least squares mixed finite element methods for non selfadjoint elliptic problems i error estimates a least squares mixed finite element method for general second order non selfadjoint elliptic problems in two and three dimensional domains is formulated and analyzed the finite element spaces for the primary solution approximation u h and the flux approximation sigma h consist of piecewise polynomials of degree k and r respectively the method is mildly nonconforming on the boundary the cases k r and k 1 r are studied it is proved that the method is not subject to the lbb condition optimal l 2 and h 1 error estimates are derived for regular finite element partitions numerical experiments confirming the theoretical rates of convergence are presented

a unified theory for formulation of hybrid stress membrane elements a theory is proposed in this paper to explain in a unified manner the three rational approaches using the incompatible displacements u in the hybrid element formulation limited to the plane stress case the theory suggests that the introduction of u is to constrain the total value of the invariant i2 x y of the assumed stresses over the element to zero in the plane stress case this is the well known condition for the stress distributions to be independent of the elastic constants of the material the theory proposed is also used to explain the closeness of the performances of the four 4 node hybrid stress membrane elements 5 i 5 ii 5 a and 5 c that have been developed previously the differences among them are shown to be of the second degree in the distortion measures of the element shape when they are compared on the basis of the non vanishing total value of i2 of their respectively adopted assumed stress field several numerical examples are used to verify and to illustrate the proposed theory

generalized mixed variational principles and solutions of ill conditioned problems in computational mechanics part ii shear locking abstract although the finite element method fem has been extensively applied to various areas of engineering the ill conditioned problems occurring in many situations are still thorny to deal with this study attempts to provide a high performing and simple approach to the solutions of ill conditioned problems the theoretical foundation of it is the parametrized variational principles called the generalized mixed variational principles gmvps initiated by rong in 1981 gmvps can solve many kinds of ill conditioned problems in computational mechanics among them four cases are investigated in detail the volumetric locking the shear locking the inhomogeneousness and the membrane locking problems composing four parts of the study part i part iv respectively this paper is part ii wherein a gmvp specially suited to the reissner plate theory and timoshenko beam theory is constructed providing a mathematical foundation for establishing fem formulations which can automatically unlock the shear locking and produce no spurious zero energy modes

well posedness and numerical performances of the strain gap method a mixed method of approximation is discussed starting from a suitably modified expression of the hu washizu variational principle in which the independent fields are displacements stresses and strain gaps defined as the difference between compatible strains and strain fields the well posedness of the discrete problem is discussed and necessary and sufficient conditions are provided the analysis of the mixed method reveals that the discrete problem can be split into a reduced problem and in a stress recovery accordingly the discrete stress solution is univocally determined once an interpolating stress subspace is chosen the enhanced assumed strain method by simo and rifai is based on an orthogonality condition between stresses and enhanced strains and coincides with the reduced problem it is shown that the mixed method is stable and converges computational issues in the context of the finite element method are discussed in detail and numerical performances and comparisons are carried out copyright 2001 john wiley sons ltd

variable v cycle multigrid preconditioners for the discrete systems from combined hybrid quadrilateral elements abstract combined hybrid element method is an absolutely convergent and stable hybrid element method in which approximation spaces for field variables avoid the restriction of babuska brezzi condition so the spaces can be adopted in a larger range compared with other kinds of mixed hybrid element methods in this paper two variable v cycle multigrid preconditioners are proposed for the algebraic system resulting from combined hybrid quadrilateral element discretization of linear elasticity problem based on two kinds of simple intergrid transfer operators constructed on quadrilateral meshes we prove that the condition numbers of the preconditioned systems are bounded by a constant independent of the mesh size and the number of levels a numerical example is given to indicate the asymptotically optimal performance of the algorithm

an efficient hybrid quadrilateral kirchhoff plate bending element this paper discusses the formulation of a hybrid stress quadrilateral kirchhoff plate bending element based on an extended complementary energy functional first proposed by tong with the inclusion of a lagrange multiplier in the functional to enforce a constraint on the assumed moment space the construction of the c1 deflection profile inside the element is no longer necessary the continuity requirement on the deflection across the element interfaces is fulfilled by interpolating the generalized nodal displacements over the element boundary in the usual way special attention is paid to the selection of assumed moment space such that the element stability convergency invariance and nodal point numbering insensitivity are secured while the implementational cost of the element is kept low quadratic serendipity interpolation of the transverse deflection is adopted to discretize the distributed transverse loading numerical examples are presented and the accuracy achieved is found to be satisfactory

general related inequalities to carlson type inequality for the sugeno integral in this paper the carlson type inequality for the sugeno integral is generalized on an abstract fuzzy measure space x moreover several examples are given to illustrate the validity of main results

stability and convergence of a class of enhanced strain methods a stability and convergence analysis is presented of a recently proposed variational formulation and finite element method for elasticity which incorporates an enhanced strain field the analysis is carried out for problems posed on polygonal domains in r n the finite element meshes of which are generated by affine maps from a master element the formulation incorporates as a special case the classical method of incompatible modes the problem initially has three variables viz displacement stress and enhanced strain but the stress is later eliminated by imposing a condition of orthogonality with respect to the enhanced strains two other conditions on the choice of finite element spaces ensure that the approximations are stable and convergent some features of nearly incompressible and incompressible problems are also investigated for these cases it is possible to argue that locking will not occur and that the only spurious pressures present are the so called checkerboard modes it is shown th

uniform convergence and a posteriori error estimation for assumed stress hybrid finite element methods assumed stress hybrid methods are known to improve the performance of standard displacement based finite elements and are widely used in computational mechanics the methods are based on the hellinger reissner variational principle for the displacement and stress variables this work analyzes two existing 4 node hybrid stress quadrilateral elements due to pian and sumihara t h h pian k sumihara rational approach for assumed stress finite elements int j numer methods engrg 20 9 1984 1685 1695 and due to xie and zhou x p xie t x zhou optimization of stress modes by energy compatibility for 4 node hybrid quadrilaterals int j numer methods engrg 59 2004 293 313 which behave robustly in numerical benchmark tests for the finite elements the isoparametric bilinear interpolation is used for the displacement approximation while different piecewise independent 5 parameter modes are employed for the stress approximation we show that the two schemes are free from poisson locking in the sense that the error bound in the a priori estimate is independent of the relevant lame constant we also establish the equivalence of the methods to two assumed enhanced strain schemes finally we derive reliable and efficient residual based a posteriori error estimators for the stress in l2 norm and the displacement in h1 norm and verify the theoretical results by some numerical experiments

scale space and edge detection using anisotropic diffusion a new definition of scale space is suggested and a class of algorithms used to realize a diffusion process is introduced the diffusion coefficient is chosen to vary spatially in such a way as to encourage intraregion smoothing rather than interregion smoothing it is shown that the no new maxima should be generated at coarse scales property of conventional scale space is preserved as the region boundaries in the approach remain sharp a high quality edge detector which successfully exploits global information is obtained experimental results are shown on a number of images parallel hardware implementations are made feasible because the algorithm involves elementary local operations replicated over the image

new stress assumption for hybrid stress elements and refined four node plane and eight node brick elements a new stress assumption for hybrid stress elements is presented generalized incompatible modes are proposed and incorporated into the constraint equations for assumed stresses the physical meaning of the resulting constraint equations is discussed the present stress assumption which can consider the mesh distortion more rigorously is based on the physical interpretation of the role of the generalized incompatible modes and substantiated with simple mesh distortion measures defined in this paper the stress assumption is adapted to the previous four node hybrid stress element 5 i and the eight node hybrid stress brick element 18 which results in a new four node plane element m5 and an new eight node brick element m18 numerical results show that the refined elements are noticeable in low sensitivity to mesh distortion and in high accuracy of stresses 1997 john wiley sons ltd

on stress interpolation for hybrid models a technique is proposed for the selection of stress interpolations for hybrid models the present paper applies this approach to plane problems the stiffness matrix is derived using the hellinger reissner variational principle this formulation uses infinitesimal equilibrium relationships and divides the assumed stress into its lower order and higher order parts the patch test can be passed and the resulting elements are generally invariant a plane four node quadrilateral element is described and compared with existing elements numerical studies show that the accuracy of the element is generally good

sugeno integral of monotone functions based on lebesgue measure roman flores et al h roman flores a flores franulic y chalco cano the fuzzy integral for monotone functions applied mathematics and computation 185 2007 492 498 gave some optimal upper bounds for the sugeno integral of continuous and strictly monotone functions and provided yong type inequalities for the sugeno integral these results are generalized to monotone functions in this paper two algorithms are given for calculating the sugeno integral of monotone functions based on lebesgue measure several illustrative examples are presented

on the comonotonic property for sugeno integral the so called comonotonic property for sugeno integral is introduced and investigated where 0 2 0 is a binary operation under the assumption that lim b a email protected a and lim a a email protected b we prove that sugeno integral possesses comonotonic property if and only if equals to one of the four operators minimum maximum pf the first projection and pl the last projection we also discuss comonotonic property when this assumption does not hold

the patch test for mixed formulations this paper presents a simple extension of the patch test to mixed formulations to provide the necessary and sufficient conditions for convergence the general algebraic conditions of babuska and brezzi are given a simple form and a conceptual application of the patch tests serves to point out the instability of several well known formulations for incompressible problems the test is also applied to mixed displacement strain formulations of elasticity and limiting formulations are noted

stabilized hybrid finite element methods based on the combination of saddle point principles of elasticity problems how in a discretized model to utilize the duality and complementarity of two saddle point variational principles is considered in the paper a homology family of optimality conditions different from the conventional saddle point conditions of the domain decomposed hellinger reissner principle is derived to enhance stability of hybrid finite element schemes based on this a stabilized hybrid method is presented by associating element interior displacement with an element boundary one in a nonconforming manner in addition energy compatibility of strain enriched displacements with respect to stress terms is introduced to circumvent poisson locking

improved enhanced strain four node element with taylor expansion of the shape functions a class of enhanced strain four node elements with taylor expansion of the shape function derivatives is presented a new concept of enhancement using besides the standard enhanced strain fields also two other enhanced fields is developed on the basis of the hu washizu principle for first order taylor expansion enhanced modes become uncoupled thus only a negligible amount of computing effort for the static condensation of enhanced modes is needed furthermore the formulation permits a symbolic integration which leads to a closed form solution for the element tangent matrix several numerical examples show that the element is stable invariant passes the patch test and yields good results especially in the highly distorted regime 1997 by john wiley sons ltd

an unsymmetric 4 node 8 dof plane membrane element perfectly breaking through macneal s theorem summary among numerous finite element techniques few models can perfectly without any numerical problems break through macneal s theorem any 4 node 8 dof membrane element will either lock in in plane bending or fail to pass a c0 patch test when the element s shape is an isosceles trapezoid in this paper a 4 node plane quadrilateral membrane element is developed following the unsymmetric formulation concept which means two different sets of interpolation functions for displacement fields are simultaneously used the first set employs the shape functions of the traditional 4 node bilinear isoparametric element while the second set adopts a novel composite coordinate interpolation scheme with analytical trail function method in which the cartesian coordinates x y and the second form of quadrilateral area coordinates qacm ii s t are applied together the resulting element us atfq4 exhibits amazing performance in rigorous numerical tests it is insensitive to various serious mesh distortions free of trapezoidal locking and can satisfy both the classical first order patch test and the second order patch test for pure bending furthermore because of usage of the second form of quadrilateral area coordinates qacm ii the new element provides the invariance for the coordinate rotation it seems that the behaviors of the present model are beyond the well known contradiction defined by macneal s theorem copyright 2015 john wiley sons ltd

a consistent approach for mixed stress finite element formulations in linear elastodynamics abstract in this paper a mixed stress formulation for linear elastodynamic analysis based on a modified hellinger reissner functional and a consistent approach for selecting finite element approximations are presented the key idea in this new approach is to choose stress approximations by taking into account for suitable modes to equilibrate inertia forces feasibility and effectiveness of the proposed approach are numerically verified through three benchmark tests

hybrid and enhanced finite element methods for problems of soil consolidation hybrid and enhanced finite element methods with bi linear interpolations for both the solid displacements and the pore fluid pressures are derived based on mixed variational principles for problems of elastic soil consolidation both plane strain and axisymmetric problems are studied it is found that by choosing appropriate interpolation of enhanced strains in the enhanced method and by choosing appropriate interpolations of strains effective stresses and enhanced strains in the hybrid method the oscillations of nodal pore pressures can be eliminated several numerical examples demonstrating the capability and performance of the enhanced and hybrid finite element methods are presented it is also shown that for some situations such as problems involving high poisson s ratio and in other related problems where bending effects are evident the performance of the enhanced and hybrid methods are superior to that of the conventional displacement based method the results from the hybrid method are better than those from the enhanced method for some situations such as problems in which soil permeability is variable or discontinuous within elements since all the element parameters except the nodal displacements and nodal pore pressures are assumed in the element level and can be eliminated by static condensation the implementations of the enhanced method and the hybrid method are basically the same as the conventional displacement based finite element method the present enhanced method and hybrid method can be easily extended to non linear consolidation problems copyright 2006 john wiley sons ltd

consistent tangent operators for rate independent elastoplasticity abstract it is shown that for problems involving rate constitutive equations such as rate independent elastoplasticity the notion of consistency between the tangent stiffness operator and the integration algorithm employed in the solution of the incremental problem plays a crucial role in preserving the quadratic rate of asymptotic convergence of iterative solution schemes based upon newton s method within the framework of closest point projection algorithms a methodology is presented whereby tangent operators consistent with this class of algorithms may be systematically developed to wit associative j 2 flow rules with general nonlinear kinematic and isotropic hardening rules as well as a class of non associative flow rules are considered the resulting iterative solution scheme preserves the asymptotic quadratic convergence characteristic of newton s method whereas use of the socalled elastoplastic tangent in conjunction with a radial return integration algorithm a procedure often employed results in newton type of algorithms with suboptimal rate of convergence application is made to a set of numerical examples which include saturation hardening laws of exponential type

finite element methods of least squares type we consider the application of least squares variational principles to the numerical solution of partial differential equations our main focus is on the development of least squares finite element methods for elliptic boundary value problems arising in fields such as fluid flows linear elasticity and convection diffusion for many of these problems least squares principles offer numerous theoretical and computational advantages in the algorithmic design and implementation of corresponding finite element methods that are not present in standard galerkin discretizations most notably the use of least squares principles leads to symmetric and positive definite algebraic problems and allows us to circumvent stability conditions such as the inf sup condition arising in mixed methods for the stokes and navier stokes equations as a result application of least squares principles has led to the development of robust and efficient finite element methods for a large class of problems of practical importance

a convergence condition for the quadrilateral wilson element the paper deals with the convergence properties of the nonconforming quadrilateral wilson element which violates the patch test the convergence of the element is proved under a certain condition on mesh subdivisions without any modifications of the variational formulation this result extends the range of applicability of wilson s element the necessity of the proposed condition is also discussed

improved four node hellinger reissner elements based on skew coordinates mixed four node elements based on the hellinger reissner hr functional are developed for stress representations in various coordinates including the skew natural and cartesian ones the two field hr functional is used in the classical form and in the incremental form suitable for non linear materials we argue that the skew coordinates not the natural ones should be associated with the natural basis at the element s center if 5 and 7 parameter stress representations are assumed in these coordinates then for a linear elastic case the homogenous equilibrium equations and the stress form of compatibility equation are satisfied point wise two mixed four node elements are developed and tested 1 an assumed stress element hr5 s is developed from the non enhanced hr functional for a 5 parameter representation of stresses formally identical as the one used for example in pian and sumihara int j numer meth engng 1984 20 1685 1695 but in terms of skew coordinates this element is very simple and uses a smaller number of parameters but is equally accurate as the elements by yuan et al int j numer meth engng 1993 36 1747 1763 and by piltner and taylor int j numer meth engng 1995 38 1783 1808 2 an assumed stress enhanced strain element hr9 is developed from the enhanced hr functional for a 7 parameter representation of stress and a 2 parameter enhanced assumed displacement gradient or enhanced assumed strain enhancement various forms of 7 parameter representations appearing in the literature are reviewed and we prove that they are linked by a linear onto transformation the choice of coordinates for the stress and the enhancement turns out to be the crucial factor and four combinations of coordinates for which the element performs the best are identified both elements are based on the green strain and several numerical tests show their good accuracy in particular their robustness to shape distortions for coarse meshes two update schemes for the multipliers of modes and the incremental constitutive procedure accounting for the plane stress condition for non linear materials are tested for large deformation problems copyright 2008 john wiley sons ltd

further discussion on four node isoparametric quadrilateral elements in plane bending the aim of the study is first to show that the finite element method for plane bending is not sensitive to the distorted geometry of isoparametric quadrilateral elements second to close out further investigations on irregular elements based on wilson incompatible functions employing ad hoc methods to force elements to pass the patch test regardless of the type of the variational formulation used for the problem a systematic review of papers dealing with finite four node plane elements with two degrees of freedom at each node is presented selected results of the benchmark example of the mesh distortion test used by all cited authors are compared suggesting that no improvement has been made in more than two decades of intensive development of new elements and methods in the field an attempt has been made to localize the pathological behaviour of irregular elements under consideration by calculating the areas of the elements after deformation for different values of the distortion parameter it made possible to observe the mass density of the whole deformed system the tip deflections at the lower and upper edge at the free end of the cantilever beam were depicted as well illustrating unexpected physical phenomena of the longitudinal fibers deviating from being parallel the horizontal displacement components at two common nodes of the adjacent elements have been compared with the analytical solution of the problem for the varying distortion parameter the resulting horizontal displacement distribution along the common side of the elements has been shown to be the source of unreal behavior of all classes of irregular elements based on wilson incompatible functions increasing the order of the interpolation functions for the displacement field i e application of subparametric elements makes the finite element method insensitive to element distortion copyright 2000 john wiley sons ltd

a return mapping algorithm for plane stress elastoplasticity an unconditionally stable algorithm for plane stress elastoplasticity is developed based upon the notion of elastic predictor return mapping plastic corrector enforcement of the consistency condition is shown to reduce to the solution of a simple nonlinear equation consistent elastoplastic tangent moduli are obtained by exact linearization of the algorithm use of these moduli is essential in order to preserve the asymptotic rate of quadratic convergence of newton methods the accuracy of the algorithm is assessed by means of iso error maps the excellent performance of the algorithm for large time steps is illustrated in numerical experiments

an isostatic assumed stress triangular element for the reissner mindlin plate bending problem the paper describes a new assumed stress triangular element for reissner mindlin plates called tip3 with three nodes and three degrees of freedom per node the kinematics is constructed by means of the so called linked interpolation ruled by technically significant degrees of freedom i e one transversal displacement and two rotations per node without using additional bubble modes the static representation starts from a moment shear uncoupled polynomial approximation and is constrained to satisfy some equilibrium conditions in order to reduce the stress parameters to a minimum number the resulting element is locking free presents correct rank and passes the bending patch test even for very thin plates the good performances of the element are demonstrated by several comparisons with other triangular plate elements available in the literature copyright 2007 john wiley sons ltd

alternative ways for formulation of hybrid stress elements an element stiffness matrix can be derived by the conventional potential energy principle and indirectly also by generalized variational principles such as the hu washizu principle and the hellinger reissner principle the present investigation has the objective to show an approach which is concerned with the formulation of incompatible elements for solid continuum and for plate bending problems by the hellinger reissner principle it is found that the resulting scheme is equivalent to that considered by tong 1982 for the construction of hybrid stress elements in tong s scheme the inversion of a large flexibility matrix can be avoided it is concluded that the introduction of additional internal displacement modes in mixed finite element formulations by the hellinger reissner principle and the hu washizu principle can lead to element stiffness matrices which are equivalent to the assumed stress hybrid method

treatment of internal constraints by mixed finite element methods unification of concepts a general method to generate assumed stress and strain fields within the context of mixed finite element methods is presented the assumed fields are constructed in such a way that internal constraints are satisfied a priori consequently the locking behaviour commonly observed in finite element solutions of problems with internal constraints is avoided to this end the assumed stress and strain fields are constructed to satisfy a priori the homogeneous part of the equilibrium equations thus avoiding fraeijs de veubeke s limitation principle results obtained using the proposed methodology on a nearly incompressible plane strain problem and thin plate application using a shear deformable theory are indicated

the hybrid trefftz finite element model and its application to plate bending this paper presents a new hybrid element approach and applies it to plate bending in contrast to more conventional models the formulation is based on displacement fields which fulfil a priori the non homogeneous lagrange equation trefftz method the interelement continuity is enforced by using a stationary principle together with an independent interelement displacement the final unknowns are the nodal displacements and the elements may be implemented without any difficulty in finite element libraries of standard finite element programs the formulation only calls for integration along the element boundaries which enables arbitrary polygonal or even curve sided elements to be generated where relevant known local solutions in the vicinity of a singularity or stress concentration may be used as an optional expansion basis to obtain for example particular singular corner elements elements presenting circular holes etc thus a high degree of accuracy may be achieved without a troublesome mesh refinement another important advantage of the formulation is the possibility of generating by a single element subroutine a large number of various elements triangles quadrilaterals etc presenting an increasing degree of accuracy the paper summarizes the results of numerical studies and shows the excellent accuracy and efficiency of the new elements the conclusions present some ideas concerning the adaptive version of the new elements extension to nonlinear problems and some other developments

plane isoparametric hybrid stress elements invariance and optimal sampling formulation and applications of the hybrid stress finite element model to plane elasticity problems are examined conditions for invariance of the element stiffness are established for two dimensional problems the results of which are easily extended to three dimensional cases next the hybrid stress functional for a 3 d continuum is manipulated into a more convenient form in which the location of optimal stress strain sampling points can be identified to illustrate these concepts 4 and 8 node plane isoparametric hybrid stress elements which are invariant and of correct rank are developed and compared with existing hybrid stress elements for a 4 node element lack of invariance is shown to lead to spurious zero energy modes under appropriate element rotation alternative 8 node elements are considered and the best invariant element is shown to be one in which the stress compatibility equations are invoked results are also presented which demonstrate the validity of the optimal sampling points the effects of reduced orders of numerical integration and the behaviour of the elements for nearly incompressible materials

use of a tracer specific deep artificial neural net to denoise dynamic pet images application of kinetic modeling km on a voxel level in dynamic pet images frequently suffers from high levels of noise drastically reducing the precision of parametric image analysis in this paper we investigate the use of machine learning and artificial neural networks to denoise dynamic pet images we train a deep denoising autoencoder dae using noisy and noise free spatiotemporal image patches extracted from the simulated images of 11c raclopride a dopamine d2 receptor agonist the dae processed dynamic and corresponding parametric images simulated and acquired are compared with those obtained with conventional denoising techniques including temporal and spatial gaussian smoothing iterative spatiotemporal smoothing deconvolution and the highly constrained backprojection processing hypr the simulated acquired parametric image non uniformity was 7 75 19 49 with temporal and 5 90 14 50 with spatial smoothing 5 82 16 21 with smoothing deconvolution 5 49 13 38 with hypr and 3 52 11 41 with dae the dae also produced the best results in terms of the coefficient of variation of voxel values and structural similarity index denoising induced bias in the regional mean binding potential was 7 8 with temporal and 26 31 with spatial smoothing 28 61 with smoothing deconvolution 27 63 with hypr and 14 8 with dae when the test data did not match the training data erroneous outcomes were obtained our results demonstrate that a deep dae can provide a substantial reduction in the voxel level noise compared with the conventional spatiotemporal denoising methods while introducing a similar or lower amount of bias the better dae performance comes at the cost of lower generality and requiring appropriate training data

towards adaptive mesh refinement application of new rectangular hybrid finite elements in 2d elasticity problems a modified global approach to choosing stress terms for hybrid finite elements in plane stress problems is based on the known requirement of minimum number of stress parameters let n be the number of independent stress parameters nq the number of nodal displacements and nr the number of rigid body degrees of freedom then the satisfaction of the criterion n nq nr of the assembled structure instead of the individual element enables the reduction of n new rectangular hybrid transition elements applied in adaptive mesh refinement and a new eight node rectangular invariant element including only 12 parameters based on the modified criterion are presented here the new elements which are used in order to analyse the stress singularity of two bonded elastic plates of different materials yield reliable results compared with results based on classical hybrid elements displacement elements and the analytic solution

research of combined hybrid method applied in the reissner mindlin plate model this paper has introduced two kinds of combined hybrid variational formulations for plate bending finite elements based upon the reissner mindlin theory according to whether assumed constant moment stress is introduced when assumed constant shear stress has been introduced due to two options for incompatible displacement modes four new types of combined hybrid elements are proposed a set of standard tests for both thin and thick plates show that new elements perform well

accuracy and stability of integration algorithms for elastoplastic constitutive relations an analysis of accuracy and stability of algorithms for the integration of elastoplastic constitutive relations is carried out in this paper reference is made to a very general internal variable formulation of plasticity and to two families of algorithms that generalize the well known trapezoidal and midpoint rules to fit the present context other integration schemes such as the radial return mean normal and closest point procedures are particular cases of this general formulation the meaning of first and second order accuracy in the presence of the plastic consistency condition is examined in detail and the criteria derived are used to identify two second order accurate members of the proposed algorithms a general methodology is also derived whereby the numerical stability properties of integration schemes can be systematically assessed with the aid of this methodology the generalized midpoint rule is seen to have far better stability properties than the generalized trapezoidal rule finally numerical examples are presented that illustrate the performance of the algorithms

general minkowski type inequalities for sugeno integrals minkowski type inequalities for the sugeno integral on abstract spaces are studied in a rather general form thus closing the series of papers on the topic dealing with special cases restricted to the pseudo additive operation

a rational approach for choosing stress terms for hybrid finite element formulations a new approach for choosing the stress terms for hybrid stress elements is based on the condition of vanishing of the virtual work along the element boundary due to the stress terms higher than constant and the additional incompatible displacements examples using 4 node plane stress elements have shown that when the incompatible displacements also satisfy the constant strain patch test the resulting element will provide the most accurate solutions

improving the accuracy of xfem crack tip fields using higher order quadrature and statically admissible stress recovery this study is concerned with improving the accuracy of crack tip fields obtained using the extended generalized finite element method xfem first the numerical integration of the element stiffness matrices which guarantees convergence with quadrature of not only the regular nodal displacements but also additional degrees of freedom corresponding to the enrichment functions is studied as the accuracy of the stresses obtained by direct differentiation of the converged with quadrature regular nodal displacements and of the coefficients corresponding to enrichment functions is still not satisfactory a statically admissible stress recovery sar scheme is introduced sar uses basis functions which meet the equilibrium equations within the domain and the local traction conditions on the boundary and moving least squares mls to fit the stresses at sampling points e g quadrature points obtained by the xfem important parameters controlling the accuracy of crack tip fields using the xfem and sar namely the order of quadrature the number of retained terms in the crack tip asymptotic field the number of enriched layers and use of arbitrary branch functions a proper choice of the sampling points in the enriched element and the size of the domain of influence doi of mls are investigated copyright 2005 john wiley sons ltd

a finite strain solid shell using local lowdin frames and least squares strains abstract a finite strain solid shell element is proposed it is based on least squares in plane assumed strains assumed natural transverse shear and normal strains the singular value decomposition svd is used to define local integration point orthogonal frames of reference solely from the jacobian matrix the complete finite strain formulation is derived and tested assumed strains obtained from least squares fitting are an alternative to the enhanced assumed strain eas formulations and in contrast with these the result is an element satisfying the patch test there are no additional degrees of freedom as it is the case with the enhanced assumed strain case even by means of static condensation least squares fitting produces invariant finite strain elements which are shear locking free and amenable to be incorporated in large scale codes with that goal we use automatically generated code produced by acegen and mathematica all benchmarks show excellent results similar to the best available shell and hybrid solid elements with significantly lower computational cost

general chebyshev type inequalities for sugeno integrals chebyshev type inequalities for the sugeno integral on abstract spaces are studied in a rather general form thus closing the series of papers on the topic dealing with special cases restricted to the real line and product operation

improved formulations of qcs6 hybrid element for enhancing computational efficiency this article discusses two alternative methods of formulating the recently proposed quadrilateral plane element qcs6 which is based on a generalized functional with multiple stress fields the first method is derived by an extended hu washizu principle with the presence of incompatible modes and enforcement of energy orthogonality while the second one is established on a non conventional discrete local stress smoothing both methods can be applied to other structural element formulations with enhanced efficiency

deep convolutional neural network for inverse problems in imaging in this paper we propose a novel deep convolutional neural network cnn based algorithm for solving ill posed inverse problems regularized iterative algorithms have emerged as the standard approach to ill posed inverse problems in the past few decades these methods produce excellent results but can be challenging to deploy in practice due to factors including the high computational cost of the forward and adjoint operators and the difficulty of hyperparameter selection the starting point of this paper is the observation that unrolled iterative methods have the form of a cnn filtering followed by pointwise non linearity when the normal operator h h where h is the adjoint of the forward imaging operator h of the forward model is a convolution based on this observation we propose using direct inversion followed by a cnn to solve normal convolutional inverse problems the direct inversion encapsulates the physical model of the system but leads to artifacts when the problem is ill posed the cnn combines multiresolution decomposition and residual learning in order to learn to remove these artifacts while preserving image structure we demonstrate the performance of the proposed network in sparse view reconstruction down to 50 views on parallel beam x ray computed tomography in synthetic phantoms as well as in real experimental sinograms the proposed network outperforms total variation regularized iterative reconstruction for the more realistic phantoms and requires less than a second to reconstruct a 512 times 512 image on the gpu

a jensen type inequality for fuzzy integrals in this paper we show a jensen type inequality for the sugeno integral we also discuss some conditions assuring the satisfaction of opposite inequality reverse jensen inequality

stacked denoising autoencoders learning useful representations in a deep network with a local denoising criterion we explore an original strategy for building deep networks based on stacking layers of denoising autoencoders which are trained locally to denoise corrupted versions of their inputs the resulting algorithm is a straightforward variation on the stacking of ordinary autoencoders it is however shown on a benchmark of classification problems to yield significantly lower classification error thus bridging the performance gap with deep belief networks dbn and in several cases surpassing it higher level representations learnt in this purely unsupervised fashion also help boost the performance of subsequent svm classifiers qualitative experiments show that contrary to ordinary autoencoders denoising autoencoders are able to learn gabor like edge detectors from natural image patches and larger stroke detectors from digit images this work clearly establishes the value of using a denoising criterion as a tractable unsupervised objective to guide the learning of useful higher level representations

an incompatible element for axisymmetric structure and its modification by hybrid method this paper introduces three four node quadrilateral axisymmetric elements the first one is an incompatible element while the second one is a modification of the first element by an extended hellinger reissner principle the second element is then simplified by incorporating the conceptual idea of free formulation and thus forms the third element all of the three elements are found to be invariant insensitive to nodal point numbering free of locking for nearly incompressible material able to pass the patch test and do not exhibit the false shear phenomenon numerical examples are given and satisfactory predictions are achieved

on the suppression of zero energy deformation modes based on the hellinger reissner principle and the deformation energy due to assumed stresses and displacements the problem of the kinematic deformation modes in assumed stress hybrid mixed finite elements has been examined basic schemes are developed for the choice of assumed stress terms that will suppress all kinematic deformation modes quadrilateral membrane and axisymmetric elements and three dimensional hexahedral elements are used to illustrate the suggested procedure

h continuity of fuzzy measures and set defuzzification the purpose of this work is to analyze the continuity of fuzzy measures with respect to the hausdorff metric on k r n the class of all nonempty compact subsets of r n as an application we study the continuity of set defuzzification processes on r n which are defined by aumann integral methods

a systematic construction of b bar functions for linear and non linear mixed enhanced finite elements for plane elasticity problems in a previous paper a modified hu washizu variational formulation has been used to derive an accurate four node plane strain stress finite element denoted qe2 for the mixed element qe2 two enhanced strain terms are used and the assumed stresses satisfy the equilibrium equations a priori for the linear elastic case in this paper an alternative approach is discussed the new formulation leads to the same accuracy for linear elastic problems as the qe2 element however it turns out to be more efficient in numerical simulations especially for large deformation problems using orthogonal stress and strain functions we derive b functions which avoid numerical inversion of matrices the b strain matrix is sparse and has the same structure as the strain matrix b obtained from a compatible displacement field the implementation of the derived mixed element is basically the same as the one for a compatible displacement element the only difference is that we have to compute a b strain matrix instead of the standard b matrix accordingly existing subroutines for a compatible displacement element can be easily changed to obtain the mixed enhanced finite element which yields a higher accuracy than the q4 and qm6 elements copyright 1999 john wiley sons ltd

parameter extension for combined hybrid finite element methods and application to plate bending problems abstract based on a weighted average of the modified hellinger reissner principle and its dual the combined hybrid finite element chfe method was originally proposed with a combination parameter limited in the interval 0 1 in actual computation this parameter plays an important role in adjusting the energy error of discretization models in this paper a novel expression of the combined hybrid variational form is used to show the relationship between the resultant method and some galerkin least squares stabilized finite scheme for plate bending problems the choice of combination parameter is then extended to 0 0 1 existence uniqueness and convergence of the solution of discrete schemes are proved and the advantage of the parameter extension in computation is discussed as an application improvement of adini s rectangular element by the chfe approach is performed

extended embedded finite elements with continuous displacement jumps for the modeling of localized failure in solids abstract this paper addresses novel extended embedded finite elements with continuous displacement jumps for the modeling of localized failure in solids on one hand based upon the unified multiscale kinematics of strong discontinuities standard finite elements at the coarse scale are enriched with fine scale kinematics in which non uniform discontinuity modes are incorporated on the other hand the traction continuity condition across the discontinuity is enforced in the statically optimal form as the fine scale statics the admissible discontinuity modes satisfying a priori the traction continuity condition are derived in addition to the relative rigid body motions translations and rotations more general relative stretching modes that induce discontinuous strain stress fields in the bulk are obtained with no limit of a vanishing poisson s ratio the proposed model then particularizes to 2d quadrilateral elements the displacement jumps at the discontinuity nodes are selected as the enrichment parameters and regarded as global variables shared by neighboring elements the resulting model not only is intrinsically stress locking free for a fully softened discontinuity but also automatically guarantees global continuity of the displacement jumps another benefit is that the numerical instability suffered under the unfavorable element discontinuity configuration can be easily circumvented furthermore the vanishing displacement jumps at the discontinuity tip can be enforced trivially as conventional essential boundary conditions and those complex strategies introduced in existing models are avoided together with the failure criterion related to the element average stress and the propagation orientation based on a simplified nonlocal stress a local crack tracking algorithm is adopted to guarantee global continuity of the discontinuity path representative numerical simulations of element and structure benchmark tests are presented to verify the performance of the proposed approach in the modeling of arbitrary discontinuity propagation in solids

a chebyshev type inequality for fuzzy integrals abstract in this paper we prove a chebyshev type inequality for fuzzy integrals more precisely we show that 0 1 fg d 0 1 f d 0 1 g d where is the lebesgue measure on r and f g 0 1 0 are two continuous and strictly monotone functions both increasing or both decreasing also some examples and applications are presented

a quadrilateral mixed finite element with two enhanced strain modes summary an improved plane strain stress element is derived using a hu washizu variational formulation with bilinear displacement interpolation seven strain and stress terms and two enhanced strain modes the number of unknowns of the four node element is increased from eight to ten degrees of freedom for linear and non linear applications the two unknowns associated with the enhanced strain terms can be eliminated by static condensation so that eight displacement degrees of freedom remain for the proposed element which is denoted by qe2 the excellent performance of the proposed element is demonstrated using several linear and non linear examples

a hybrid finite element method for heterogeneous materials with randomly dispersed rigid inclusions a hybrid finite element approach is proposed for the mechanical response of two dimensional heterogeneous materials with linearly elastic matrix and randomly dispersed rigid circular inclusions of arbitrary sizes in conventional finite element methods many elements must be used to represent one inclusion in this work each inclusion is embedded inside a polygonal element and only one element is required to represent one inclusion in numerically approximating stress and displacement distributions around the inclusion classical elasticity solutions for a multiply connected region are employed a modified hybrid functional is used as the basis of the element formulation where the displacement boundary conditions of the element are automatically considered in a variational sense the accuracy and efficiency of the proposed method are demonstrated by two boundary value problems in one example the results based on the proposed method with only 64 hybrid elements 450 degrees of freedom are shown to be almost identical to those based on the traditional method with 2928 conventional elements 5526 degrees of freedom

analysis of a family of hdg methods for second order elliptic problems in this paper we analyze a family of hybridizable discontinuous galerkin hdg methods for second order elliptic problems in two and three dimensions the methods use piecewise polynomials of degree k 0 for both the flux and numerical trace and piecewise polynomials of degree k 1 for the potential we establish error estimates for the numerical flux and potential under the minimal regularity condition moreover we construct a local postprocessing for the flux which produces a numerical flux with better conservation numerical experiments in two space dimensions confirm our theoretical results

hybrid stress formulation for higher order theory of laminated shell analysis abstract based upon a modified hellinger reissner principle a new four node hybrid stress element is proposed for the linear elastic analysis of laminated orthotropic or anisotropic plates and shells a constrained initial stress trial is introduced so that equilibrium constraints can be relaxed by the variational principle thus the complicated work of selecting an equilibrating stress field can be avoided the example problems illustrate the performance of the element which is seen to be reliable and efficient

efficient formulation of robust hybrid elements using orthogonal stress strain interpolants and admissible matrix formulation this paper presents an investigation of using orthogonal constant and higher order stress modes in formulating efficient hybrid elements by equipping the primary idea of bergan and hanssen two sample elements modified from pian sumihara 5 plane and pian tong 18 hexahedral assumed contravariant stress elements are derived with the suggested admissible simplifications of the flexibility matrices incorporated into the two new elements new plane and hexahedral elements requiring respectively no and a negligible amount of computing efforts for inverting the flexibility matrices are formed all proposed elements are stable invariant contain no empirically determined factor and strictly pass the patch test popular benchmark problems are studied and the accuracy of the proposed elements is close to their parent models

improved hybrid stress axisymmetric elements includng behaviour for nearly incompressible materials a series of 4 node axisymmetric solid of revolution elements with quadrilateral cross section are developed based on the hybrid stress finite element model the displacement interpolation is identical and the elements differ in the stress field chosen alternative schemes for selection of stress distribution are investigated the performance of these elements is assessed and compared for the example problems of a thick cylinder and thick sphere under internal pressure of particular importance are convergence intra element stress distributions and element performance as the incompressible state is approached

the fuzzy integral for monotone functions abstract in this paper we give some optimal upper bounds for the sugeno s integral of monotone functions more precisely we show that if g 0 0 is a continuous and strictly monotone function then the fuzzy integral value p 0 a g d with respect to the lebesgue measure verifies the following sharp inequalities a g a p p for the increasing case and b g p p for the decreasing case moreover we show that under adequate conditions these optimal inequalities provides a powerful tool for solving fuzzy integrals also some examples and application are presented

finite element concepts for finite elastoplastic strains and isotropic stress response in shells theoretical and computational analysis this paper presents appropriate finite element concepts accounting for finite elastoplastic strains and isotropic stress response in arbitrary shells three parameterization strategies for the calculation of thin and thick smooth shells as well as shell intersections are discussed in detail in this context the importance of the deformation gradient for an efficient implementation is especially emphasized according to the parameterizations the computational plasticity algorithms are derived in general three dimensional 3 d form for thick shell structures and a restricted 2 d form satisfying the plane stress state underlying thin shells in order to describe arbitrary shell geometries the isoparametric concept is applied to all proposed finite element formulations these are based on quadrilateral 4 node mixed finite shell elements the variational approaches of the enhanced assumed strain method the assumed natural strain concept and the reduced integration technique are accurately considered by means of representative numerical examples the performance of the three different finite element concepts is demonstrated furthermore their individual properties are addressed with respect to efficiency and numerical accuracy thus crucial consequences for an optimal modelling of finite plastic strains in shells can be outlined

reduction of excessive energy in the four noded membrane quadrilateral element part i linear theory compressible materials abstract the objective of the paper is to set forth in a consistent manner reasons for the appearance of excessive energy in the four noded membrane quadrilateral element and to propose a formulation leading to simple and reliable elements that are less sensitive to distortions of the geometrical shape by presenting the differential geometry emphasis is placed upon those geometrical attributes which are inherently related to the quadrilateral a modified version of the functional of hu washizu is employed for the discretization appropriate approximations for the displacements rotations are chosen and the physical meaning of the various parameters is identified a systematic procedure is followed for the approximation of stress and strain the convergence of the formulation is investigated by examining the inf sup condition and applying the patch test also results of numerical examples and comparisons with other elemental formulations are presented

the patch test a condition for assessing fem convergence this paper discusses various forms of the irons patch test and shows again that its satisfaction is a necessary convergence condition being equivalent to consistency further it is shown that the test can be applied for verification of stability requirements thus providing also a sufficient condition of convergence the patch test is useful in testing the order of asymptotic convergence and the satisfaction of the test gives a guide for development of certain incompatible element forms

a material based finite element analysis of heterogeneous media involving dirichlet tessellations abstract in this paper a new finite element formulation has been developed for analysis of heterogeneous media in which the second phase is randomly dispersed within the matrix it introduces a tessellation based mesh generation technique to account for the arbitrariness in location shape and size of the second phase an assumed stress hybrid formulation has been implemented to utilize the resulting voronoi polygons as elements in a finite element model the effect of the second phase has been accounted for by introducing a transformation strain based constitutive formulation numerical examples have been conducted to validate the model

consistent thermal stress calculation by using a new approach of the enhanced assumed strain method a three field hybrid functional with displacement strain and stress assumptions has been proposed by introducing the enhanced assumed strain concept to the proposed functional a more general finite element formulation for the enhanced assumed strain method has been derived unlike the previous version of the enhanced assumed strain method the stresses can be evaluated from variational formulation within variational framework the present formulation has been applied to the thermal stress problems and it has been addressed that by suitable assumption of the enhanced assumed strains the spurious oscillation of the thermal stresses can be successfully overcome the process of designing the interpolation functions of the enhanced strains which guarantee the field consistency of the strain field is rational and systematic

a unified analysis for stress strain hybrid methods of high performance abstract several methods have been developed in the literatures of computational mechanics to improve the performance of the conventional lower order displacement finite elements which yield poor results for problems with bending and for nearly incompressible medium this paper is devoted to a unified analysis of convergence for pian sumihara s chen cheung s and piltner taylor s enhanced stress strain schemes by virtue of the energy compatibility and the rank condition error estimates for these typical finite elements of high performance are obtained in a unified framework and especially weakly locking free error estimates with respect to the poisson s ratio in energy norms are obtained uniformly for 1 ch 2 as h 0 where c is a constant independent of and the mesh size h very much the same about the three methods is pointed out

stress analysis around holes or notches by special finite elements in this paper three special elements for stress concentration analysis around holes or notches are presented one is based on a variational principle involving displacements unsymmetric stresses and rotations as independent variables the other two on the classical hellinger reissner principle the new elements are designed to be used in a single layer along the cavity rim where enhanced properties are needed to get a satisfactory level of accuracy special properties are obtained by enforcing the stress approximation to satisfy a priori the traction free boundary condition on the element side positioned along the cavity rim and by properly enriching the displacement interpolation the proposed elements are applicable to geometries of arbitrary shape easy to use low cost and readily implementable into existing finite element codes copyright 2005 john wiley sons ltd

rational approach for assumed stress finite elements a new method for the formulation of hybrid elements by the hellinger reissner principle is established by expanding the essential terms of the assumed stresses as complete polynomials in the natural coordinates of the element the equilibrium conditions are imposed in a variational sense through the internal displacements which are also expanded in the natural co ordinates the resulting element possesses all the ideal qualities i e it is invariant it is less sensitive to geometric distortion it contains a minimum number of stress parameters and it provides accurate stress calculations for the formulation of a 4 node plane stress element a small perturbation method is used to determine the equilibrium constraint equations the element has been proved to be always rank sufficient

a class of mixed assumed strain methods and the method of incompatible modes a three field mixed formulation in terms of displacements stresses and an enhanced strain field is presented which encompasses as a particular case the classical method of incompatible modes within this frame work incompatible elements arise as particular compatible mixed approximations of the enhanced strain field the conditions that the stress interpolation contain piece wise constant functions and be l2 ortho gonal to the enhanced strain interpolation ensure satisfaction of the patch test and allow the elimination of the stress field from the formulation the preceding conditions are formulated in a form particularly convenient for element design as an illustration of the methodology three new elements are developed and shown to exhibit good performance a plane 3d elastic plastic quad an axisymmetric element and a thick plate bending quad the formulation described herein is suitable for non linear analysis

new strategy for assumed stresses for 4 node hybrid stress membrane element an oblique skew co ordinate system defined at the origin of the isoparametric co ordinates is introduced as the reference co ordinate system for assumed stresses in the formulation of a 4 node hybrid membrane element the initially uncoupled stresses in these reference co ordinates can be constrained to satisfy the equilibrium conditions pointwise by using the procedure of pian and wu7 when suitable incompatible displacements are introduced such strategy allows the element stiffness to be formulated by using either the hellinger reissner or the complementary energy functional numerical results show that the performances of three elements constructed by using different sets of incompatible displacements in this paper are practically identical and are all of slightly higher accuracy than that of the pian sumihara element6

relations between incompatible displacement model and hybrid stress model an examination of the variational formulations confirms the similarity between the incompatible displacement model and the assumed stress hybrid model that was pointed out by irons in 1972 but the basic differences between the two are also identified for 8 node solid elements the assumed stress terms obtained through a rational procedure also agree with those deduced by irons purely from his physical insight

a sugeno integral inequality of carleman knopp type and some refinements abstract in this paper a carleman knopp type inequality for sugeno integrals is studied in a similar form than classical one considering all involved integrals in the sugeno sense with respect to the lebesgue measure also some refinements and examples are presented