advantages of the mixed format in geometrically nonlinear analysis of beams and shells using solid finite elements summary the paper deals with two main advantages in the analysis of slender elastic structures both achieved through the mixed stress and displacement format with respect to the more commonly used displacement one i the smaller error in the extrapolations usually employed in the solution strategies of nonlinear problems and ii the lower polynomial dependence of the problem equations on the finite element degrees of freedom when solid finite elements are used the smaller extrapolation error produces a lower number of iterations and larger step length in path following analysis and a greater accuracy in koiter asymptotic method to focus on the origin of the phenomenon the two formats are derived for the same finite element interpolation the reduced polynomial dependence improves the koiter asymptotic strategy in terms of both computational efficiency accuracy and simplicity copyright 2016 john wiley sons ltd

stress resultant geometrically nonlinear shell theory with drilling rotations part i a consistent formulation abstract in this work we present a consistent theoretical framework for a novel stress resultant geometrically nonlinear shell theory the main feature of the present shell theory development which stands in contrast with the classical developments in the shell theory is the presence of a rotation component around the shell normal so called drilling rotation in the description of shell finite rotations the relationship of the proposed theory with a finite deformation theory of a three dimensional continuum with independent rotation field is clearly identified the latter is shown to be an important link which facilitates the proper choice of the shell constitutive model and a proper construction of the regularized form of the theory capable of supporting the drilling rotations the corresponding linearized form of the present shell theory is discussed in the closure

the role of symmetry in the post buckling behaviour of structures symmetry plays an integral role in the post buckling analysis of elastic structures we show that the post buckling response of engineering systems with given symmetry properties can be described u

derivatives of tangential stiffness matrices for equilibrium path descriptions the paper describes how several procedures based on expressions from analytical elastic stability theory are introduced as numerical tools in a general finite element program for geometrically non linear structural analysis especially is discussed how derivatives of the tangential stiffness matrix can be utilized in several contexts in the solution algorithm these include improved predictions for the step wise solution of equilibrium states identification of critical points and accurate descriptions of initial post bifurcation behaviour for two plane beam and bar elements formulations have been developed giving analytical expressions for these derivatives the corresponding numerical approximations needed in other element types are also discussed the paper discusses the relative efficiency of higher order predictions in relation to these different element types and different solution strategies some numerical examples showing different types of behaviour are analysed and discussed

weighted extended b spline approximation of dirichlet problems we describe a new finite element method which uses weighted extended b splines on a regular grid as basis functions for solving dirichlet problems on bounded domains in arbitrary dimensions this web method does not require any grid generation and can be implemented very efficiently it yields smooth high order accurate approximations with relatively low dimensional subspaces

spherical functions on homogeneous superspaces homogeneous superspaces arising from the general linear supergroup are studied within a hopf algebraic framework spherical functions on homogeneous superspaces are introduced and the structures of the superalgebras of the spherical functions on classes of homogeneous superspaces are described explicitly

normal modes for non linear vibratory systems a methodology is presented which extends to non linear systems the concept of normal modes of motion which is well developed for linear systems the method is constructive for weakly non linear systems and provides the physical nature of the normal modes along with the non linear differential equations which govern their dynamics it also provides the non linear co ordinate transformation which relates the original system co ordinates to the modal co ordinates using this transformation we demonstrate how an approximate non linear version of superposition can be employed to reconstruct the overall motion from the individual non linear modal dynamics the results presented herein for non linear systems reduce to modal analysis for the linearized system when non linearities are neglected even though the approach is entirely different from the traditional one the tools employed are from the theory of invariant manifolds for dynamical systems and were inspired by the center manifold reduction technique in this paper the basic ideas are outlined a few examples are presented and some natural extensions and applications of the method are briefly described in the conclusions

asymptotic study of the elastic postbuckling behavior of structures by the finite element method abstract within the framework of finite element analysis an asymptotic method is presented for the study of geometrically nonlinear static behavior of thin structures under one parameter conservative loading the method can be applied when the prebuckling behavior is moderately non linear so that the bifurcation analysis is no longer accurate enough an iterative process makes it possible to find suitable deformation modes which enable a good approximation of the structural behavior around the buckling point as in the rayleigh ritz approach a reduced energy can be formulated with only a small number of generalized degrees of freedom the influence of small initial imperfections on the buckling load can easily be analyzed as in koiter s asymptotic method a comprehensive treatment and several improvements of this asymptotic iterative method are given and selected examples illustrate the basic features of the method

classification of all star irreps of gl m n all the finite dimensional star irreps of gl m n are classified in terms of their highest weights thereby completing the classification of all finite dimensional star irreps of the basic classical lie superalgebras the lowest weights of such irreps are determined explicitly and it is shown that the contravariant and covariant tensor irreps of gl m n are star irreps of type 1 and 2 respectively this explains the applicability of the young diagram method to these two classes of representations however it is shown that one parameter families of typical star irreps occur that are intrinsically different from the tensorial irreps

implicit boundary method for finite element analysis using non conforming mesh or grid in the finite element method fem a mesh is used for representing the geometry of the analysis and for representing the test and trial functions by piece wise interpolation recently analysis techniques that use structured grids have been developed to avoid the need for a conforming mesh the boundaries of the analysis domain are represented using implicit equations while a structured grid is used to interpolate functions such a method for analysis using structured grids is presented here in which the analysis domain is constructed by boolean combination of step functions implicit equations of the boundary are used in the construction of trial and test functions such that essential boundary conditions are guaranteed to be satisfied furthermore these functions are constructed such that internal elements through which no boundary passes have the same stiffness matrix this approach has been applied to solve linear elastostatic problems and the results are compared with analytical and finite element analysis solutions to show that the method gives solutions that are similar to the fem in quality but is less computationally expensive for dense mesh grid and avoids the need for a conforming mesh copyright 2007 john wiley sons ltd

the general linear supergroup and its hopf superalgebra of regular functions abstract the structure of the hopf superalgebra b of regular functions on the general linear supergroup is developed and applied to study the representation theory of the supergroup it is shown that the general linear supergroup can be reconstructed from b in a way reminiscent of the tannaka krein theory a borel weil type realization is also obtained for the irreducible integrable representations as a side result on the structure of b schur superalgebras are introduced and are shown to be semi simple over the complex field with the simple ideals determined explicitly

genuinely resultant shell finite elements accounting for geometric and material non linearity the underlying theory is statically and geometrically exact and it naturally includes small strain and finite strain problems of thin as well as thick shells this paper examines the development of computational procedures employing the newton kantorovich linearization process and the galerkin type discretization method the treatment of finite rotations through an arbitrary parametrization of the rotation group the interpolation procedure of so 3 valued functions underlying the construction of finite element basis

a mathematical and numerical study of the sensitivity of a reduced order model by pod rom pod for a 2d incompressible fluid flow abstract in this work we present contributions concerning a mathematical study of the sensitivity of a reduced order model rom by the proper orthogonal decomposition pod technique applied to a quasi linear parabolic equation in particular we apply our theoretical study to the navier stokes equations for a 2d incompressible fluid flow we present a numerical test of our theoretical result for an unsteady fluid flow in a channel around a circular cylinder

weak imposition of essential boundary conditions in the finite element approximation of elliptic problems with non matching meshes this is the accepted version of the following article codina r and baiges j 2015 weak imposition of essential boundary conditions in the finite element approximation of elliptic problems with non matching meshes int j numer meth engng 104 624 654 doi 10 1002 nme 4815 which has been published in final form at http onlinelibrary wiley com doi 10 1002 nme 4815 abstract

asymptotic post buckling fem analysis using corotational formulation finite element asymptotic post buckling analysis being based on fourth order expansions of the strain energy requires that nonlinear structural modeling be accurate to same order at least with respect to the rigid motions of the elements a corotational description is proposed here as a general tool to satisfy this requirement of objectivity by referring each element to a local frame which moves rotates with the element so filtering its rigid motion in this description nonlinearity of the problem derives essentially from the change of reference from the global fixed frame to the local one the strain energy being governed by their relative rotations in finite kinematics this noticeably complicates the algebra for obtaining exact expressions of its variations quite simple basic expressions for the first four corotational derivatives of the strain energy are provided allowing the set up of a fourth order accurate asymptotic analysis starting from standard finite elements based on linear or simplified nonlinear local modelings the formulation is implemented for the analysis of 3d beam assemblages and several numerical results are presented and discussed showing the effectiveness and robustness of the proposed approach in reproducing the nonlinear equilibrium path in both cases of monomodal and coupled multimodal buckling

the koiter newton approach using von karman kinematics for buckling analyses of imperfection sensitive structures the koiter newton approach is a reduced basis method for nonlinear structural analyses the method combines koiter s approach as a predictor step and the newton arc length technique as a corrector step to trace the entire load displacement equilibrium path of a structure in a step by step manner this computationally highly efficient and accurate solution method has recently demonstrated a superior performance in nonlinear analyses compared to standard techniques in this paper we propose an extension to buckling imperfection sensitivity analyses exploiting the method s stability and reliability we present two different modeling techniques for imperfection loads that both profit from the koiter newton approach reducing the initial computation steps to a small fraction thereof we introduce von karman kinematics which neglect some nonlinear terms of the green strain displacement relations to further increase the computational efficiency of the analysis by an essential reduction of the computation effort required to obtain higher order derivatives of the strain energy using various numerical examples and benchmark tests we demonstrate the overall high quality and performance of the proposed method

the first fundamental theorem of invariant theory for the orthosymplectic super group we give an elementary and explicit proof of the first fundamental theorem of invariant theory for the orthosymplectic supergroup by generalising the geometric method of atiyah bott and patodi to the supergroup context we use methods from super algebraic geometry to convert invariants of the orthosymplectic supergroup into invariants of the corresponding general linear supergroup on a different space in this way super schur weyl brauer duality is established between the orthosymplectic supergroup of superdimension m 2n and the brauer algebra with parameter m 2n the result may be interpreted either in terms of the group scheme osp v over mathbb c where v is a finite dimensional super space or as a statement about the orthosymplectic lie supergroup over the infinite dimensional grassmann algebra lambda we take the latter point of view here and also state a corresponding theorem for the orthosymplectic lie superalgebra which involves an extra invariant generator the super pfaffian

a method for interpolating on manifolds structural dynamics reduced order models a rigorous method for interpolating a set of parameterized linear structural dynamics reduced order models roms is presented by design this method does not operate on the underlying set of parameterized full order models hence it is amenable to an online real time implementation it is based on mapping appropriately the rom data onto a tangent space to the manifold of symmetric positive definite matrices interpolating the mapped data in this space and mapping back the result to the aforementioned manifold algorithms for computing the forward and backward mappings are offered for the case where the roms are derived from a general galerkin projection method and the case where they are constructed from modal reduction the proposed interpolation method is illustrated with applications ranging from the fast dynamic characterization of a parameterized structural model to the fast evaluation of its response to a given input in all cases good accuracy is demonstrated at real time processing speeds copyright 2009 john wiley sons ltd

imposing essential boundary conditions in mesh free methods imposing essential boundary conditions is a key issue in mesh free methods the mesh free interpolation does not verify the kronecker delta property and therefore the imposition of prescribed values is not as straightforward as for the finite element method the aim of this paper is to present a general overview on the existing techniques to enforce essential boundary conditions in galerkin based mesh free methods special attention is paid to the mesh free coupling with finite elements for the imposition of prescribed values and to methods based on a modification of the galerkin weak form particular examples are used to analyze and compare their performance in different situations

koiter s analysis of thin walled structures by a finite element approach summary this paper refers to the analysis of the postbuckling behaviour of thin walled structures by means of an asymptotic approach based on a finite element implementation of koiter s non linear theory of instability the analysis has been accomplished by using the following assumptions i the structure is described as an assemblage of flat slender rectangular panels ii a non linear kirchhoff type plate theory is used to model each panel iii hc finite elements discretization is used iv linear and quadratic extrapolations are assumed for the fundamental and the postbuckling paths respectively v multimodal buckling is considered and vi imperfection sensitivity analysis is performed in both multimodal and monomodal form based on the steepest descent path criterion several numerical results are presented and discussed comparisons with numerical solution obtained by standard incremental codes are given which show the accuracy and reliability of the proposed approach

the hp d adaptive finite cell method for geometrically nonlinear problems of solid mechanics summary the finite cell method fcm combines the fictitious domain approach with the p version of the finite element method and adaptive integration for problems of linear elasticity it offers high convergence rates and simple mesh generation irrespective of the geometric complexity involved this article presents the integration of the fcm into the framework of nonlinear finite element technology however the penalty parameter of the fictitious domain is restricted to a few orders of magnitude in order to maintain local uniqueness of the deformation map as a consequence of the weak penalization nonlinear strain measures provoke excessive stress oscillations in the cells cut by geometric boundaries leading to a low algebraic rate of convergence therefore the fcm approach is complemented by a local overlay of linear hierarchical basis functions in the sense of the hp d method which synergetically uses the h adaptivity of the integration scheme numerical experiments show that the hp d overlay effectively reduces oscillations and permits stronger penalization of the fictitious domain by stabilizing the deformation map the hp d adaptive fcm is thus able to restore high convergence rates for the geometrically nonlinear case while preserving the easy meshing property of the original fcm accuracy and performance of the present scheme are demonstrated by several benchmark problems in one two and three dimensions and the nonlinear simulation of a complex foam sample copyright 2011 john wiley sons ltd

a cartesian grid embedded boundary method for poisson s equation on irregular domains we present a numerical method for solving poisson s equation with variable coefficients and dirichlet boundary conditions on two dimensional regions the approach uses a finite volume discretization which embeds the domain in a regular cartesian grid we treat the solution as a cell centered quantity even when those centers are outside the domain cells that contain a portion of the domain boundary use conservative differencing of second order accurate fluxes on each cell volume the calculation of the boundary flux ensures that the conditioning of the matrix is relatively unaffected by small cell volumes this allows us to use multigrid iterations with a simple point relaxation strategy we have combined this with an adaptive mesh refinement amr procedure we provide evidence that the algorithm is second order accurate on various exact solutions and compare the adaptive and nonadaptive calculations

composition factors of kac modules for the general linear lie superalgebras the composition factors of kac modules for the general linear lie superalgebras open image in new window are explicitly determined in particular a conjecture of hughes king and van der jeugt in j math phys 33 1992 470 491 is proved

weak coupling for isogeometric analysis of non matching and trimmed multi patch geometries nitsche s method can be used as a coupling tool for non matching discretizations by weakly enforcing interface constraints we explore the use of weak coupling based on nitsche s method in the context of higher order and higher continuity b splines and nurbs we demonstrate that weakly coupled spline discretizations do not compromise the accuracy of isogeometric analysis we show that the combination of weak coupling with the finite cell method opens the door for a truly isogeometric treatment of trimmed b spline and nurbs geometries that eliminates the need for costly reparameterization procedures we test our methodology for several relevant technical problems in two and three dimensions such as gluing together trimmed multi patches and connecting non matching meshes that contain b spline basis functions and standard triangular finite elements the results demonstrate that the concept of nitsche based weak coupling in conjunction with the finite cell method has the potential to considerably increase the flexibility of the design through analysis process in isogeometric analysis

discussion about parameterization in the asymptotic numerical method application to nonlinear elastic shells abstract the asymptotic numerical method anm is a family of algorithms for path following problems based on the computation of truncated vectorial series with respect to a path parameter a b cochelin n damil m potier ferry methode asymptotique numerique hermes lavoisier paris 2007 in this paper we discuss and compare three concepts of parameterizations of the anm curves i e the definition of the path parameter a the first concept is based on the classical arc length parameterization e riks some computational aspects of the stability analysis of nonlinear structures computer methods in applied mechanics and engineering 47 1984 219 259 the second is based on the so called local parameterization w c rheinboldt j v burkadt a locally parameterized continuation acm transaction on mathematical software 9 1983 215 235 r seydel a tracing branches world of bifurcation online collection and tutorials of nonlinear phenomena http www bifurcation de 1999 j j gervais h sadiky a new steplength control for continuation with the asymptotic numerical method iam j numer anal 22 no 2 2000 207 229 and the third is based on a minimization condition of a rest s lopez an effective parametrization for asymptotic extrapolation computer methods in applied mechanics and engineering 189 2000 297 311 we demonstrate that the third concept is equivalent to a maximization condition of the anm step lengths to illustrate the performance of these proposed parameterizations we give some numerical comparisons on nonlinear elastic shell problems

a nitsche type formulation and comparison of the most common domain decomposition methods in isogeometric analysis this paper provides a detailed elaboration and assessment of the most common domain decomposition methods for their application in isogeometric analysis the methods comprise a penalty approach lagrange multiplier methods and a nitsche type method for the nitsche method a new stabilized formulation is developed in the context of isogeometric analysis to guarantee coercivity all these methods are investigated on problems of linear elasticity and eigenfrequency analysis in 2d in particular focus is put on non uniform rational b spline patches which join nonconformingly along their common interface thus the application of isogeometric analysis is extended to multi patches which can have an arbitrary parametrization on the adjacent edges moreover it has been shown that the unique properties provided by isogeometric analysis that is high order functions and smoothness across the element boundaries carry over for the analysis of multiple domains copyright 2013 john wiley sons ltd

a fictitious domain method for dirichlet problem and applications abstract in this article we discuss the solution of the dirichlet problem for a class of elliptic operators by a lagrange multiplier fictitious domain method this approach allows the use of regular grids and therefore of fast specialized solvers for problems on complicated geometries the resulting saddle point system can be solved by an uzawa conjugate gradient algorithm in the case of two dimensional problems a quasi optimal preconditioner has been found by fourier analysis and numerical experiments confirm its nice scaling properties the resulting methodology is applied to a nonlinear time dependent problem namely the flow of a viscous plastic medium in a cylindrical pipe showing the potential of this methodology for some classes of nonlinear problems

an accurate and efficient implementation of initial geometrical imperfections in the predictor corrector reduced order modeling method abstract a predictor corrector reduced order modeling method based on koiter theory is proposed for nonlinear buckling analysis of thin walled structures with initial geometric imperfections the imperfections are implemented into the von karman kinematics and are considered using an a priori and a posteriori manners respectively in buckling analysis since the nonlinear predictor obtained from the reduced order model with imperfections provides a fairly large step size in path tracing the a priori account of imperfections still shows advantages in computational efficiency the advantages are more significant when considering a posteriori the effects of imperfections in the reduced order model of the structure without imperfections which means building once and for all by simply adding some independent imperfection terms in the reduced system the a posteriori accounts of imperfections with the first second order accuracies are developed respectively to deal with the linear nonlinear prebuckling behaviors and small large imperfection amplitudes the good performance of the proposed method in terms of reliability accuracy and computational effort is demonstrated with several examples using the linear buckling modes or measured geometric shapes as whole field geometric imperfections

high order predictor corrector algorithms new predictor corrector algorithms are presented for the computation of solution paths of non linear partial differential equations the predictors and the correctors are based on perturbation techniques and pade approximants this extends the asymptotic numerical method anm which is an efficient high order continuation technique without corrector the efficiency and the reliability of the new technique are assessed by several examples within thin shell theory and navier stokes equations many variants have been tested to establish an optimal algorithm

a comparison of three algorithms for tracing nonlinear equilibrium paths of structural systems the relative efficiencies of the riks wempner crisfield and normal flow solution algorithms for tracking nonlinear equilibrium paths of structural systems are compared it is argued that the normal flow algorithm may be both more computationally efficient and more robust compared to the other two algorithms when tracing the path through severe nonlinearities such as those associated with structural collapse this is demonstrated qualitatively by comparing the relative behaviors of each algorithm in the vicinity of a severe nonlinearity quantitative results are presented for the collapse a blade stiffened panel

invariant supersymmetric multilinear forms and the casimir elements of p type lie superalgebras the casimir elements of the p type lie superalgebras are investigated depending on the class of algebras under consideration either there do not exist any nontrivial casimir elements at all or else the casimir elements are highly degenerate basic to the investigation is a lemma about invariant supersymmetric multilinear forms on a finite dimensional module over a lie superalgebra some comments on the cartan subalgebras of a lie superalgebra are also included an appendix provides some information on multilinear algebra with e commuting scalars

indecomposable representations of special linear lie superalgebras abstract the main result of this paper is a classification of finite dimensional representations of the lie superalgebras sl m 1 of supertraceless endomorphisms of the vector superspace of dimension m 1 the classification extends to the so called singly atypical blocks of the lie superalgebras sl m n but there exist wild representation type blocks as soon as bothmandnare 2

invariant integration on classical and quantum lie supergroups invariant integrals on hopf superalgebras in particular the classical and quantum lie supergroups are studied the uniqueness up to scalar multiples of a left integral is proved and a z2 graded version of maschke s theorem is discussed a construction of left integrals is developed for classical and quantum lie supergroups applied to several classes of examples the construction yields the left integrals in explicit form

goal oriented model constrained optimization for reduction of large scale systems optimization oriented reduced order models should target a particular output functional span an applicable range of dynamic and parametric inputs and respect the underlying governing equations of the system to achieve this goal we present an approach for determining a projection basis that uses a goal oriented model constrained optimization framework the mathematical framework permits consideration of general dynamical systems with general parametric variations and is applicable to both linear and nonlinear systems results for a simple linear model problem of the two dimensional heat equation demonstrate the ability of the goal oriented approach to target a particular output functional of interest application of the methodology to a more challenging example of a subsonic blade row governed by the unsteady euler flow equations shows a significant advantage of the new method over the proper orthogonal decomposition

structure and representations of the quantum general linear supergroup the structure and representations of the quantum general linear supergroup gl q m n are studied systematically by investigating the hopf superalgebra g q of its representative functions g q is factorized into g q pi g q bar pi and a peter weyl basis is constructed for each factor parabolic induction for the quantum supergroup is developed the underlying geometry of induced representations is discussed and an analog of frobenius reciprocity is obtained a quantum borel weil theorem is proven for the irreducible covariant and contravariant tensorial representations and explicit realizations are given for classes of irredducible tensorial representatins in terms of sections of quantum super vector bundles over quantum projective superspaces

effectiveness of linear bifurcation analysis for predicting the nonlinear stability limits of structures as an effort to predict effectively the actual collapse load of a structure a series of numerical studies on the stability of shell structures are made the difference in formulation between the two types of linear buckling loads the classical and the fully linearized is first demonstrated their correlations with respect to the actual stability limit of the structure are compared and finally the two types of critical load approximations are obtained at various stages of a nonlinear analysis to study the pattern of convergence to the actual collapse load it is found that the fully linearized buckling analysis when combined with nonlinear analysis can serve as a useful tool for prediction of the stability limit of a structure while for most types of structures the approximation is within engineering accuracy the rate of convergence of the extrapolated critical load also gives some insight to the accuracy of the approximation

asymptotic numerical methods and pade approximants for non linear elastic structures in this paper we apply asymptotic numerical methods for computing non linear equilibrium paths of elastic beam plate and shell structures the non linear branches are sought in the form of asymptotic expansions and they are determined by solving numerically fem several linear problems with a single stiffness matrix a large number of terms of the series can be easily computed by using recurrence formulas in comparison with a more classical step by step procedure the method is rapid and automatic we show with some examples that the choice of the expansion s parameter and the use of pade approximants play an important role in the determination of the size of the domain of convergence

cohomology of lie superalgebras m n and 2 2n we explicitly compute the first and second cohomology groups of the classical lie superalgebras mathfrak sl m n and mathfrak osp 2 2n with coefficients in the finite dimensional irreducible modules and the kac modules we also show that the second cohomology groups of these lie superalgebras with coefficients in the respective universal enveloping algebras under the adjoint action vanish the latter result in particular implies that the universal enveloping algebras rm u mathfrak sl m n and rm u mathfrak osp 2 2n do not admit any non trivial formal deformations of gerstenhaber type

the first fundamental theorem of invariant theory for the orthosymplectic supergroup we give an elementary and explicit proof of the first fundamental theorem of invariant theory for the orthosymplectic supergroup by generalising the geometric method of atiyah bott and patodi to the supergroup context we use methods from super algebraic geometry to convert invariants of the orthosymplectic supergroup into invariants of the corresponding general linear supergroup on a different space in this way super schur weyl brauer duality is established between the orthosymplectic supergroup of superdimension m 2n and the brauer algebra with parameter m 2n the result may be interpreted either in terms of the group scheme osp v over mathbb c where v is a finite dimensional super space or as a statement about the orthosymplectic lie supergroup over the infinite dimensional grassmann algebra lambda we take the latter point of view here and also state a corresponding theorem for the orthosymplectic lie superalgebra which involves an extra invariant generator the super pfaffian

asymptotic numerical method for buckling analysis of shell structures with large rotations in this paper the buckling and post buckling of elastic structures taking into account large rotations are investigated using an asymptotic numerical method the critical points are detected by two different ways first by a bifurcation indicator second by analysing the poles of a pade approximant the first step of the post buckling branch is computed starting from the bifurcation point and using an extended system the remaining bifurcating branch is followed by the same algorithm as for the fundamental path several examples are tested to show the effectiveness of the proposed method

weak impositions of dirichlet boundary conditions in solid mechanics a critique of current approaches and extension to partially prescribed boundaries abstract in this article we first review various approaches developed to date for the weak imposition of dirichlet boundary conditions in fictitious domain analysis for elasticity problems the hellinger reissner h r principle the linked lagrange multiplier llm method the implicit boundary method and the fat boundary method are discussed along with the well known lagrange multiplier penalty and nitsche s methods we state these approaches in a common form starting with energy functionals and weak forms and discretise using the fictitious domain finite element method previous formulations of these methods were in general developed for full prescription along the dirichlet boundary which generally implies no local effect of boundary inclination however partially prescribed conditions such as the structural roller boundary condition with inclination have wide practical applications in engineering here we provide techniques of imposing such boundary conditions in these methods in detail for those methods that contain algorithmic parameters such as the penalty and nitsche s methods extra computation or empirical estimation is necessary to decide values of the parameters and hence we discuss parametric and convergence behaviours through numerical examples to provide guidance on the choice of parameters

mode jumping and attractive paths in multimode elastic buckling this paper summarizes a part of the first author s ph d thesis completely devoted to multimode elastic buckling within an fem strategy the theoretical arguments unfold among critical points on radial paths the unique post critical paths variationally defined algebraic characterizations proposition demonstrations and so on by aiming to prove that the complexity of the phenomenon of multimode buckling secondary bifurcations post critical attractive paths can be theoretically explained 1997 by john wiley sons ltd

an effective parametrization for asymptotic extrapolations abstract when considering the range of validity of asymptotic expansions the choice of the expansion parameter plays an essential role in effect with the exception of a posteriori adjustments of the expansion components the definition of this parameter is the only way of improving the approximation at a finite distance from the initial point good parametrization equations are usually obtained by norms that involve all variables of the problem or based on the nature of the mechanical phenomena here this equation is constructed following the criteria of reducing the residual error and at the same time exactly reproducing solutions that admit a polynomial second degree representation that choice is automatic in the analysis and improves the domain of accurate approximations an appropriate predictor corrector scheme was implemented to compare extrapolations obtained by this and several standard parametrizations the solution scheme was used to analyse geometrically nonlinear plane frame structures

an arc length method including line searches and accelerations this paper describes a method for introducing line searches into the arc length solution procedure such line searches may be used at each iteration to calculate an optimum scalar step length which scales the normal iterative vector in practice a loose tolerance is provided so that on many iterations the line searches are avoided however on difficult iterations the line searches are shown to lead to a substantial improvement in the convergence characteristics a simple single parameter acceleration is also developed using line search concepts the new arc length method is applied to both the geometrically nonlinear analysis of shallow shells and the materially nonlinear analysis of reinforced concrete beams and slabs significant improvements are demonstrated in relation to the standard arc length method

hook young diagrams with applications to combinatorics and to representations of lie superalgebras definition et etude des tableaux k l semi standards applications a la combinatoire et aux representations des superalgebres de lie des diagrammes de young a crochets