further results for enhanced strain methods with isoparametric elements abstract in this contribution the enhanced strain finite element method is investigated further with particular attention given to the analysis of the method for isoparametric elements it is shown that the results established earlier b d reddy and j c simo stability and convergence of a class of enhanced strain methods siam j numer anal 32 1995 in press for affine equivalent meshes carry over to the case of isoparametric elements that is the method is stable and convergent provided that a set of three criteria is satisfied and for plane elements at least convergence is at the same rate as in the standard method a procedure for recovering the stress is shown to lead to an approximate stress which converges at the optimal rate to the actual stress with regard to computations a new basis for enhanced strains is introduced and numerical results are presented for this basis as well as for existing bases the results for enhanced strain methods are distinguished by the fact that the constant appearing in asymptotic error estimates is much smaller for these methods than for standard approaches

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

an adaptive boundary element method this paper explores the concept of moving singularities in the boundary element analysis the singularities are placed on an auxiliary boundary which is located outside the domain of the problem and are allowed to move as part of the solution process this results in a highly adaptive but non linear method examples involving the two and three dimensional laplace s equations are solved excellent agreement with exact solutions is obtained using a minimal number of singularities also the trajectories of the singularity motion are plotted the behaviour seen here is that as the solution approaches convergence the singularities exhibit a general trend of moving away from the domain of the problem

a 4 node finite shell element for the implementation of general hyperelastic 3d elasticity at finite strains abstract in this paper a finite shell element for large deformations is presented based on extensible director kinematics the essential feature is an interface to arbitrary three dimensional material laws the non linear lagrangian formulation is based on the three field variational principle parametrized with the displacement vector enhanced green lagrangian strain tensor and second piola kirchhoff stress tensor the developed quadrilateral shell element is characterized by a course mesh accuracy and distortion insensitivity compared with bilinear displacement approaches furthermore plane stress response is approximately recovered in the asymptotic case of vanishing thickness a number of example problems investigating large deformation as well as finite strain applications are presented compressible and incompressible hyperelastic materials of the st venant kirchhoff neo hookean and mooney rivlin type are particularly used

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

a p adaptive scheme for overcoming volumetric locking during plastic flow a feature of many classical plasticity yield functions is that they impose a volumetric constraint on plastic deformation for low order finite elements this results in kinematic restraints on possible deformation modes of an element leading to an overly stiff response the most robust procedure for overcoming volumetric locking is to use higher order finite elements however low order elements are popular for their efficiency and simplicity to remedy volumetric locking in low order elements a p adaptive scheme is proposed where through the partition of unity property of finite element shape functions the underlying basis of low order finite elements undergoing plastic flow is enhanced with higher order polynomial functions the computational result is extra degrees of freedom at existing nodes of elements undergoing plastic flow while the rest of the nodes remain unaltered the performance of the scheme is illustrated through two and three dimensional numerical examples

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

mixed stabilized finite element methods in nonlinear solid mechanics part i formulation abstract this paper exploits the concept of stabilized finite element methods to formulate stable mixed stress displacement and strain displacement finite elements for the solution of nonlinear solid mechanics problems the different assumptions and approximations used to derive the methods are exposed the proposed procedure is very general applicable to 2d and 3d problems implementation and computational aspects are also discussed showing that a robust application of the proposed formulation is feasible numerical examples show that the results obtained compare favorably with those obtained with the corresponding irreducible formulation

a stability study of some mixed finite elements for large deformation elasticity problems we consider the finite elasticity problem for incompressible materials proposing a simple bidimensional problem for which we provide an indication on the solution stability furthermore we study the stability of discrete solutions obtained by means of some well known mixed finite elements and we present several numerical experiments

enhanced assumed strain elements and locking in membrane problems abstract the assumptions which guarantee convergence of eas elements first introduced by simo and rifai can be reduced to two postulates specifically the stability condition refers to a relaxed stability of an associated hu washizu principle we investigate the problem of volume locking of membrane problems estimates of a certain type which for instance imply volume locking of the q1 element are fortunately not present with eas elements finally we verify an equivalence of the eas concept with a hellinger reissner method which was observed in numerical computations by andelfinger and ramm

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

convergence in the incompressible limit of finite element approximations based on the hu washizu formulation the classical hu washizu mixed formulation for plane problems in elasticity is examined afresh with the emphasis on behavior in the incompressible limit the classical continuous problem is embedded in a family of hu washizu problems parametrized by a scalar for which alpha lambda big mu corresponds to the classical formulation with and being the lame parameters uniform well posedness in the incompressible limit of the continuous problem is established for 1 finite element approximations are based on the choice of piecewise bilinear approximations for the displacements on quadrilateral meshes conditions for uniform convergence are made explicit these conditions are shown to be met by particular choices of bases for stresses and strains and include bases that are well known as well as newly constructed bases though a discrete version of the spherical part of the stress exhibits checkerboard modes it is shown that a independent a priori error estimate for the displacement can be established furthermore a independent estimate is established for the post processed stress the theoretical results are explored further through selected numerical examples

an analysis of some mixed enhanced finite element for plane linear elasticity the paper investigates mixed enhanced strain finite elements developed within the context of the u p formulation for nearly incompressible linear elasticity problems a rigorous convergence and stability analysis is detailed providing also l2 error estimates for the displacement field extensive numerical tests are developed showing in particular the accordance of the computational results with the theoretical predictions

relations between enhanced strain methods and the hr method abstract the three field hu washizu functional is the starting point to develop a comparative analysis of approximate linear elastostatic problems in particular we will analyse the limitation phenomena concerning two mixed methods respectively denoted the strain gap method and the mixed enhanced strain method and the two field hellinger reissner hr finite element formulation accordingly two original limitation principles are contributed we provide the theoretical motivation of the numerical observations provided in computational literature on the coincidence of the displacement and stress solutions between the enhanced assumed strain method and the hr method if different choices of shape functions are made it is further shown that the hr method provides the exact stress solution and the exact nodal displacements with one element the related analytical motivation are thus given the theoretical analyses presented in the paper are supported by numerical examples on tipical benchmarks

conditions for equivalence between the hu washizu and related formulations and computational behavior in the incompressible limit the relationship of the hu washizu mixed formulation to other mixed and enhanced formulations is examined in detail in the context of linear elasticity with a view to presenting a unified framework for such formulations the hu washizu formulation is considered in both its classical form and in a modified form that is suited to establishing well posedness in the incompressible limit recently established theoretical results on uniform well posedness are studied computationally by considering a range of numerical examples which illustrate where appropriate the good behavior predicted by the theory as well as the locking behavior that is evident in those problems in which the conditions for stability and convergence are not satisfied 2005 elsevier b v all rights reserved

a stable affine approximate finite element method the notion of the affine figure closest to a given quadrilateral can be given a precise mathematical definition the resulting figure is referred to as the equivalent parallelogram associated with a quadrilateral equipped with such a concept it is then feasible to consider finite element approximations in which the original quadrilateral elements are replaced by their equivalent parallelograms the idea is appealing not least because of the resulting economy arising from computations performed on an element generated by an affine map furthermore numerical experiments reported recently indicate that highly efficient and accurate schemes result when such a concept is combined with the enhanced strain method or the method of incompatible modes the purpose of this work is to analyze finite element schemes resulting from approximation of quadrilaterals by their equivalent parallelograms the focus is on low order bilinear elements and the analysis is carried out in the context of linear elasticity for standard approximations as well as for those which use enhanced strains the affine approximation applies only to the element map and the primary unknown the displacement vector in the context of elasticity is approximated by conventional piecewise bilinear functions the analysis confirms convergence at the optimal rate provided that the deviations of the quadrilaterals from their equivalent parallelograms are at most o h

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

size velocity correlations in hybrid high order moment multi fluid methods for polydisperse evaporating sprays modeling and numerical issues kah et al 2010 30 33 recently developed the eulerian multi size moment model emsm which tackles the modeling and numerical simulation of polydisperse multiphase flows using a high order moment method in a compact interval they suggested to reconstruct the number density function ndf by entropy maximization which leads to a unique and realizable ndf potentially in several size intervals thus leading to an hybrid method between multifluid and high order this reconstruction is used to simulate the evaporation process by an evaluation of the flux of droplet disappearance at zero size the fluxes of droplets between size intervals and an accurate description of the size shift induced by evaporation massot et al 2010 15 although this method demonstrated its potential for evaporating polydisperse flows two issues remain to be addressed first the emsm only considers one velocity for all droplets thus decoupling size from velocity which is too restrictive for distributions with a large size spectrum in most applications size conditioned dynamics have to be accounted for second the possibility to have separated dynamics for each size can lead to quasi monodisperse distributions which corresponds to a hard limiting case for the em algorithm so the behavior of the algorithm needs to be investigated in order to reproduce the entire moment space with a reasonable accuracy the aim of this paper is thus twofold the em and its related algorithm are enhanced by using a more accurate integration method in order to handle ndf close to the frontier of the moment space associated with an adaptive number of parameters to reconstruct the ndf accurately and efficiently as well as tabulated initial guess to optimize the computational time then a new model called csvm coupled size velocity moments model is introduced size velocity correlations are addressed either in the evaporation and drag processes or in the convective transport to reach this goal a velocity reconstruction for each size is suggested using only one additional moment per dimension and which can be directly applied to several size intervals thus this method is a direct generalization of emsm to handle the convective transport a flux splitting scheme is proposed based on the underlying kinetic description of the disperse phase comparing to existing approaches a main novelty of the csvm is that our kinetic approach ensures built in realizability conditions no additional corrections of the moments being needed at each time step the full strategy is first evaluated in 0d and 1d cases which either demonstrates the ability to reproduce both evaporation drag force and convection with size velocity correlations or the possible extension to several size intervals finally the method is applied on 2d cases with only one section showing the ability of the csvm and its related algorithms to capture the main physics of polydisperse evaporating sprays with a minimal number of moments

scaling integration method for singular integrals and its application to bem abstract a new accurate and efficient algorithm is developed for the numerical evaluation of a class of singular integrals which arise in the bem boundary element method analyses the algorithm is based on an idea of scaling integration that utilizes a proportional relationship inherent in the numerical computation of the singular integrals over flat triangular elements the present algorithm scaling integration method avoids the direct numerical evaluation of the integrand in the neighborhood of singularities it is shown and demonstrated that the method is simpler faster and more accurate than standard gaussian integration algorithms an application of the method to the bem analysis is also described and the results are favorably compared with the exact solution

large elasto plastic finite element analysis of solids and shells with the enhanced assumed strain concept abstract a finite element simulation of arbitrarily large elasto plastic deformations of three dimensional and shell structures is described two numerical aspects originally developed by j c simo have been combined i e the multiplicative large strain plasticity and the enhanced assumed strain finite element concept the constitutive model is worked out in its algorithmic version applying projection methods and consistent linearization the enhanced strain field is added to the conventional hexahedral displacement elements avoiding volumetric locking in the plastic range in addition to solid structures the three dimensional material model without any modifications is also applied to thin walled shell structures here an extended shell formulation a so called seven parameter model is used in which the thickness strain is augmented by a linear term the applicability of the entire formulation is demonstrated by several numerical examples

the equivalent parallelogram and parallelepiped and their application to stabilized finite elements in two and three dimensions a new class of quadrilateral and hexahedral elements four and eight noded in two and three dimensions respectively is presented these elements are obtained by combining the concept of the equivalent parallelogram for plane problems and the equivalent parallelepiped for three dimensional problems with the notion of incompatible modes a key feature of the new elements is that integration of the element stiffness matrices is carried out using one point integration the use of affine equivalent elements parallelograms and parallelepipeds permits a closed form eigenvalue analysis which includes the incompatible modes and a stabilization procedure based on the eigenvalue analysis ensures the full rank of the stiffness matrix numerical results for problems in elasticity and plasticity indicate equivalent or superior performance of the new elements when compared with various elements based on enhanced strains or incompatible modes

an adaptive stabilization strategy for enhanced strain methods in non linear elasticity this paper proposes and analyzes an adaptive stabilization strategy for enhanced strain es methods applied to quasistatic non linear elasticity problems the approach is formulated for any type of enhancements or material models and it is distinguished by the fact that the stabilization term is solution dependent the stabilization strategy is first constructed for general linearized elasticity problems and then extended to the non linear elastic regime via an incremental variational principle a heuristic choice of the stabilization parameters is proposed which in the numerical examples proved to provide stable approximations for a large range of deformations different problems and material models we also provide explicit lower bounds for the stabilization parameters that guarantee that the method will be stable these are not advocated since they are generally larger than the ones based on heuristics and hence prone to deteriorate the locking free behavior of es methods numerical examples with two different non linear elastic models in thin geometries and incompressible situations show that the method remains stable and locking free over a large range of deformations finally the method is strongly based on earlier developments for discontinuous galerkin methods and hence throughout the paper we offer a perspective about the similarities between the two

numerical aspects of finite hausdorff moment problem by maximum entropy approach some numerical aspects of the finite hausdorff moment problem in the framework of maximum entropy have been reviewed as stability of lagrange s multipliers computation entropy decreasing averages estimate spectral properties of hankel matrices have been considered determinant and conditioning number have been estimated finally entropy estimate has been provided

the multidimensional moment constrained maximum entropy problem a bfgs algorithm with constraint scaling in a recent paper we developed a new algorithm for the moment constrained maximum entropy problem in a multidimensional setting using a multidimensional orthogonal polynomial basis in the dual space of lagrange multipliers to achieve numerical stability and rapid convergence of the newton iterations here we introduce two new improvements for the existing algorithm adding significant computational speedup in situations with many moment constraints where the original algorithm is known to converge slowly the first improvement is the use of the bfgs iterations to progress between successive polynomial reorthogonalizations rather than single newton steps typically reducing the total number of computationally expensive polynomial reorthogonalizations for the same maximum entropy problem the second improvement is a constraint rescaling aimed to reduce relative difference in the order of magnitude between different moment constraints improving numerical stability of iterations due to reduced sensitivity of different constraints to changes in lagrange multipliers we observe that these two improvements can yield an average wall clock time speedup of 5 6 times compared to the original algorithm

analytical treatment of boundary integrals in direct boundary element analysis of plate bending problems a direct type boundary element method bem for the analysis of simply supported and built in plates is employed the integral equations due to a combined biharmonic and harmonic governing equations are first established the boundary integrals developed are then evaluated analytically the domain integrals due to external body forces are also transformed over the boundary and subsequently evaluated analytically thus it needs only the boundary to be discretized without loss of generality the exact expression for the integrals would enhance the solution accuracy of the bem this is due to the fact that at locations where the fundamental solutions approach their singular points the value determined by numerical quadrature may be inconsistent and inaccurate also another major advantage of the exact expressions for integrations is the insensitivity to the geometrical location of the source point on the boundary the distribution of boundary quantities is approximated either over linear or quadratic boundary elements general type of plate bending problems with plates of different geometrical shapes supported simply or fixed can be handled loading may be applied point concentrated uniformly distributed within the domain or over the boundary also hydrostatic pressure can be applied the results obtained by bem in comparison with those obtained by analytical or other approximate solutions are found to be very accurate and the solution method is efficient

an algorithm based on incompatible modes for the global tracking of strong discontinuities in shear localization analyses abstract numerical methods for predicting localized shear failure in elasto plastic solids have experienced considerable advancements in the last decades among these approaches the so called embedded strong discontinuity esd method is often successfully used to accurately simulate the post localization response with negligible dependence on the finite element discretization however it was observed that the employed discontinuity tracking strategy plays a crucial role in the successful localization analysis in this contribution we propose a novel strategy for the global tracking of discontinuity surfaces it is based on exploiting information obtained from the enhanced parameters employed in enhanced assumed strain eas formulations it is well known that enhanced strain element formulations are able to better capture localized shear deformations as compared to standard finite elements this can be explained as a consequence of the improved performance in bending we observed that the approximation of the strain jumps delimiting the shear band is connected with a deformation field characterized by opposite bending curvatures across these two discontinuities hence in view of the relations existing between the kinematics of strong and weak discontinuities we formulate a proper scalar function of the enhanced parameters to identify potential strong discontinuity surfaces which are evaluated in each step of the analysis with negligible computational cost this proposed approach has a global character as it is based upon evaluating discontinuity surfaces defined in the complete analysis domain that are by construction continuous across elements we demonstrate that the tracking algorithm correctly identifies the potential strong discontinuity surface already in early loading stages even before a localization condition is fulfilled in those elements which are crossed by the potential failure surface and which also satisfy the localization condition the kinematics of embedded strong discontinuities is activated to capture the shear failure surface the performance of the new tracking algorithm is demonstrated by means of several numerical shear localization analyses using associative and non associative drucker prager elastoplastic models to simulate 2 d and 3 d benchmarkanalyses

mixed linear linear simplicial elements for incompressible elasticity and plasticity this paper exploits the concept of orthogonal sub grid scales to stabilize the behaviour of mixed linear linear simplicial elements triangles and tetrahedra in incompressible or nearly incompressible situations both incompressible elastic and j2 plastic constitutive behaviours have been considered the different assumptions and approximations used to derive the method are exposed implementation and computational aspects are also discussed showing that a robust application of the proposed formulation is feasible numerical examples show that the elements derived are free of volumetric locking and spurious oscillations of the pressure and that the results obtained compare favourably with those obtained with the q1p0 quadrilateral

on the orthogonal subgrid scale pressure stabilization of finite deformation j2 plasticity the use of stabilization methods is becoming an increasingly well accepted technique due to their success in dealing with numerous numerical pathologies that arise in a variety of applications in computational mechanics in this paper a multiscale finite element method technique to deal with pressure stabilization of nearly incompressibility problems in nonlinear solid mechanics at finite deformations is presented a j2 flow theory plasticity model at finite deformations is considered a mixed formulation involving pressure and displacement fields is used as starting point within the finite element discretization setting continuous linear interpolation for both fields is considered to overcome the babuska brezzi stability condition a multiscale stabilization method based on the orthogonal subgrid scale osgs technique is introduced a suitable nonlinear expression of the stabilization parameter is proposed the main advantage of the method is the possibility of using linear triangular or tetrahedral finite elements which are easy to generate and therefore very convenient for practical industrial applications numerical results obtained using the osgs stabilization technique are compared with results provided by the p1 standard galerkin displacements linear triangular tetrahedral element p1 p1 standard mixed linear displacements linear pressure triangular tetrahedral element and q1 p0 mixed bilinear trilinear displacements constant pressure quadrilateral hexahedral element for 2d 3d nearly incompressible problems in the context of a nonlinear finite deformation j2 plasticity model

a mixed finite element method for non linear and nearly incompressible elasticity based on biorthogonal systems we present a finite element method for non linear and nearly incompressible elasticity the formulation is based on petrov galerkin discretization for the pressure and is closely related to the average nodal pressure formulation presented earlier in the context of incompressible and nearly incompressible dynamic explicit applications commun numer meth engng 1998 14 437 449 some numerical examples are presented to show the efficiency of the approach copyright 2009 john wiley sons ltd

analysis of some quadrilateral nonconforming elements for incompressible elasticity in this work some nonconforming elements on arbitrary quadrilateral meshes in solving incompressible elastic equations are analyzed a uniform optimal convergence rate is established at the incompressible limit nu 0 5 for both displacement and stresses or pressure in the case of incompressible flow

stabilization of bi linear mixed finite elements for tetrahedra with enhanced interpolation using volume and area bubble functions in order to overcome the oscillatory effects of the mixed bi linear galerkin formulation for tetrahedral elements a stabilization approach is presented to this end the mixed method of incompatible modes and the mixed method of enhanced strains are reformulated thus giving both the interpretation of a mixed finite element method with stabilization terms for non linear problems these are non linearly dependent on the current deformation state and therefore are replaced by linearly dependent stabilization terms the approach becomes most attractive for the numerical implementation since the use of quantities related to the previous newton iteration step typically arising for mixed enhanced elements is completely avoided the stabilization matrices for the mixed method of incompatible modes and the mixed method of enhanced strains are obtained with volume and area bubble functions various numerical examples are presented which illustrate successfully the stabilization effect for bi linear tetrahedral elements copyright 2007 john wiley sons ltd

uniform convergence and a posteriori error estimators for the enhanced strain finite element method enhanced strain elements frequently employed in practice are known to improve the approximation of standard non enhanced displacement based elements in finite element computations the first contribution in this work towards a complete theoretical explanation for this observation is a proof of robust convergence of enhanced element schemes it is shown that such schemes are locking free in the incompressible limit in the sense that the error bound in the a priori estimate is independent of the relevant lame constant the second contribution is a residual based a posteriori error estimate the l 2 norm of the stress error is estimated by a reliable and efficient estimator that can be computed from the residuals

discretization by finite elements of a model parameter dependent problem the discretization by finite elements of a model variational problem for a clamped loaded beam is studied with emphasis on the effect of the beam thickness which appears as a parameter in the problem on the accuracy it is shown that the approximation achieved by a standard finite element method degenerates for thin beams in contrast a large family of mixed finite element methods are shown to yield quasioptimal approximation independent of the thickness parameter the most useful of these methods may be realized by replacing the integrals appearing in the stiffness matrix of the standard method by gauss quadratures

analysis of some mixed finite element methods for plane elasticity equations we analyze some mixed finite element methods based on rectangular elements for solving the two dimensional elasticity equations we prove error estimates for a method proposed by taylor and zienkiewicz and for some new variants of the known equilibrium methods a numerical example is given demonstrating the performance of the various algorithms considered 1 introduction in the numerical solution of problems of continuum mechanics the stresses are normally of primary interest in the elastic region it is therefore natural to design the numerical algorithms so that the stresses can be obtained directly without first computing the displacements such methods can be derived from the dual variational formulation of the elasticity problem the corresponding finite element algorithms are usually formulated as mixed methods where both the displacements and the stresses are first approximated and the displacements are then eliminated from the discrete equations in many cases the elimination can be rather effectively done using penalty perturbation techniques or their iterative variants cf 3 11 12 the best known finite element methods of the above type are the so called equilibrium methods first proposed by fraejis de veubeke 17 cf also 14 16 18 and analyzed theoretically by johnson and mercier 9 cf also 8 in these methods one uses specific composite elements which allow the equilibrium condi tion between the stresses and the volume load to be satisfied exactly in the case where the volume load is zero

numerical implementation of the lumped parameter model for the acoustic power output of a vibrating structure in a previous paper a lumped parameter model for the acoustic radiation from a vibrating structure was defined by dividing the surface of the structure into elements expanding the acoustic field from each of the elements in a multipole expansion and truncating all but the lowest order terms in the expansion here the lumped parameter model is implemented numerically by requiring the boundary condition for the normal surface velocity to be satisfied in a lumped parameter sense this alleviates the difficulties typically encountered in enforcing the boundary condition leading to a relatively simple numerical solution with well defined convergence properties the basis functions for the numerical analysis are taken as the acoustic fields of discrete simple dipole and tripole sources located at the geometrical centers of the surface elements the different source types are used to represent the radiation from different kinds of surface elements simple sources for elements in the plane of an infinite baffle dipole sources for very thin structures which deform only in bending and tripole sources for elements associated with parts of a structure enclosing a finite volume the convergence of the numerical solution for the power output as a function of both frequency and element size is demonstrated through several example problems

droplet size and velocity distributions for spray modelling methods for constructing droplet size distributions and droplet velocity profiles are examined as a basis for the eulerian spray model proposed in beck and watkins 2002 2003 5 6 within the spray model both distributions must be calculated at every control volume at every time step where the spray is present and valid distributions must be guaranteed results show that the maximum entropy formalism combined with the gamma distribution satisfy these conditions for the droplet size distributions approximating the droplet velocity profile is shown to be considerably more difficult due to the fact that it does not have compact support an exponential model with a constrained exponent offers plausible profiles

stability of finite elements under divergence constraints a finite dimensional stability test for checking velocity pressure finite element trial spaces is presented applications are made to a new class of element pairs proposed in this paper as well as to existing spaces

shear locking in a plane elasticity problem and the enhanced assumed strain method the enhanced assumed strain eas method is a popular tool for avoiding locking phenomena e g a remedy for shear locking in plane elasticity we consider bending dominated problems on thin bodies which can be treated as beams and prove that the degree of approximation of the eas method is at least as good as that of a beam model the hypercircle method is combined with arguments of nonconforming methods

stress induced phase transformations in elastic solids under anti plane deformations dissipative constitutive models and numerical simulation abstract the present paper addresses modeling and numerical description of stress induced phase transformations in solids the study is developed in the setting of a generalized neo hookean elastic material under anti plane deformations it is assumed that the kinetics of phase transformation is governed by inequality constraints which lead to a dissipative behavior of the material a thermodynamic analysis motivates the assumption of stress continuity across the surface of separation between phases we propose a new finite element for the description of phase boundaries characterized by strain discontinuities in any position within the element the inequality constraints of the problem are enforced by means of a return mapping algorithm dendritic formations are represented in the numerical results corresponding to the resulting model

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

two mixed finite element formulations with area bubble functions for tetrahedral elements abstract we address the solution of geometrically linear elastic problems for three dimensional solid mechanics using tetrahedral finite elements starting from a five field weak formulation involving fields for compatible displacements incompatible displacements pressure enhanced strains and stresses both the mixed method of incompatible modes and the mixed method of enhanced strains are considered as special cases as a key idea area bubble functions are used for both mixed finite element formulations in order to enrich the displacement field and the enhanced strain field respectively appropriate conditions for satisfaction of the patch test and unique solution of the discrete equation are verified we also observe that contrary to a the standard enhanced assumed strain method applied to triangles and tetrahedra our mixed formulations with pressure as an independent variable are not degenerate in the representative examples firstly a numerical verification of the patch test is obtained two additional examples cook s membrane problem and a plate with a ring hole illustrate the good performance of the presented approaches in comparison to existing finite element formulations

mixed finite element methods reduced and selective integration techniques a unification of concepts the equivalence of certain classes of mixed finite element methods with displacement methods which employ reduced and selective integration techniques is established this enables one to obtain the accuracy of the mixed formulation without incurring the additional computational expense engendered by the auxiliary field of the mixed method applications and numerical examples are presented for problems with constraints which can be difficult to enforce in finite element approximations and have often dictated the use of mixed principles these include thin beams and plates and linear and nonlinear incompressible and nearly incompressible continuum problems in solid and fluid mechanics

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

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

stability of incompressible formulations enriched with x fem abstract the treatment of near incompressibility is a major concern for applications involving rubber like materials or when important plastic flows occurs as in forming processes the use of mixed finite element methods is known to prevent the locking of the finite element approximation in the incompressible limit however it also introduces a critical condition for the stability of the formulation called the inf sup or lbb condition recently the finite element method has evolved with the introduction of the partition of unity method the extended finite element method x fem uses the partition of unity method to remove the need to mesh physical surfaces or to re mesh them as they evolve the enrichment of the displacement field makes it possible to treat surfaces of discontinuity inside finite elements in this paper some strategies are proposed for the enrichment of low order mixed finite element approximations in the incompressible setting the case of holes material interfaces and cracks are considered numerical examples show that for well chosen enrichment strategies the finite element convergence rate is preserved and the inf sup condition is passed

a mixed three field fe formulation for stress accurate analysis including the incompressible limit abstract in previous works the authors have presented the stabilized mixed displacement pressure formulation to deal with the incompressibility constraint more recently the authors have derived stable mixed stress displacement formulations using linear linear interpolations to enhance stress accuracy in both linear and non linear problems in both cases the variational multi scale vms stabilization technique and in particular the orthogonal subgrid scale oss method allows the use of linear linear interpolations for triangular and tetrahedral elements bypassing the strictness of the inf sup condition on the choice of the interpolation spaces these stabilization procedures lead to discrete problems which are fully stable free of volumetric locking or stress oscillations this work exploits the concept of mixed finite element methods to formulate stable displacement stress pressure finite elements aimed for the solution of nonlinear problems for both solid and fluid finite element fe analyses the final goal is to design a finite element technology able to tackle simultaneously problems which may involve isochoric behavior preserve the original volume of the strain field together with high degree of accuracy of the stress field these two features are crucial in nonlinear solid and fluid mechanics as used in most numerical simulations of industrial manufacturing processes numerical benchmarks show that the results obtained compare very favorably with those obtained with the corresponding mixed displacement pressure formulation

analysis of some mixed finite element methods related to reduced integration we prove error estimates for the following two mixed finite element methods related to reduced integration a method for stokes problem using rectangular elements with piecewise bilinear approximations for the velocities and piecewise constants for the pressure and one method for a plate problem using bilinear approximations for transversal displacement and rotations and piecewise constants for the shear stress the main idea of the proof in the case of stokes problem is to combine a weak babuska brezzi type stability estimate for the pressure with a superapproximability property for the velocities a similar technique is used in the case of the plate problem