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

polynomial time algorithm for an optimal stable assignment with multiple partners this paper considers the many to many version of the stable marriage problem where each man and woman has a strict preference ordering on the members of the opposite sex that he or she considers acceptable further each man and woman wishes to be matched to as many acceptable partners as possible up to his or her specified quota in this setup a polynomial time algorithm for finding a stable matching that minimizes the sum of partner ranks across all men and women is provided it is argued that this sum can be used as an optimality criterion for minimizing total dissatisfaction if the preferences over partner combinations satisfy a no complementarities condition the results in this paper extend those already known for the one to one version of the problem

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

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

polyhedral aspects of stable marriage in the setting of the stable matching sm problem it has been observed that some of the man woman pairs cannot be removed although they participate in no stable matching since such a removal would alter the set of solutions these pairs are yet to be identified likewise and despite the sizeable literature some of the fundamental characteristics of the sm polytope e g its dimension its facets etc have not been established in the current work we show that these two seemingly distant open issues are closely related more specifically we identify the pairs with the above mentioned property and present a polynomial algorithm for producing a set of minimal preference lists we utilize this result in the context of two different representations of the sm structure rotation poset graph and algebraic formulation and derive the dimension of the sm polytope to obtain all alternative minimal linear descriptions

many to one stable matching geometry and fairness baiou and balinski characterized the stable admissions polytope using a system of linear inequalities the structure of feasible solutions to this system of inequalities fractional stable matchings is the focus of this paper the main result associates a geometric structure with each fractional stable matching this insight appears to be interesting in its own right and can be viewed as a generalization of the lattice structure for integral stable matchings to fractional stable matchings in addition to obtaining simple proofs of many known results the geometric structure is used to prove the following two results first it is shown that assigning each agent their median choice among all stable partners results in a stable matching which can be viewed as a fair compromise second sufficient conditions are identified under which stable matchings exist in a problem with externalities in particular in the stable matching problem with couples

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

voronoi cell finite element model based on micropolar theory of thermoelasticity for heterogeneous materials in this paper a new voronoi cell finite element model is developed for solving steady state heat conduction and micropolar thermoelastic stress analysis problems in arbitrary heterogeneous materials the method is based on the natural discretization of a multiple phase domain into basic structural elements by dirichlet tessellation tessellation process results in a network of polygons called voronoi polygons in this paper formulations are developed for treating these polygons as elements in a finite element mesh furthermore a composite voronoi cell finite element model is developed to account for the presence of a second phase inclusion within a polygonal element various numerical examples are executed for validating the effectiveness of this model in the analysis of the temperature and stress fields for micropolar elastic materials effective material properties are derived for microstructures containing different distributions of second phase

stable matchings optimal assignments and linear programming vande vate 1989 described the polytope whose extreme points are the stable core matchings in the marriage problem rothblum 1989 simplified and extended this result this paper explores a corresponding linear program its dual and consequences of the fact that the dual solutions have an unusually direct relation to the primal solutions this close relationship allows us to provide simple proofs both of vande vate and rothblum s results and of other important results about the core of marriage markets these proofs help explain the structure shared by the marriage problem without sidepayments and the assignment game with sidepayments the paper further explores fractional matchings which may be interpreted as lotteries over possible matches or as time sharing arrangements we show that those fractional matchings in the stable marriage polytope form a lattice with respect to a partial ordering that involves stochastic dominance thus all expected utility functions corresponding to the same ordinal preferences will agree on the relevant comparisons finally we provide linear programming proofs of slightly stronger versions of known incentive compatibility results

the complexity of counting stable marriages in an instance of size n of the stable marriage problem each of n men and n women ranks the members of the opposite sex in order of preference a stable matching is a complete matching of men and women such that no man and woman who are not partners both prefer each other to their actual partners under the matching it is well known that at least one stable matching exists for every stable marriage instance so that the decision version of the problem always has a yes answer furthermore efficient algorithms are known for the determination of such a stable matching so that the search version of the problem is polynomially solvable however by exploring the structure of the set of stable matchings for any particular instance of the problem and exploiting its relationship with the set of antichains of an associated partially ordered set we prove that the enumeration version of the problem determining the number of stable matchings is p complete and therefore cannot be solved in polynomial time if

a general degree hybrid equilibrium finite element for kirchhoff plates summary we present a family of hybrid equilibrium finite elements for the quasistatic linear elastic analysis of plates governed by kirchhoff theory the moments are approximated by self balanced polynomial fields of general degree and in order to impose strong codiffusivity the normal boundary rotations are approximated with complete polynomials of the same degree whereas the transverse deflections use polynomials one degree lower furthermore it is also necessary to include an independent approximation of the vertex translations we show that the triangular form of this element is stable that is free from spurious kinematic modes and the formulation that we present allows these elements to be used as a standard displacement element examples of computed values and convergence of the solutions are presented which demonstrate the performance of these elements copyright 2013 john wiley sons ltd

a hierarchic family of isogeometric shell finite elements a hierarchic family of isogeometric shell finite elements based on nurbs shape functions is presented in contrast to classical shell finite element formulations inter element continuity of at least c1 enables a unique and continuous representation of the surface normal within one nurbs patch this does not only facilitate formulation of kirchhoff love type shell models for which the standard galerkin weak form has a variational index of 2 but it also offers significant advantages for shear deformable reissner mindlin type shells and higher order shell models for a 5 parameter shell formulation with reissner mindlin kinematics a hierarchic difference vector which accounts for shear deformations is superimposed onto the rotated kirchhoff love type director of the deformed configuration this split into bending and shear deformations in the shell kinematics results in an element formulation which is free from transverse shear locking without the need to apply further remedies like reduced integration assumed natural strains or mixed finite element formulations the third member of the hierarchy is a 7 parameter model including thickness change and allowing for application of unmodified three dimensional constitutive laws the phenomenon of curvature thickness locking coming along with this kinematic extension again is automatically avoided by the hierarchic difference vector concept without any further treatment membrane locking and in plane shear locking are removed by two different approaches firstly elimination via the discrete strain gap dsg method and secondly removal of parasitic membrane strains using a hybrid mixed method based on the hellinger reissner variational principle the hierarchic kinematic structure of the three different shell formulations allows a straightforward combination of these elements within one mesh and is thus the ideal basis for a model adaptive approach

hellinger reissner principles for plate and shell finite elements the hellinger reissner generalized variational principle is used to deduce further principles directed especially towards formulation of high integrity finite elements for plates and curved shells in polynomial parametric representation assumed stresses in these principles are derived from displacements and supplemented with stresses derived from stress functions

extrapolated fields in the formulation of the assumed strain elements part ii three dimensional problems abstract a new assumed strain quadrilateral element with accurate in plane bending behavior is presented the basic idea consists in introduction of a parallelogram domain associated with the given quadrilateral element development of the related assumed strain field for the parallelogram and subsequent extrapolation of this field to the domain of the original quadrilateral the assumed strain field for the parallelogram is constructed by identification of various modes of its deformation and then by proper modification of the strain field in some of these modes in particular the strain operator with respect to the so called in plane bending modes is modified so as to simulate the strain field resulting from the assumptions usually made in structural mechanics the modification of the strain fields leads to the assumed strain operator the proposed new assumed strain quadrilateral element exhibits remarkably accurate performance for both membrane and bending dominated problems even when severely distorted and high aspect ratio meshes are considered and when materials are nearly incompressible

finite element criteria for some shells simple solutions are extracted from the exact compatibility equations of inextensional bending for a special class of shell shapes and it is speculated that these solutions provide useful criteria towards evaluating finite elements for these and closely related shapes curved finite elements of a quadratic parametric representation which do not belong to the special class are then studied by using a series of exact inextensional bending displacements it is concluded from numerical evidence that the criteria apply to finite element shapes in this representation when they are shallow as is usually the case in practice criteria for homogeneous membrane actions follow from gol denveizer s static geometric analogue

characterization of stable matchings as extreme points of a polytope the purpose of this paper is to extend a modified version of a recent result of vande vate 1989 which characterizes stable matchings as the extreme points of a certain polytope our proofs are simpler and more transparent than those of vande vate

a stabilization procedure for the quadrilateral plate element with one point quadrature a stabilization procedure is developed for controlling the kinematic modes of the four node bilinear quadrilateral element when single point quadrature is used these kinematic modes manifest themselves by spatial oscillations or singularity of the total stiffness in this stabilization procedure additional generalized strains are defined which are activated by the kinematic modes these generalized modes are furthermore not activated by rigid body motions regardless of the shape of the quadrilateral by using a scaling law developed in an earlier paper the stabilization parameters are defined so they do not adversely affect the element s performance several problems which are subject to kinematic modes are presented to illustrate the performance of this stabilization procedure for linear problems

eigenvalues and stable time steps for the bilinear mindlin plate element eigenvalues are obtained for the 4 node mindlin plate element with one point quadrature both isotropic and some anisotropic matenals are considered but for the latter only bounds are obtained on the eigenvalues these eigenvalues provide stable time steps for explicit time integration algorithms

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

blockers and antiblockers of stable matchings an implicit linear description of the stable matching polytope is provided in terms of the blocker and antiblocker sets of constraints of the matroid kernel polytope the explicit identification of both these sets is based on a partition of the stable pairs in which each agent participates here we expose the relation of such a partition to rotations we provide a time optimal algorithm for obtaining such a partition and establish some new related results most importantly that this partition is unique

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

physical shape functions in finite element analysis of moderately thick plates a new rectangular finite element for moderately thick plates is presented the element is based on the concept of physical shape functions i e functions which contain in themselves physical and geometrical properties of the element the analytic formulae of stiffness geometric stiffness and mass matrices are presented for isotropic material the element is free from locking and zero energy modes not corresponding to rigid body motions several examples are presented for static initial stability and free vibration problems

finite element stabilization matrices a unification approach abstract in this paper we show that the stabilization vector can be obtained naturally by taking the partial derivatives with respect to the natural coordinates hence the components of the strains and stresses can be expressed in terms of a set of orthogonal coordinates with these definitions of stresses and strains a general form of the finite element stabilization matrices is then constructed for underintegrated irregular shape and anisotropic elements the explicit expressions of the stabilization matrices for the 4 9 and 8 node laplace and continuum elements and the 4 node plate element are then derived from the general form these are sufficiently general for the developments herein the generalization of the stabilization matrices concept to nonlinear problems which usually require the numerical integration of a fairly general class of nonlinear finite deformation constitutive equations is also presented the computer implementation aspects and numerical evaluation of these stabilized elements are also considered numerical tests confirm the stability and accuracy characteristics of the resulting elements in particular the numerical experiments reported here also show that the rates of convergence in the l2 norm and in the energy norm agree well with the expected convergence rates

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

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

a 3d cosserat point element cpe for nonlinear orthotropic solids generalization for an initially distorted mesh and an arbitrary orientation of material orthotropy summary the objective of the present paper is to develop a cosserat point element cpe formulation for the numerical solution of three dimensional problems of general hyperelastic orthotropic materials under finite deformations with initially distorted element shapes generally speaking the accuracy of the cpe depends on the constitutive coefficients of the strain energy function that controls the inhomogeneous deformations in the present study a new methodology for the determination of the constitutive coefficients is presented which allows the cpe to model any elastic material including isotropic orthotropic and anisotropic materials and with initially distorted element geometry a number of example problems are considered which verify and compare the performance of the developed cpe with other 3d brick elements that exist in the commercial finite element package abaqus these examples demonstrate that the developed cpe is accurate robust free of hourglass instabilities and can be used for modeling both 3d and thin structures that undergo large deformations copyright 2015 john wiley sons ltd

a three node mindlin plate element with improved transverse shear abstract a displacement methodology for mindlin elements recently employed in the development of an efficient four node quadrilateral min4 is the basis for a three node explicitly integrated triangular element min3 the approach herein referred to as anisoparametric is founded upon two kinematic requirements that are auxiliary to the standard convergence criteria the initial complete quadratic deflection field is constrained by continuous shear edge constraints to achieve an isoparametric like three node configuration much success of the element is due to an innovative shear correction factor concept several numerical experiments are performed in the linear elasto static regime to ascertain the element performance

trunc for shells an element possibly to the taste of bruce irons in his delightful and original textbook 18 bruce irons introduces the chapter of plate bending with the remark history of disasters but the pioneering days are past this is certainly true on the other hand we learn in the same context from irons we believe that the world has not yet exhausted the older formulations in this paper we present a review of theoretical aspects of the plate bending triangle trunc reference 4 together with extensive tests in linear statics dynamics buckling and nonlinear large deformations both for plates and shells the unconventional trunc model is based on the patch test which was originated by irons 1 in spite of its limited theoretical foundation the performance of this element on a fairly broad field of applications appears at least from the practical point of view very satisfactory

extension of field consistence approach into developing plane stress elements in this research paper the possibilities for extending the field consistence approach l yunhua on shear locking in finite elements licentiate thesis stockholm 1997 l yunhua explanation and elimination of shear locking and membrane locking with field consistence approach comput methods appl mech engrg in press starting from different variational principles to plane stress elements are investigated in the extension two main difficulties are explicitly solving a set of coupled partial differential equations and satisfying inter element compatibility the first one is alleviated by constructing element interpolations from a set of quasi general solutions rather than the real general solutions to the euler lagrangian equations the second one is solved by combining the field consistence approach with the iso parametric interpolation technique the traditional assumed stress method is improved and an efficient plane stress element is obtained it seems that the relations between the three commonly used variational principles can be more reasonably established in the framework of the field consistence approach

a total lagrangian formulation for the geometrically nonlinear analysis of structures using finite elements part i two dimensional problems shell and plate structures a total lagrangian finite element formulation for the geometrically nonlinear analysis large displacement large rotations of shells is presented explicit expressions of all relevant finite element matrices are obtained by means of the definition of a local co ordinate system based on the shell principal curvature directions for the evaluation of strains and stresses a series of examples of nonlinear analysis of shell and plate structures is given

a kirchhoff mode method for c0 bilinear and serendipity plate elements abstract a new formulation for the c0 quadrilateral and serendipity plate elements is presented it is an extension of the mode decomposition approach that has been successfully applied in evaluating the c0 triangular linear plate element in contrast to the triangular element the concept of an equivalent discrete kirchhoff configuration is utilized the elements are applied to several examples and the performance of these elements is shown to be quite good

an efficient algorithm for the optimal stable marriage in an instance of size n of the stable marriage problem each of n men and n women ranks the members of the opposite sex in order of preference a stable matching is a complete matching of men and women such that no man and woman who are not partners both prefer each other to their actual partners under the matching it is well known 2 that at least one stable matching exists for every stable marriage instance however the classical gale shapley algorithm produces a marriage that greatly favors the men at the expense of the women or vice versa the problem arises of finding a stable matching that is optimal under some more equitable or egalitarian criterion of optimality this problem was posed by knuth 6 and has remained unsolved for some time here the objective of maximizing the average or equivalently the total satisfaction of all people is used this objective is achieved when a person s satisfaction is measured by the position of his her partner in his her preference list by exploiting the structure of the set of all stable matchings and using graph theoretic methods an o n 4 algorithm for this problem is derived

new nonconforming finite elements on arbitrary convex quadrilateral meshes in this paper we construct new nonconforming finite elements on the meshes consisting of arbitrary convex quadrilaterals especially for the quadratic and cubic cases for each case we first define a quadrilateral element that adopts edge moments as the degrees of freedom dofs and then enforce a linear constraint on this element we have for the quadratic case eight degrees of freedom per element and for the cubic case eleven dofs per element respectively the dimensions and the bases of different types for the global finite element spaces are provided we consider the approximations of two dimensional second order elliptic problems for both of these elements error estimates with optimal convergence order in both broken h 1 norm and l 2 norm are given moreover we consider the discretization of the stokes equations adopting our quadratic element to approximate each component of the velocity along with piecewise discontinuous p 1 element for the pressure this mixed scheme is stable and optimal error estimates both for the velocity and the pressure are also achieved numerical examples verify our theoretical analysis

on improved hybrid finite elements with rotational degrees of freedom a set of three new hybrid elements with rotational degrees of freedom d o f s is introduced the solid 8 node hexahedron element is developed for solving three dimensional elasticity problems this element has three translational and three rotational d o f s at each node and is based on a 42 parameter three dimensional stress field in the natural convected co ordinate system for two dimensional plane elasticity problems an improved triangular hybrid element and a quadrilateral hybrid element are presented these elements use two translational and one rotational d o f at each node three different sets of five parameter stress fields defined in a natural convected co ordinate system for the entire element are used for the mixed triangular element the mixed quadrilateral element is based on a nine parameter complete linear stress field in natural space the midside translational d o f s are expressed in terms of the corner nodal translations and rotations using appropriate transformations the stiffness matrix is derived based on the hellinger reissner variational principle the elements pass the patch test and demonstrate an improved performance over the existing elements for prescribed test examples

inextensional bending of a shell triangular element in quadratic parametric representation abstract exact closed form inextensional bending solutions are developed for a class of shell triangular elements in quadratic parametric representation these elements may have positive zero or negative gaussian curvature previous exact closed form inextensional solutions of the equations of thin shell theory are known for non zero gaussian curvature only for spherical surfaces the polynomial solutions are relevant to finite element design and provide inextensional bending behaviours with slowly varying curvature changes ready for use in patch test validation of any shell finite element

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

8 and 12 node plane hybrid stress function elements immune to severely distorted mesh containing elements with concave shapes abstract by simply improving the first version of hybrid stress element method proposed by pian several 8 and 12 node plane quadrilateral elements which are immune to severely distorted mesh containing elements with concave shapes are successfully developed firstly instead of the stresses the stress function is regarded as the functional variable and introduced into the complementary energy functional then the fundamental analytical solutions in global cartesian coordinates of are taken as the trial functions for 2d finite element models and meanwhile the corresponding unknown stress function constants are introduced thus the resulting stress fields must be more reasonable because both the equilibrium and the compatibility relations can be satisfied thirdly by using the principle of minimum complementary energy these unknown stress function constants can be expressed in terms of the displacements along element boundaries which can be interpolated directly by the element nodal displacements finally the complementary energy functional can be rewritten in terms of element nodal displacement vector and thus the element stiffness matrix of such hybrid stress function hs f element is obtained this technique establishes a universal frame for developing reasonable hybrid stress elements based on the principle of minimum complementary energy and the first hybrid stress element proposed by pian is just a special case within this frame following above procedure two 8 node and two 12 node quadrilateral plane elements are constructed by employing different fundamental analytical solutions of airy stress function numerical results show that the 8 node and 12 node models can produce the exact solutions for pure bending and linear bending problems respectively even the element shape degenerates into triangle and concave quadrangle furthermore these elements do not possess any spurious zero energy mode and rotational frame dependence

a mixed formulation of c0 linear triangular plate shell element the role of edge shear constraints a simple and effective linear c0 triangular element for plates and shells is developed on the basis of the hellinger reissner mixed variational principle with independently assumed stress and displacement fields two main features are emphasized in this development concerning the assumed transverse shear stress field firstly this assumption results in edge type penalty constraints in the thin plate shell regimes secondly the element is used in the form of a four triangle cross diagonal macroelement mesh as a result the element is shown to be free from shear locking in thin plate shell applications and it satisfied all the appropriate patch tests required for kirchhoff plate models in addition the element exhibits good overall convergence properties in a variety of test problems for plates and shells finally from the computational standpoint the element is very efficient since all stiffness component matrices are derived in explicit forms

a regularized dual mixed element for plane elasticity implementation and performance of the bdm element abstract in the present work we consider aspects of the formulation and numerical implementation of the bdm element 1 2 this element is based on an extended dual hellinger reissner principle which leads to optimal convergence rates for the stresses and displacements the element is characterized by a non symmetric approximation of the stress field 3 which implies an approximation of the work conjugate rotation field by adding the couple equilibrium with a lagrangian multiplier in order to get a generalized displacement method the displacement and rotation fields approximation have to be discontinuous and only the interelement tractions have to be continuous conditions for stability checks and optimal convergence of this element have been pointed out by stein and rolfes 4 within this paper we discuss in detail algorithmic aspects of the implementation and give comparisons with respect to the approximation behaviour of the q1 pian sumihara and the recently developed q1 e5 element

the stable admissions polytope the stable admissions polytope the convex hull of the stable assignments of the university admissions problem is described by a set of linear inequalities it depends on a new characterization of stability and arguments that exploit and extend a graphical approach that has been fruitful in the analysis of the stable marriage problem

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

the geometry of fractional stable matchings and its applications we study the classical stable marriage and stable roommates problems using a polyhedral approach we propose a new lp formulation for the stable roommates problem which has a feasible solution if and only if the underlying roommates problem has a stable matching furthermore for certain special weight functions on the edges we construct a 2 approximation algorithm for the optimal stable roommates problem our technique exploits features of the geometry of fractional solutions of this formulation for the stable marriage problem we show that a related geometry allows us to express any fractional solution in the stable marriage polytope as a convex combination of stable marriage solutions this also leads to a genuinely simple proof of the integrality of the stable marriage polytope

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

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

an improved treatment of transverse shear in the mindlin type four node quadrilateral element abstract an improved displacement methodology based on mindlin theory is developed and applied to a four node twelve degrees of freedom quadrilateral element special attention is directed toward enhancement of the transverse shear energy representation particularly a non uniform order kinematic interpolation scheme is accompanied by what is termed element appropriate shear correction factors the element matrices are consistently derived from hamilton s variational principle using exact numerical integration throughout the element stiffness matrix possesses correct rank and is well conditioned over the entire mindlin theory range of thickness to length ratios exceptionally good element performance is demonstrated by solutions to a set of static and vibrational problems

study of trial functions in shell triangular finite elements of quadratic parametric representation abstract a study is made of trial functions in a curved triangular finite element for the solution of problems in first approximation shell theory the element geometry is in quadratic parametric representation of the real shell surface while the displacement and stress function trial functions are in cubic parametric representation special attention is given to inextensional bending and homogeneous membrane states numerical examples are provided for specimen elements with positive zero and negative gaussian curvature vector equations are listed for the underlying shell theory together with fortran subroutines for the element geometry kinematics and statics

stabilized rapidly convergent 18 degrees of freedom flat shell triangular element a rank sufficient flat triangular shell element with driling degrees of freedom is described a variational basis for this element has been provided by a three fiels variational principle with relaxed interelement compatibility and traction continuity conditions

a unified approach for variationally consistent finite elements in elastoplasticity abstract a general variationally consistent approach for elastoplastic finite element analysis is presented a weak formulation of the finite step i e in terms of finite increments elastoplastic boundary value problem is obtained by enforcing the stationarity of a mixed functional of hu washizu type a peculiarity of the present formulation is that the constitutive equations are expressed in weak form also all fields are then independently discretized in terms of so called generalized variables the result is a set of non linear algebraic equations a subset of which can be interpreted as the backward difference time integrated constitutive law of the finite element an iterative procedure where all calculations are at the element and not at the gauss point level resting on newton raphson scheme is proposed for the solution of the governing equations it is shown how the customary displacement approach and also some other mixed formulations in elastoplasticity can be regarded as special cases of the present formulation

a fixed point approach to stable matchings and some applications we describe a fixed point based approach to the theory of bipartite stable matchings by this we provide a common framework that links together seemingly distant results like the stable marriage theorem of gale and shapley the mendelsohn dulmage theorem the kundu lawler theorem tarski s fixed point theorem the cantor bernstein theorem pym s linking theorem or the monochromatic path theorem of sands et al in this framework we formulate a matroid generalization of the stable marriage theorem and study the lattice structure of generalized stable matchings based on the theory of lattice polyhedra and blocking polyhedra we extend results of vande vate and rothblum on the bipartite stable matching polytope

a consistent control of spurious singular modes in the 9 node lagrange element for the laplace and mindlin plate equations abstract when 2 2 quadrature is used with the 9 node lagrange element which is essential in c 0 plate elements to avoid locking spurious singular modes appear on the element level which can lead to singularity or near singularity of the global equations here these modes are controlled by a procedure that introduces additional generalized stresses and strains so that the spurious modes are eliminated and the consistency of the resulting finite difference equations is not impaired hence the procedure passes the patch test applications to the diffusion and mindlin plate equations are presented results show that h 3 convergence in the l 2 norm is almost retained

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

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

three fast algorithms for four problems in stable marriage the stable marriage problem is a well known problem of matching n men to n women to achieve a certain type of stability the o n 2 time gale shapley gs algorithm for finding two particular but extreme stable marriages out of a possibly exponential number of stable marriages is also well known in this paper we consider four problems concerned with finding information about the set of all stable marriages and with finding stable marriages other than those obtained by the gale shapley algorithm in particular we give an o n 2 time algorithm which for any problem instance of n men and n women finds every man woman pair that is contained in at least one stable marriage we show that the same algorithm finds all the rotations for the problem instance in o n 2 time we give an o n 2 n s time and o n 2 space bounded algorithm which is time and space optimal to enumerate all stable marriages where s is the set of them and we give an o n 2 time algorithm to find the mini

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 family of hybrid plate elements hybrid stress elements are known to provide accurate results for analyses of plate bending in particular for the prediction of moment distribution the construction of hybrid stiffness matrix requires numerical inversion of a moment matrix evaluation of some relatively complicated boundary integrals and several matrix transformations each of these operations can be time consuming and the matrix inversion can result in a loss of numerical accuracy this paper devises methods to explicitly invert the moment matrices we find that for triangular elements the inverse is independent of the element shape and is only inversely proportional to its size we also use a novel set of displacement variables which greatly simplifies the boundary integration the displacement variables are chosen in a hierarchical form so that lower order elements can be determined by straightforward reduction of excess terms in a higher order element except for the nodal displacements at the vertices the present approach involves only variables at the midpoints of the sides of an element

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 new triangular discrete kirchhoff plate shell element we present a new 6 node triangular bending element called dktp based on a discrete kirchhoff model a corresponding new flat shell element dltp having quadratic variation of in plane displacement is also presented this element has 6 degrees of freedom u v w x y z at each corner node and 3 degrees of freedom u v w at each mid side node detailed numerical experimentation is presented to demonstrate the efficiency and reliability of these elements

courtship and linear programming this paper demonstrates that the celebrated gale shapley algorithm for obtaining stable matchings in stable marriage problems is essentially an application of the dual simplex method