an efficient method for simulation of noisy coupled multi dimensional oscillators we present an efficient computational method for the study of populations of noisy coupled oscillators by taking a population density approach in which the probability density of observing an oscillator at a point of state space is the primary variable instead of the states of all of the oscillators we are able to seamlessly account for intrinsic noise within the oscillators and global coupling within the population the population is assumed to consist of a large number of oscillators so that the noise process is well sampled over the population our numerical method is able to solve the governing equation even in the challenging case of limit cycle oscillators with a large number of state variables instead of simulating a prohibitive number of oscillators our particle method simulates relatively few particles allowing for the efficient solution of the governing equation

a simplified finite element method for large deformation post buckling analyses of large frame structures using explicitly derived tangent stiffness matrices in this paper a simplified economical and highly accurate method for large deformation post buckling analyses of frame type structures is presented using the concepts of polar decomposition of deformation an explicit expression for the tangent stiffness matrix of a member element of the frame that accounts for the nonlinear bending stretching coupling is derived in closed form at any point in the load deformation path the ranges of validity of the present simplified approach are discussed several example problems to demonstrate the feasibility of the present approach over ranges of deformation that are well beyond those likely to occur in practical large frame structures are included

method of quantum characters in equivariant quantization let g be a reductive lie group g its lie algebra and m a g manifold suppose h m is a h g equivariant quantization of the function algebra m on m we develop a method of building h g equivariant quantization on g orbits in m as quotients of h m we are concerned with those quantizations that may be simultaneously represented as subalgebras in h g and quotients of h m it turns out that they are in one to one correspondence with characters of the algebra h m we specialize our approach to the situation g gl n m end n and h m the so called reflection equation algebra associated with the representation of h g on n for this particular case we present in an explicit form all possible quantizations of this type they cover symmetric and bisymmetric orbits we build a two parameter deformation family and obtain as a limit case the g equivariant quantization of the kirillov kostant souriau bracket on symmetric orbits

vortex methods and vortex motion vortex phenomena in fluid flows and the experimental theoretical and numerical methods used to characterize them are discussed in reviews by leading experts chapters are devoted to an overview of vortex methods the convergence of vortex methods graphic displays from numerical simulations physical vortex visualizations the four principles of vortex motion the visualization and computation of hovering mode vortex dynamics turbulence and vortices in superfluid he and statistical mechanics approaches to vortices and turbulence extensive photographs and sample computer graphics are provided

computational methods for inverse finite elastostatics abstract in the inverse motion problem in finite hyper elasticity the classical formulation relies on conservation laws based on eshelby s energy momentum tensor this formulation is shown to be lacking in several regards for a particular class of inverse motion problems where the deformed configuration and cauchy traction are given and the undeformed configuration must be calculated it is shown that for finite element calculations a simple re examination of the equilibrium equations provides a more suitable finite element formulation this formulation is also shown to involve only minor changes to existing elements designed for forward motion calculations examples illustrating the method in simple and complex situations involving a neo hookean material are presented

a robust riks like path following method for strain actuated snap through phenomena in soft solids abstract in this paper a practical and robust riks like path following method is developed to automatically trace the nonlinear equilibrium path for initial finite strain induced snap through phenomena in soft solids the deformation gradient is decomposed into an elastic part and an initial strain part where the initial strain is characterized through a prescribed pattern tensor and an unknown strain factor describing the magnitude in the non linear finite element fe solution scheme an equivalent body force proportional to the increment of the strain factor is derived which varies in each iteration step due to its dependence on deformed configuration and stress both the displacement and the strain factor increments are introduced as unknowns in the linearized equation which permits to predict the critical equilibrium states before and after the snap through several examples with various configurations and strain histories are constructed including multilayer beams and film substrate systems which demonstrate the effectiveness and robustness of the algorithm to capture the strain induced snap through phenomena

work increment control method for non linear analysis to perform non linear structural analysis including large displacements and rotations requires evaluation of the non linear equilibrium equations a quadratically converging fixed point iteration scheme referred to as the work increment control solution method is presented to iteratively evaluate the non linear algebraic equations the work increment control method is superior in many respects to other published solution strategies

fast adaptive 2d vortex methods we present a new approach to vortex methods for the 2d euler equations we obtain long time high order accuracy at almost optimal cost by using three tools fast adaptive quadrature rules a free lagrangian formulation and a useful new analysis of the consistency error our error analysis halves the order of differentiability required of the flow and suggests an efficient new balance of smoothing parameters which works well with fast summation schemes numerical experiments with our methods confirm our theoretical predictions and display excellent long time accuracy

quantization of borderline levi conjugacy classes of orthogonal groups we construct an equivariant quantization of a special family of levi conjugacy classes of the complex orthogonal group so n whose stabilizer contains a cartesian factor so 2 so p 1 p n p n mod 2

mixed formulation and locking in path following nonlinear analysis abstract the arc length riks strategy has rapidly become a standard tool for path following analysis of nonlinear structures due to its theoretical ability to surpass limit points the aim of this paper is to show that the failures in convergence that are occasionally experienced are not related to proper defects of the algorithm but come from a subtle locking effect intrinsic to the nonlinear nature of the problem as a consequence its sanitization has to be pursued within a reformulation of the structural model the use of a mixed stress displacement variant of the algorithm in particular appears very promising in this respect the topic is discussed with reference to the analysis of nonlinear frames using a mixed version of the nonlinear beam model discussed in 39 it is shown that with no extra computational cost and only a minor modification in coding with respect to a purely compatible formulation it is possible to achieve a noticeable improvement in convergence and a real gain in both computational time and overall robustness of the algorithm

a hybrid method for efficient solution of geometrically nonlinear structures abstract we propose a novel hybrid method for calculating accurate responses of geometrically nonlinear structures exhibiting complex snap through and snap back behaviours the proposed method employs a hybrid evolutionary algebraic method to obtain each point of the equilibrium path where the equilibrium is formulated generally as a minimisation problem genetic algorithm and nelder mead simplex methods are used together as the hybrid optimiser to obtain any arbitrary point of the equilibrium path we only need a series of sparse matrix to vector multiplications and do not require information about previous equilibrium states the assembly of tangent stiffness matrix the solution of a set of system of linear equations or factorisation processes both primary and secondary paths can be followed in addition utilising the tangent stiffness matrix this method can effectively find both the limit and bifurcation points directly the state of non proportional loading can also be considered successfully additionally we show how to generate the solution of a structure whose geometrical and mechanical properties vary slightly starting from the original solution finally to demonstrate the efficiency and capabilities of the present approach three examples that are well known for their complex snap through snap back load deflection curves are comprehensively studied and the results obtained are compared with those reported in the literature

an orthogonal residual procedure for non linear finite element equations a general and robust solution procedure for non linear finite element equations with limit points is developed at each equilibrium iteration the magnitude of the load is adjusted such that the residual force is orthogonal to the current displacement increment from the last equilibrium state the method implements the physical condition that the orthogonal residual force will neither increase nor decrease the magnitude of the current displacement increment vector the orthogonality condition is formulated directly in terms of conjugate variables and therefore does not contain any scaling parameters passage of load and displacement limit points is discussed as well as the relation to line search minimum residual and arc length methods the method is illustrated by two examples

stability boundaries of two parameter non linear elastic structures abstract the load bearing capacity of structures can be influenced by variations in parameters such as initial geometric defects multi parameter loadings material specifications and temperature this paper aims to introduce a new formulation to trace the stability boundaries of two parameter elastic structures the proposed procedure can find a set of critical points both limit and bifurcation ones via a modified newton s method in the authors formulation the residual force is set to zero and a critically constraint is satisfied simultaneously numerical examples presented in this paper demonstrate the efficiency of the suggested method

the dynamics of an elastic membrane using the impulse method a validation study of the impulse method applied to the motion of a closed elastic membrane under tension separating two incompressible inviscid fluids in two dimensions is presented the approach consists of a nonlinear analysis based on a small amplitude perturbation of an exact solution the equations of motion for the fourier coefficients of the solution are developed to two orders beyond the leading order problem the nonlinear terms in the equations depict the coupling of the fourier modes and account for the temporal variation of the tension the last order of the expansion is used to compute frequency corrections to the driving modes solutions for various problems are found and compared with a numerical method based on impulse variables the results show that the numerical periods and amplitudes of the oscillations approach the values predicted by the perturbation analysis as the numerical smoothing parameter is reduced this validates the use of impulse methods for free boundary motion with surface forces

stability of long transversely isotropic elastic cylindrical shells under bending abstract the present paper investigates buckling of cylindrical shells of transversely isotropic elastic material subjected to bending considering the nonlinear prebuckling ovalized configuration a large strain hypoelastic model is developed to simulate the anisotropic material behavior the model is incorporated in a finite element formulation that uses a special purpose tube element for comparison purposes a hyperelastic model is also employed using an eigenvalue analysis bifurcation on the prebuckling ovalization path to a uniform wrinkling state is detected subsequently the postbuckling equilibrium path is traced through a continuation arc length algorithm the effects of anisotropy on the bifurcation moment the corresponding curvature and the critical wavelength are examined for a wide range of radius to thickness ratio values the calculated values of bifurcation moment and curvature are also compared with analytical predictions based on a heuristic argument finally numerical results for the imperfection sensitivity of bent cylinders are obtained which show good comparison with previously reported asymptotic expressions

the method of images for regularized stokeslets the image system for the method of regularized stokeslets is developed and implemented the method uses smooth localized functions to approximate a delta distribution in the derivation of the fluid flow due to a concentrated force in order to satisfy zero flow boundary conditions at a plane wall the method of images derived for a standard singular stokeslet is extended to give exact cancellation of the regularized flow at the wall as the regularization parameter vanishes the expressions reduce to the known images for singular stokeslets the advantage of the regularized method is that it gives bounded velocity fields even for isolated forces or for distributions of forces along curves these are useful in the simulation of ciliary beats flagellar motion and particle suspensions the expression relating force and velocity can be inverted to find the forces that generate a given velocity boundary condition the latter is exemplified by modeling a cilium as a filament moving in a three dimensional flow the cilium velocity at various times is constructed from known data and used to determine the force field along the filament those forces can then reproduce the flow everywhere the validity of the method is evaluated by computing the drag on a sphere moving near a wall comparisons with known expressions for the drag show that the method gives accurate results for spheres even within a distance from the wall equal to the surface discretization size

structural stability of multi folding structures with contact problem this paper presents the theoretical basis for both static and dynamic numerical approaches to the elastic stability of a folding multi layered truss both analyses are based on bifurcation theory and include geometrical nonlinearity the dynamic analysis includes an allowance for contact between nodes comparisons are made between published experimental folding patterns and the patterns obtained from both numerical methods in which bifurcations are demonstrated as elastic unstable snap through behaviour several folding patterns are identified during the elastic instability where the folding behaviour of the truss is shown to be a function of the initial geometry and velocity of the dynamic loading the authors suggest that the understanding of the behaviour will be very useful for the development of light weight structures subject to dynamic loading based on the bifurcation static analysis and dynamic analysis using both the displacement control method and the load control method

post buckling analysis of shallow shells by the field boundary element method the non linear field boundary element technique is applied to the analysis of snap through phenomena in thin shallow shells the equilibrium path is traced by using the arc length method and the solution strategy is discussed in detail the results show that as compared to the approaches based on the popular symmetric variational galerkin finite element formulation the current approach based on an unsymmetric variational petrov galerkin field boundary element formulation gives a faster convergence while using fewer degrees of freedom the illustrative numerical examples deal with post buckling responses of several shallow shells with different geometries

a force method for elastic plastic analysis of frames by quadratic optimization abstract a numerical method for the analysis of elastoplastic planar frames is developed on the basis of a minimum principle in finite increments of stresses and plastic factors local elastic unloading and plastic admissibility of final stresses are considered in this theoretical formulation avoiding additional iterative procedures since all possible stress distributions can be represented exactly only an interpolation of plastic multiplier fields is required to transform the formulation in the functional space into a problem with a finite number of variables plastic admissibility for any section along a beam element is substituted by a finite number of contraints the interpretation of this approximation is used to choose appropriate interpolation bases the resulting discrete version of the principle is a quadratic optimization problem solved in this work by dualization condensation to a problem in plastic factors only and application of lemke s algorithm the advantages of the force method when compared with kinematical approaches for planar frames are discussed and demonstrated by examples

a formal inverse to the cayley hamilton theorem abstract we prove that a q algebra r with formal trace can be realized as n n matrices if and only if it satisfies the cayley hamilton identity of degree n

a multiscale finite element method with embedded strong discontinuity model for the simulation of cohesive cracks in solids abstract a multiscale finite element method with the embedded strong discontinuity model is proposed to simulate the cohesive cracks in solids in the proposed method the kinematic descriptions of the strong discontinuity and space discretization are considered based on the fine scale with the strong discontinuity approach then in order to correctly and conveniently deliver the discontinuous information between the coarse scale and fine scale an enhanced coarse element strategy is proposed to construct the multiscale base functions that can well capture the discontinuous characteristics and preserve an adequate accuracy for the unit cells exhibiting a strong discontinuity the main idea is that the coarse nodes of the enhanced coarse element can be dynamically added according to the identification of the intersection between the crack path and the boundaries of the unit cell during the computational procedure the strategy overcomes the deficiency that the traditional coarse elements in the multiscale finite element method cannot well characterize the displacement jump property on the boundary of the unit cell moreover to accurately obtain the microscopic displacement the displacement decomposition technique is adopted to modify the downscale computations by adding the perturbation solutions numerical examples of normal tension and bending tests are presented to validate the proposed method by comparing the results with the analytical or fine finite element solutions finally the three point bending and four point bending benchmarks are performed to further demonstrate the effectiveness and high efficiency of the method

extended voronoi cell finite element model for multiple cohesive crack propagation in brittle materials this paper introduces an extended voronoi cell finite element model x vcfem for modelling cohesive crack propagation in brittle materials with multiple cracks the cracks are modelled by a cohesive zone model and their incremental directions and growth lengths are determined in terms of the cohesive energy near the crack tip extension to vcfem is achieved through enhancements in stress functions in the assumed stress hybrid formulation in addition to polynomial terms the stress functions include branch functions in conjunction with level set methods and multi resolution wavelet functions in the vicinity of crack tips the wavelet basis functions are adaptively enriched to accurately capture crack tip stress concentrations conditions and methods of stability are enforced in x vcfem for improved convergence with propagating cracks two classes of problems are solved and compared with existing solutions in the literature for validation of the x vcfem algorithms the first set corresponds to results for static cracks while in the latter set the propagation of cohesive cracks are considered comparison of x vcfem simulation results with results in literature for several fracture mechanics problems validates the effectiveness of x vcfem copyright 2005 john wiley sons ltd

on the solution of a minimum weight elastoplastic problem involving displacement and complementarity constraints this paper deals with a special class of minimum weight design problem involving discretized structures holonomic reversible plasticity and constraints on displacements a key feature of the optimization problem is the presence of complementarity conditions involving the orthogonality of two sign constrained vectors this problem falls within the important class of so called mathematical programs with equilibrium constraints mpecs two simple algorithms are proposed to solve our synthesis problem and application is illustrated by some examples concerning truss like structures

an asymptotic numerical method to compute the postbuckling behaviour of elastic plates and shells in this paper we apply an asymptotic numerical method for computing the postbuckling behaviour of plate and shell structures the bifurcating branch is sought in the form of polynomial expansions and it is determined by solving numerically fem several linear problems with a single stiffness matrix a large number of terms of the series can easily be computed by using recurrent formulas in comparison with a more classical step by step procedure the method is rapid and automatic however the polynomial expansions have a radius of convergence which limits the validity of the solution to a neighbourhood of the bifurcation point in the present form the method should be viewed as a cheap and automatic way of completing a linear buckling analysis it is illustrated in two examples a square plate under in plane compression and a cylindrical shell under pressure

finite element modelling of spatially chaotic structures a simple non linear mechanical system comprising a pin jointed string of finite length links supported by elastic springs at the pins and compressed by an axial load is viewed from two perspectives when seen as an initial value problem equilibrium equations provide an iterative non linear mapping when seen as a boundary value problem it becomes a simple finite element model at loads less than the critical buckling load a preferred buckling configuration is found that is localized along the length in the limit of infinite length this is described as a homoclinic connection in phase space joining the flat equilibrium state to itself the infinite sequence of homoclinic points thus defined embeds within the complex topological structure of a homoclinic tangle within which also appear periodic quasi periodic and chaotic spatial solutions implications in the finite element setting are discussed 1997 john wiley sons ltd

algorithmically imposed thermodynamic compliance for material models in mechanical simulations using the aim method thermodynamic irreversibility can be imposed on empirical material behaviour by using an appropriate algorithm which takes the path dependence of the degradation process into account this new algorithm algorithmically imposed mechanics aim for algorithmically irreversible mechanics is described and the convergence and unicity of the solutions obtained are proven aim is applicable to a range of mechanical behaviour and is demonstrated to work in conjunction with non local damage with rotating cracks as well as a mixed plastic and damage behaviour copyright c 2015 john wiley sons ltd

a path integral for turbulence in incompressible fluids in this paper a classical path integral is formulated for incompressible fluids that evolve according to the navier stokes equation the path integral propagates probability distributions deterministically on the space gvol of solenoidal velocity fields we construct a set of isp 2 charges associated with the geometry of gvol and its poisson structure and a pair of supersymmetry charges connected with the hamiltonian these charges generate exact symmetries of the classical path integral when the viscosity is set equal to zero when the effect of dissipation is included the charges associated with the poisson structure and the hamiltonian are no longer conserved charges that generate kolmogorov scaling and galilean transformations are also constructed the classical path integral is formulated in terms of vorticity as well

solution method for nonlinear problems with multiple critical points a generalized displacement control method has been proposed for geometrically nonlinear analysis and has been proven to be bery effective by several problems with multiple limit points and snap back points this method can be implemented easily in a general purpose finite element program

a semi analytical approach to the non linear dynamic response problem of beams at large vibration amplitudes part ii multimode approach to the steady state forced periodic response abstract the semi analytical approach to the non linear dynamic response of beams based on multimode analysis has been presented in part i of this series of papers azrar et al 1999 journal of sound and vibration 224 183 207 1 the mathematical formulation of the problem and single mode analysis have been studied the objective of this paper is to take advantage of applying this semi analytical approach to the large amplitude forced vibrations of beams various types of excitation forces such as harmonic distributed and concentrated loads are considered the governing equation of motion is obtained and can be considered as a multi dimensional form of the duffing equation using the harmonic balance method the equation of motion is converted into non linear algebraic form techniques of solution based on iterative incremental procedures are presented the non linear frequency and the non linear modes are determined at large amplitudes of vibration the basic function contribution coefficients to the displacement response for various beam boundary conditions are calculated the percentage of participation for each mode in the response is presented in order to appraise the relation to higher modes contributing to the solution also the percentage contributions of the higher modes to the bending moment near to the clamps are given in order to determine accurately the error introduced in the non linear bending stress estimated by different approximations solutions obtained in the jump phenomena region have been determined by a careful selection of the initial iteration at each frequency the non linear deflection shapes in various regions of the solution the corresponding axial force ratios and the bending moments are presented in order to follow the behaviour of the beam at large vibration amplitudes the numerical results obtained here for the non linear forced response are compared with those from the linear theory with available non linear results based on various approaches and with the single mode analysis

an arc length control procedure to solve parabolic problems abstract an arc length method is applied as a time step selector for a class of stiff parabolic problems related to heat conduction and radiation the resulting system of nonlinear equations is solved by iteration not only on the temperature vector but also on the current time step the procedure is linked with an a posteriori estimate of the time integration error used as input to the arc length selection algorithm in addition a quasi newton method us used to obtain approximate factorizations of the jacobian matrix during the iterative process

explicit quantization of dynamical r matrices for finite dimensional semisimple lie algebras 1 1 classical r matrices in the early eighties belavin and drinfeld bd classified nonskewsymmetric classical r matrices for simple lie algebras it turned out that such r matrices up to isomorphism and twisting by elements from the exterior square of the cartan subalgebra are classified by combinatorial objects which are now called belavin drinfeld triples by definition a belavin drinfeld triple for a simple lie algebra g is a triple 1 2 t where 1 2 are subsets of the dynkin diagram of g and t 1 2 is an isomorphism which preserves the inner product and satisfies the nilpotency condition if 1 then there exists k such that t k 1 1 but t 1 the r matrix corresponding to such a triple is given by a certain explicit formula these results generalize in a straightforward way to semisimple lie algebras in s the third author generalized the work of belavin and drinfeld and classified classical nonskewsymmetric dynamical r matrices for simple lie algebras it turns out that they have an even simpler classification up to gauge transformations they are classified by generalized belavin drinfeld triples which are defined as the usual belavin drinfeld triples but without any nilpotency condition the dynamical rmatrix corresponding to such a triple is given by a certain explicit formula as before these results can be generalized to semisimple lie algebras

an eulerian approach for large displacements of thin shells including geometrical non linearities abstract this paper is devoted to the problem of large displacement of shells the only non linearity being geometrical the geometry of the mid surface of the shell is determined thanks to the knowledge of nodes and normal vectors and is continuously updated stresses are also carried from one configuration to another which enables us to linearize the equilibrium equations it is then possible to build an eulerian formulation moreover some control strategies are proposed in order to find limit points and unstable solutions finally we check in some classical examples the accuracy of this technique

quantum zonal spherical functions and macdonald polynomials abstract a unified theory of quantum symmetric pairs is applied to q special functions previous work characterized certain left coideal subalgebras in the quantized enveloping algebra and established an appropriate framework for quantum zonal spherical functions here a distinguished family of such functions invariant under the weyl group associated to the restricted roots is shown to be a family of macdonald polynomials as conjectured by koornwinder and macdonald our results place earlier work for lie algebras of classical type in a general context and extend to the exceptional cases

tracing post limit point paths with reduced basis technique abstract a reduced basis technique and a problem adaptive computational algorithm are presented for predicting the post limit point paths of structures in the proposed approach the structure is discretized by using displacement finite element models the nodal displacement vector is expressed as a linear combination of a small number of vectors and a rayleigh ritz technique is used to approximate the finite element equations by a small system of nonlinear algebraic equations to circumvent the difficulties associated with the singularity of the stiffness matrix at limit points a constraint equation defining a generalized arc length in the solution space is added to the system of nonlinear algebraic equations and the rayleigh ritz approximation functions or basis vectors are chosen to consist of a nonlinear solution of the discretized structure and its various order derivatives with respect to the generalized arc length the potential of the proposed approach and its advantages over the reduced basis load control technique are outlined the effectiveness of the proposed approach is demonstrated by means of numerical examples of structural problems with snap through and snap back phenomena

secant structural solution strategies under element constraint for incremental damage abstract two major difficulties in the nonlinear analysis of post peak structural behavior are the occurrence of an ill conditioned tangent stiffness matrix around critical points namely limit and bifurcation points and the selection of a suitable constrain on the solution path as an attempt to make failure prediction available in a routine manner new solution strategies are proposed in which a secant structural stiffness matrix is formulated for incremental damage models and the solution path is controlled through a suitable measure of failure at the most severely damaged point in the body numerical solutions are given for plane strain and plane stress problems to show that snap back and snap through associated with shear band formation can be inexpensively predicted

parameter identification of quasibrittle materials as a mathematical program with equilibrium constraints the identification of the cohesive fracture parameters of quasibrittle materials forms the focus of the present work this important and challenging task is formulated as an inverse problem requiring the solution of a special type of constrained optimization problem known as a mathematical program with equilibrium constraints mpec a key feature of which is the presence of complementarity conditions involving the orthogonality of two nonnegative vectors we propose a simple scheme based on transforming the mpec into a standard nonlinear programming problem through appropriate smoothing of the complementarity constraints for solving the parameter identification problem some computational results using actual experimentally obtained data are presented to assess the effectiveness of the approach

an adaptive sub incremental strategy for the solution of homogenization based multi scale problems abstract in this contribution several schemes for the solution of homogenization based multi scale constitutive problems undergoing finite strains with inelastic material behavior are investigated these schemes are aimed at improving the robustness and efficiency of the newton raphson method in the multilevel finite element ml fem framework an adaptive sub incremental strategy is proposed for the discrete representative volume element rve boundary value problem the procedure is able to ensure the convergence of the solution algorithm in the presence of several sources of non linearity and obtains improved initial guesses for the newton raphson scheme in the ml fem framework the enlargement of the convergence bowl of the newton raphson procedure at the micro scale allows larger macroscopic deformation gradients to be prescribed and significantly reduces the overall computational cost of ml fem analyses the proposed strategy preserves the quadratic rates of asymptotic convergence that characterize the newton raphson scheme at the macroscopic level numerical examples of both micro scale and two scale finite element simulations are presented to demonstrate the improved robustness and efficiency of the solution procedures proposed

a discrete formulation for elastic solids with damaging interfaces abstract an elastic solid with embedded interfaces loci of possible displacement discontinuities is considered here decohesion and quasi brittle fracture processes are simulated by making use of softening interface laws which relate tractions to displacements jumps a discrete formulation in terms of interface variables only is obtained the space discretization is carried out by means of a mixed finite element approach in which all interface variables are modelled study of uniqueness of the rate problem formulated in terms of interface variables and of stability of the equilibrium states is presented some examples are shown in order to clarify the formulation

quantum conjugacy classes of simple matrix groups let g be a simple complex classical group and mathfrak g its lie algebra let mathcal u hbar mathfrak g be the drinfeld jimbo quantization of the universal enveloping algebra mathcal u mathfrak g we construct an explicit mathcal u hbar mathfrak g equivariant quantization of conjugacy classes of g with levi subgroups as the stabilizers

symmetric pairs for quantized enveloping algebras abstract let be an involution of a semisimple lie algebra g let g denote the fixed lie subalgebra and assume the cartan subalgebra of g has been chosen in a suitable way we construct a quantum analog of u g which can be characterized as the unique subalgebra of the quantized enveloping algebra of g which is a maximal right coideal that specializes to u g

non levi closed conjugacy classes of sp q 2 n we construct an explicit quantization of semi simple conjugacy classes of the complex symplectic group sp 2n with non levi isotropy subgroups through an operator realization on highest weight modules over the quantum group u q bigl mathfrak sp 2n bigr

a stochastic particle method for the mckean vlasov and the burgers equation in this paper we introduce and analyze a stochastic particle method for the mckean vlasov and the burgers equation the construction and error analysis are based upon the theory of the propagation of chaos for interacting particle systems our objective is three fold first we consider a mckean vlasov equation in 0 t x r with sufficiently smooth kernels and the pdes giving the distribution function and the density of the measure t the solution to the mckean vlasov equation the simulation of the stochastic system with n particles provides a discrete measure which approximates k t for each time k t where t is a discretization step of the time interval 0 t an integration resp smoothing of this discrete measure provides approximations of the distribution function resp density of k t we show that the convergence rate is o 1 n for the approximation in l i x r of the cumulative distribution function at time t and of order o e 2 1 e 1 n t for the approximation in l l x r of the density at time t is the underlying probability space e is a smoothing parameter our second objective is to show that our particle method can be modified to solve the burgers equation with a nonmonotonic initial condition without modifying the convergence rate o 1 n t this part extends earlier work of ours where we have limited ourselves to monotonic initial conditions finally we present numerical experiments which confirm our theoretical estimates and illustrate the numerical efficiency of the method when the viscosity coefficient is very small

nonlinear analysis based on homogeneous incremental systems abstract the performance of path following techniques depends on so called constraint equations which are used in the augmented incremental systems it is common practice in the literature that these equations are explicitly defined following the arbitrary geometrical or physical ideas in the present paper their role is discussed in order to establish a reliable method of augmentation it is shown that the explicitly defined constraint equation is not necessary the implicit formulation is proposed which is based on the rank analysis performed on the rectangular matrix of the homogeneous incremental system the proposed method allows to solve problems where the well known continuation schemes fail the theoretical considerations are illustrated by the numerical examples

an efficient model reduction method for buckling analyses of thin shells based on iga abstract an efficient reduced basis method is proposed for buckling analyses of thin shells subject to large deformations and strains the thin shells are modeled with the classical kirchhoff love kinematics under the framework of iga isogeometric analysis which makes it possible to satisfy the requirement of c 1 continuity the analytically defined geometry of thin shells can be exactly represented by the nurbs non uniform rational b splines basis functions in addition the critical buckling point can be better pin pointed due to the exact geometric description for efficient structural analyses a simplified rom reduced order model is presented by combining the koiter perturbation technique and the finite element method fem alternative perturbation forces based on nonlinear eigenvalue analyses are also proposed embedding three strategies including arc length control accompanying eigenvalue analysis and mode injection into the analysis procedure the proposed method is extended to be applicable to nonlinear buckling analyses furthermore imperfection sensitivity analyses can be conveniently performed with the proposed method finally the effectiveness and efficiency of the proposed method are validated via three benchmark problems

non levi closed conjugacy classes of soq n we construct explicit quantization of semisimple conjugacy classes of the complex orthogonal group so n with non levi isotropy subgroups through an operator realization on highest weight modules of the quantum group uqso n

an mpec approach for the critical post collapse behavior of rigid plastic structures this paper presents a numerical method to identify and trace the critical post collapse response of rigid perfectly plastic structures to account for the possibility of multiple equilibrium paths the critical one is directly identified using the minimum 2nd order work criterion our proposed enhanced sequential limit analysis is formulated as an instance of the challenging class of optimization problems known as a mathematical program with equilibrium constraints mpec this mpec formulation minimizes the 2nd order work expression subject to the set of constraints describing the complete complementarity system in mixed static kinematic variables governing simultaneously the two adjacent equilibrium configurations namely the current one and its neighboring state we use a nonlinear programming based algorithm involving relaxation of the complementarity terms to solve the mpec four numerical examples are provided to illustrate application of the proposed scheme

mathematical programming approaches for the safety assessment of semirigid elastoplastic frames abstract this paper presents two complementary mathematical programming based approaches for the accurate safety assessment of semirigid elastoplastic frames under quasistatic loads the inelastic behavior of the flexible connections and material plasticity are accommodated through piecewise linearized nonlinear yield surfaces as is necessary for this class of structures geometric nonlinearity is taken into account moreover only a 2nd order geometric approximation is included as this is sufficiently accurate for practical structures the work described has a twofold contribution first we develop an algorithm that can robustly and efficiently process the complete path dependent nonholonomic response of the structure in a stepwise path independent holonomic fashion the governing formulation is cast in mixed static kinematic variables and leads naturally to what is known in the mathematical programming literature as a mixed complementarity problem mcp the novelty of the proposed algorithm is that it processes the mcp directly without using some iterative and often cumbersome predictor corrector procedure second in the spirit of simplified analyses the classical limit analysis approach is extended to compute the limit load multiplier under the simultaneous influence of joint flexibility material and geometric nonlinearities and limited ductility our formulation is an instance of the challenging class of optimization problems known as a mathematical program with equilibrium constraints mpec various nonlinear programming based algorithms are proposed to solve the mpec finally four numerical examples concerning practical structures and benchmark cases are provided to illustrate application of the analyses as well as to validate the accuracy and robustness of the proposed schemes

quantum flag manifolds quantum symmetric spaces and their associated universal k matrices abstract let u be a connected simply connected compact lie group with complexification g let u and g be the associated lie algebras let be the dynkin diagram of g with underlying set i and let u q u be the associated quantized universal enveloping algebra of u for some 0 q distinct from 1 let o q u be the coquasitriangular quantized function hopf algebra of u whose drinfeld double o q g r we view as the quantized function algebra of g considered as a real algebraic group we show how the datum of an involution of and a invariant function i r can be used to deform o q g r into a algebra o q id g r by a modification of the drinfeld double construction we then show how by a generalized theory of universal k matrices a specific subalgebra of o q id g r admits homomorphisms into both u q u and o q u the images being coideal subalgebras of respectively u q u and o q u we illustrate the theory by showing that two main classes of examples arise by such coideals namely quantum flag manifolds and quantum symmetric spaces except possibly for certain exceptional cases in the former case this connects to work of the first author and neshveyev while for the latter case we heavily rely on recent results of balagovic and kolb

a convergence study of monolithic simulations of flow and deformation in fractured poroelastic media a consistent linearisation has been carried out for a monolithic solution procedure of a poroelastic medium with fluid transporting fractures including a comprehensive assessment of the convergence behaviour the fracture has been modelled using a sub grid scale model with a continuous pressure across the fracture the contributions to the tangential stiffness matrix of the fracture have been investigated to assess their impact on convergence simulations have been carried out for different interpolation orders and for non uniform rational b splines as interpolants vs lagrangian polynomials to increase the generality of the results newtonian as well as non newtonian power law fluids have been considered unsurprisingly a consistent linearisation invariably yields a quadratic convergence but comes at the expense of a loss of symmetry and recalculation of the contribution of the interface to the stiffness matrix at each iteration when using a linear line search however the inclusion of only those terms of the interface stiffness which result in a symmetric and constant tangential stiffness matrix is sufficient to obtain a stable and convergent iterative process

examples of braided groups and braided matrices matrix braided groups are developed as an analog of the coordinate functions on a group or supergroup the 1 in the super case is replaced by braid statistics there are braided group analogs of all the classical simple lie groups as well as braided matrix groups and braided matrices b r for every regular solution r of the quantum yang baxter equations a direct verification of b r is provided and some of the simplest examples are computed in detail

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

large displacement elastoplastic analysis of semirigid steel frames a mathematical programming approach for the large displacement analysis of elastoplastic plane frames with flexible partial strength beam to column connections is proposed the incremental formulation is developed within the framework of a discrete model piecewise linear yield surfaces and large displacement theory it is based on the fundamental relations of equilibrium compatibility and constitutive laws all expressed in incremental form the irreversible plasticity laws are used in a stepwise holonomic format a feature of the final mathematical programming problem known as a non linear complementarity problem is that the governing relations exhibit symmetry as a result of the use of fictitious quantities and non linear residuals the iterative predictor corrector computational scheme adopted has the ability of tracing historically a sequence of plastic hinge activations and or unloadings well beyond any critical point numerical examples are presented to illustrate and validate the accuracy of the approach

a refined finite element model for the analysis of elastic plastic frames a finite element model for the elastic plastic analysis of plane frames is proposed the formulation is based on the independent modelling of the displacement and plastic strain fields the latter is modelled both over the cross section and along the element length as function of a finite number of parameters which are considered as an extra set of independent variables in addition to nodal displacements stress redistribution is allowed for over the cross section but not over the element length where the distribution of stress resultants axial forces and bending moments is imposed consistently with the assumed displacement model stress redistribution in terms of stress resultants becomes possible only because of the finite number of redundancies introduced when assembling it is shown that the model can be formulated in such a way that not only compatibility and elasticity but also equilibrium in the sense of beam theory are fully complied with and only the plastic portion of the constitutive relationship is approximately fulfilled even if in principle to any desired level of accuracy the model produces accurate results including a detailed representation of the spreading of plastic zones with a fairly limited number of elements

algebraic structures related to reflection equations quadratic algebras related to the reflection equations are introduced they are quantum group comodule algebras the quantum group fq gl 2 is taken as the example the properties of the algebras centre representation realizations real forms fusion procedure etc as well as the generalizations are discussed

a particle model of compressible fluids fluid mechanics describes the motion of mass in space under the influence of internal and external forces the particle model presented in this article is based on this fact the fluid is subdivided into a finite number of small mass packets the particles these mass packets have a finite extension and share all properties with the fluid except for the restriction that they cannot get deformed and can perform only rigid body motions the forces acting upon the particles are identical to those acting on a part of a fluid the exact conservation of mass and for the case of adiabatic flows also of entropy is automatically guaranteed by the approach when the particle size tends to zero the mean local displacement of the particles converges in the weak sense in the inviscid case the resulting flows can be regarded as solutions of the euler equations

a truncated newton lanczos method for overcoming limit and bifurcation points in this study procedures for overcoming limit and bifurcation points in large scale structural analysis problems are described and evaluated the methods are based on newton s method for the outer iterations while for the linearized problem in each iteration the preconditioned truncated lanczos method is employed special care is placed upon line search routines for accelerating the convergence properties and enhancing the stability of the outer method the proposed methodology retains all characteristics of an iterative method by avoiding the factorization of the current stiffness matrix the necessary eigenvalue information is retained in the tridiagonal matrix of the lanczos approach

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

orthogonal trajectory accession to the nonlinear equilibrium curve abstract an alternative to the riks wempner crisfield iterative correction scheme is presented that does not require an explicit displacement load accession path to the nonlinear equilibrium curve nor a known equilibrium point its symmetry with respect to the displacement and load assures success in rounding limit points as well as turning points

bending instabilities of elastic tubes the present paper examines instabilities of long thin elastic tubes both initially straight and initially bent tubes are analyzed under in plane bending tube response a combination of ovalization instability and bifurcation instability buckling is investigated using a nonlinear finite element fe technique which employs polynomial functions in the longitudinal tube direction and trigonometric functions to describe cross sectional deformation it is demonstrated that the interaction between the two instability modes depends on the value and the sign of the initial tube curvature the ovalization of initially bent tubes is examined in detail and in particular the case of opening moments furthermore the paper emphasizes on bifurcation instability it is shown that buckling may occur prior to or beyond the ovalization limit point depending on the value of the initial curvature using the nonlinear fe formulation the location of bifurcation on the primary path is detected post buckling equilibrium paths are traced and the corresponding wavelengths of the buckled configurations are calculated moreover results over a wide range of initial curvature values are presented extending the findings of previous works finally several analytical approaches introduced in previous research works are also employed to estimate the moments causing ovalization and bifurcation instability these approaches are based on nonlinear flexible shell theory or simplified ring analysis the efficiency and accuracy of those analytical methods with respect to the nonlinear fe formulation are examined

a new approach in non linear mechanics the large time increment method a new algorithm family taking into account the entire loading process in a single large time increment is proposed to compute structures with physical non linearities and is tested on some examples in elastoplasticity the method considerably reduces the number of transfers between local and global levels hence the numerical cost of calculation is also diminished