the test function is incorporated in the integration weight while the trial function the geometry parametrization and the pdes coefficients form the integrand function this approach is very effective in reducing the computational cost while maintaining the optimal order of approximation of the method analysis of the cost is confirmed by numerical testing where we show that for p large enough the time required by the floating point operations is less than the time spent in unavoidable memory operations the sparse matrix allocation and memory write the proposed algorithm allows significant time saving when assembling isogeometric galerkin matrices for all the degrees of the test spline space and paves the way for a use of high degree k refinement in isogeometric analysis

finite element and nurbs approximations of eigenvalue boundary value and initial value problems abstract we study the spectral approximation properties of finite element and nurbs spaces from a global perspective we focus on eigenfunction approximations and discover that the l 2 norm errors for finite element eigenfunctions exhibit pronounced spikes about the transition points between branches of the eigenvalue spectrum this pathology is absent in nurbs approximations by way of the pythagorean eigenvalue error theorem we determine that the squares of the energy norm errors of the eigenfunctions are the sums of the eigenvalue errors and the squares of the l 2 norm eigenfunction errors the spurious behavior of the higher eigenvalues for standard finite elements is well known and therefore inherited by the energy norm errors along with the spikes in the l 2 norm of the eigenfunction errors the eigenvalue pathology is absent for nurbs the implications of these results to the corresponding elliptic boundary value problem and parabolic and hyperbolic initial value problems are discussed

variationally consistent inertia templates for b spline and nurbs based fem inertia scaling and customization abstract in this contribution variationally consistent inertia templates for b spline and nurbs based finite elements are proposed as a unified concept for two different purposes customization of the template allows construction of masses and reciprocal masses with desired properties like higher order accuracy or improved dispersion behavior inertia scaling allows substantial speed up for explicit dynamics by increased critical time steps the derivation of the template is based on a three field parametrized functional as in previous works of the authors group but with modified primary variables namely displacement velocity and mass specific linear momentum the latter allows for mass preservation for non constant density throughout the domain and is therefore an enhancement to the formulation proposed in tkachuk and bischoff 2015 with the focus on b spline and nurbs based finite elements the proposed template provides alternatives to the row sum lumped mass matrix which is only 2nd order accurate independent of the polynomial order earlier proposed algebraically constructed higher order masses from the literature can be reconstructed in the variational setting described here as special instances furthermore higher order reciprocal masses can be constructed from the template they are especially attractive for explicit dynamics as there is no extra expense per time step compared with lumped mass for linear problems for non linear problems only small overhead is expected but this paper focuses on linear problems only and mainly undistorted meshes tuning the method towards inertia scaling a reduction of the maximum eigenfrequency by 25 40 is obtained in the examples herein whereas the accuracy is higher than for lumped or consistent mass

efficient quadrature for nurbs based isogeometric analysis abstract we initiate the study of efficient quadrature rules for nurbs based isogeometric analysis a rule of thumb emerges the half point rule indicating that optimal rules involve a number of points roughly equal to half the number of degrees of freedom or equivalently half the number of basis functions of the space under consideration the half point rule is independent of the polynomial order of the basis efficient rules require taking into account the precise smoothness of basis functions across element boundaries several rules of practical interest are obtained and a numerical procedure for determining efficient rules is presented we compare the cost of quadrature for typical situations arising in structural mechanics and fluid dynamics the new rules represent improvements over those used previously in isogeometric analysis

superconvergent isogeometric free vibration analysis of euler bernoulli beams and kirchhoff plates with new higher order mass matrices abstract a superconvergent isogeometric free vibration analysis is presented for euler bernoulli beams and kirchhoff plates this method is featured by new higher order mass matrices for the 1d euler bernoulli beam problem it is shown that a new higher order mass matrix can be directly established by optimizing a reduced bandwidth mass matrix the reduced bandwidth mass matrix is designed based upon the consistent mass matrix and it contains adjustable parameters to be determined via maximizing the order of accuracy of the vibration frequency as a result 4th and 6th orders of accuracy are observed for the proposed quadratic and cubic higher order mass matrices while their corresponding consistent mass matrices are 2nd and 4th order accurate respectively thus the higher order beam mass matrices have more superior frequency accuracy simultaneously with smaller bandwidth compared with their corresponding consistent mass matrices while for the 2d kirchhoff plate problem in order to compute arbitrary frequency in a superconvergent fashion a mixed mass matrix is formulated through a linear combination of the consistent mass matrix and the reduced bandwidth mass matrix then by introducing the wave propagation angle the higher order plate mass matrix can be rationally derived from the mixed mass matrix it is proved that the optimal combination parameter for higher order mass matrix depends on the wave propagation angle consequently a particular higher order mass matrix can always be set up for a superconvergent computation of arbitrary vibration frequency it is shown that the quadratic and cubic higher order mass matrices possess 4th and 6th orders of accuracy which are two orders higher than those of the consistent plate mass matrices the construction of higher order mass matrices and the analytical results for vibration frequencies are systematically demonstrated by a set of numerical examples

inverse mass matrix via the method of localized lagrange multipliers summary an efficient method for generating the mass matrix inverse of structural dynamic problems is presented which can be tailored to improve the accuracy of target frequency ranges and or wave contents the present method bypasses the use of biorthogonal construction of a kernel inverse mass matrix that requires special procedures for boundary conditions and free edges or surfaces and constructs the free free inverse mass matrix employing the standard fem procedure the various boundary conditions are realized by the the method of localized lagrange multipliers in particular the present paper constructs the kernel inverse matrix by employing the standard fem elemental mass matrices it is shown that the accuracy of the present inverse mass matrix is almost identical to that of a conventional consistent mass matrix or a combination of lumped and consistent mass matrices numerical experiments with the proposed inverse mass matrix are carried out to validate its effectiveness when applied to vibration analysis of bars beams and plain stress problems this article is protected by copyright all rights reserved

stable particle methods based on lagrangian kernels abstract a large deformation particle method based on the krongauz belytschko corrected gradient meshfree method with lagrangian kernels is developed in this form the gradient is corrected by a linear transformation so that linear completeness is satisfied for the test functions shepard functions are used this guarantees that the patch test is met lagrangian kernels are introduced to eliminate spurious distortions of the domain of material stability a mass allocation scheme is developed that captures correct reflection of waves without any explicit application of traction boundary conditions in addition the lagrangian kernel versions of various forms of smooth particle methods sph including the standard forms and the randles libersky modification are presented and studied results are obtained for a variety of problems that compare this method to standard forms of sph the randles libersky correction and large deformation versions of the element free galerkin method

minimization of the discretization error in mass and stiffness formulations by an inverse method this paper is concerned with the formulation of mass and sti ness matrices in the direct approach one uses assumed shape functions to develop the mass and sti ness terms alternatively we may construct the matrices by using an inverse approach the terms are assigned so that the di erence between an analytical model and a numerical discrete one is minimized here we show that more accurate models can be obtained by the latter approach the accuracy of rod beam and plate elements that have been developed by both of the approaches are discussed and an accurate model of a rectangular plate is obtained by using the inverse method the superior performance of the new element compared to other established models is demonstrated for the cases of static and dynamic response of a clamped plate 1998 john wiley sons ltd

a simple algorithm for obtaining nearly optimal quadrature rules for nurbs based isogeometric analysis we develop new quadrature rules for isogeometric analysis based on the solution of a local nonlinear problem a simple and robust algorithm is developed to determine the rules which are exact for important b spline spaces of uniform and geometrically stretched knot spacings we consider both periodic and open knot vector configurations and illustrate the efficiency of the rules on selected boundary value problems we find that the rules are almost optimally efficient but much easier to obtain than optimal rules which require the solution of global nonlinear problems that are often ill posed

metric rectification of curved document images in this paper we propose a metric rectification method to restore an image from a single camera captured document image the core idea is to construct an isometric image mesh by exploiting the geometry of page surface and camera our method uses a general cylindrical surface gcs to model the curved page shape under a few proper assumptions the printed horizontal text lines are shown to be line convergent symmetric this property is then used to constrain the estimation of various model parameters under perspective projection we also introduce a paraperspective projection to approximate the nonlinear perspective projection a set of close form formulas is thus derived for the estimate of gcs directrix and document aspect ratio our method provides a straightforward framework for image metric rectification it is insensitive to camera positions viewing angles and the shapes of document pages to evaluate the proposed method we implemented comprehensive experiments on both synthetic and real captured images the results demonstrate the efficiency of our method we also carried out a comparative experiment on the public cbdar2007 data set the experimental results show that our method outperforms the state of the art methods in terms of ocr accuracy and rectification errors