on the thermally induced bistability of composite cylindrical shells for morphing structures abstract the multistability of composite thin structures has shown potential for morphing applications the present work combines a ritz model with path following algorithms to study bistable cylindrical panels polynomial discretisations of the displacements field are used to predict stable shapes geometry and other aspects of the nonlinear structural behaviour in order to improve the inherently poor conditioning properties of ritz approximations of slender structures a non dimensional shell lamination theory with sanders nonlinear strains is developed and presented an investigation on the relative importance of different nonlinear strain terms is shown to provide useful insight into the applicability of common assumptions about shell kinematics in the current approach we continue numerical solutions in parameter space that is we path follow equilibrium configurations as the control parameter varies find stable and unstable configurations and identify bifurcations the numerics is carried out using a set of in house m atlab routines for numerical continuation results are compared with detailed finite elements analysis throughout the course of the paper

practical computation of matrix functions abstract several new representations for an analytic function f a of a complex matrix a and in particular for e at and a t are derived which also are numerically useful in that they avoid the computation of eigenvalues of a

some explicit formulas for the polynomial decomposition of the matrix exponential and applications abstract this paper is devoted to the study of some formulas for polynomial decomposition of the exponential of a square matrix a more precisely we suppose that the minimal polynomial ma x of a is known and has degree m therefore eta is given in terms of p0 a pm 1 a where the pj a are polynomials in a of degree less than m and some explicit analytic functions examples and applications are given in particular the two cases m 5 and m 6 are considered

the l and gamma factors for generic representations of mathrm gsp 4 k times mathrm gl 2 k over a local non archimedean field k

multiparameter actuation for shape control of bistable composite plates this paper studies the stable equilibrium shapes of free multilayered orthotropic plates loaded by inelastic deformations induced by thermal and piezoelectric effects starting with a von karman plate kinematics and an energetic formulation a discrete intrinsic nonlinear model in terms of curvatures only is deduced the model has 3 degrees of freedom namely the components of the symmetric curvature tensor which is supposed to be uniform in space despite of this rough assumption the analytical results about the equilibrium shapes and their stability show a good agreement with the finite element simulations performed with a commercial code literature results about the bistable behavior of isotropic plates under a single parameter loading are extended to the orthotropic case with two loading parameters in light of a global stability analysis and a phase portrait as a function of the inelastic curvatures we study possible actuation techniques for controlling the transition of the plate between its two stable configurations we show that with a suitable two parameter actuation it is possible to get a controlled quasi static transition avoiding any instability phenomenon numerical simulations on a realistic case study support the technological feasibility of the proposed actuation technique when using active piezoelectric layers to control the inelastic curvature

on the matrix powers and exponential by the r generalized fibonacci sequences methods the companion matrix case properties of some r generalized fibonacci sequences in the algebra of square matrices gl r c allow us to derive some explicit formulas for the matrix powers an n 0 and exponential eta for every a gl r c connection with the verde star method is displayed for a companion matrix a we present some explicit combinatorial formulas for an n 0 and eta furthermore the chen louck s theorem is derived

multistable composite plates with piecewise variation of lay up in the planform abstract the non linear out of plane displacements of partially unsymmetric laminates are modelled using both finite element analysis and an analytical method attention is focused on the effects that thermal stresses have on the potential multiple shapes of a composite structure the paper extends previous analytical models which could only take into account free free boundary conditions the shape functions that model the out of plane displacements are modified to include variations of the curvatures within the domain the new analytical formulation is compared with literature and finite element analysis for a square plate and then it is tested for laminates with piecewise variation of lay up in the planform the results are validated against finite element analysis and experimental tests and a good correlation is obtained finally a parametric study is made on the effect of changing the fibres orientation and the laminate thickness the results confirm that it is possible to introduce bi stable composites within structures to obtain systems that are both flexible and stiff depending on the loading environment

matrix exponentials another approach the exponential of a matrix and the spectral decomposition of a matrix can be computed knowing nothing more than the eigenvalues of the matrix and the cayley hamilton theorem the arrangement of the ideas in this paper is simple enough to be taught to beginning students of odes

the combinatorial power of the companion matrix abstract using combinatorial methods we obtain the explicit polynomials for all elements in an arbitrary power of the companion matrix depending on n variables and provide some interesting applications and relationships to waring s formula on symmetric functions the general solution to homogeneous linear recurrence relations the multiplicative inverse of formal power series the generating function of compositions of numbers a unified approach to chebyshev polynomials including two recently discovered classes that satisfy analogous smallest norm and orthogonality properties subject to different weight functions dickson polynomials of various kinds arising from the theory of finite fields combinatorial expansions of toeplitz matrices and the recent notion of cycle dissections involving a bijective study of waring s formula

computations with infinite toeplitz matrices and polynomials we relate polynomial computations with operations involving infinite band toeplitz matrices and show applications to the numerical solution of markov chains of nonlinear matrix equations to spectral factorizations and to the solution of finite toeplitz systems in particular two matrix versions of graeffe s iteration are introduced and their convergence properties are analyzed correlations between graeffe s iteration for matrix polynomials and cyclic reduction for block toeplitz matrices are pointed out the paper contains a systematic treatment of known topics and presentation of new results improvements and extensions

functions and jordan canonical forms of riordan matrices abstract this paper collects results about riordan arrays in the framework of matrix functions actually the following methodology applies to any square matrix m m with exactly one eigenvalue of algebraic multiplicity m n generalized lagrange bases are used to construct hermite polynomials that interpolate a family of functions moreover we show a parallel application of such functions via jordan canonical forms and case studies are given

on explicit formulas of the principal matrix pth root by polynomial decompositions abstract we present some explicit formulas for calculating the principal p th root of a square matrix the main tools are based on various polynomial decompositions of the principal matrix p th root and well known properties of the linear recursive sequences

tristability of thin orthotropic shells with uniform initial curvature composite shells show a rich multistable behaviour of interest for the design of shape changing morphing structures previous studies have investigated how the initial shape determines the shell

bistable plates for morphing structures a refined analytical approach with high order polynomials abstract the multistability of composite thin structures has shown potential for morphing applications the present work combines a ritz model with path following algorithms to study bistable plates behaviour classic low order ritz models predict stable shapes geometry with reasonable accuracy however they may fail when modelling other aspects of the elastic structural behaviour a refined higher order model is here presented in order to improve the inherently poor conditioning properties of ritz approximations of slender structures a non dimensional version of classical plate lamination theory with von karman nonlinear strains is developed and presented in the current approach we continue numerical solutions in parameter space that is we path follow equilibrium configurations as the control parameter varies find stable and unstable configurations and identify bifurcations the numerics are carried out using a set of in house matlab routines for numerical continuation the increased degrees of freedom within the model are shown to accurately reflect buckling loads and provide useful insight into the relative importance of different aspects of nonlinear behaviour finally the complex experimentally observed snap through geometry is captured analytically for the first time results are validated against finite elements analysis throughout the course of the paper

on explicit formulas for the principal matrix logarithm we describe a method for evaluating both the fibonacci horner and the polynomial decomposition of the principal matrix logarithm with a view to solve the lifting problem of its explicit computation the binet formula for linear recursive sequences serves as a triggering factor for giving the exact formula we supply some illustrative examples

improving formulas for the eigenvalues of finite block toeplitz tridiagonal matrices abstract after a short overview improvements based on the kronecker product are proposed for the eigenvalues of n n block toeplitz tridiagonal block tt matrices with k k matrix entries common in applications some extensions of the spectral properties of the toeplitz tridiagonal matrices are pointed out the eigenvalues of diagonalizable symmetric and skew symmetric block tt matrices are studied besides if certain matrix square root is well defined it is proved that every block tt matrix with commuting matrix entries is isospectral to a related symmetric block tt one further insight about the eigenvalues of hierarchical hermitian block tt matrices of use in the solution of pdes is also achieved

analytical investigation of structurally stable configurations in shape memory alloy actuated plates strains produced by active materials embedded in plates have been extensively used to manipulate the shape of surface like engineering structures shape memory alloys smas are active materials that provide a significant amount of strain under large stresses a characteristic of great utility in such morphing structures in this work an analytical approach to approximate the deformation of plates with sma constituents is developed via the rayleigh ritz method an additive set of kinematically admissible displacement fields with unknown coefficients is used to describe the plate displacement field the total potential energy is then calculated using the displacement field loading conditions and constitutive relations for the plate layer s composed of sma wire meshes dense sma films and or elastic material the unknown coefficients are then found via minimization of the total potential energy this approach provides closed form expressions for the approximate deformation of the plates including multistable configurations the response of circular sma based plates is studied herein the results show that temperature fields with a linear variation in the radial direction induce multistable configurations in which the plate gaussian curvature is determined by the direction of the temperature gradient an alternative inversion of the proposed approach is used to directly compute the temperature field required to morph a plate towards a prescribed goal shape the obtained closed form expressions show good agreement with detailed non linear finite element analysis simulations the proposed approach provides analysts with a low computational cost and relatively simple implementation to assess the potentially stable configurations of sma based plates under given loading conditions knowledge of such stable configurations is very valuable in the design of sma based morphing structures c 2015 elsevier ltd all rights reserved

discrete approximations of the foppl von karman shell model from coarse to more refined models abstract the problem of deducing from the foppl von karman energy functional a sequence of reduced discrete models having few degrees of freedom is analyzed similar discrete models have been recently intensively studied to analyze the multistable behavior of shallow shells the bifurcations of composite laminates under temperature loads or the wrinkling in soft tissues in particular three relevant examples are discussed and compared among them where the curvature is assumed uniform linearly and quadratically varying through the shell while the uniform curvature assumption dates back to mansfield 1962 linear variations of the shell curvatures can describe smooth transitions between everted configurations while quadratic variations can account for the usually disregarded bending boundary conditions for their deduction we revisit the maxwell mohr method accordingly a sequence of auxiliary elliptic problems of plane elasticity is solved to determine the statically unknown membranal stresses this is a key ingredient for the presented models to compare extremely well with finite element approximations or with literature models with far more degrees of freedom

nineteen dubious ways to compute the exponential of a matrix twenty five years later in principle the exponential of a matrix could be computed in many ways methods involving approximation theory differential equations the matrix eigenvalues and the matrix characteristic polyn

determination of a matrix function using the divided difference method of newton and the interpolation technique of hermite computing a function f a of an n by n matrix a is a frequently occurring problem in control theory and other applications in this paper we introduce an effective approach for the determination of matrix function f a we propose a new technique which is based on the extension of newton divided difference and the interpolation technique of hermite and using the eigenvalues of the given matrix a the new algorithm is tested on several problems to show the efficiency of the presented method finally the application of this method in control theory is highlighted

functions of matrices abstract we use the cayley hamilton theorem and the sequence of horner polynomials associated with a polynomial w z to obtain explicit formulas for functions of the form f ta where f is defined by a convergent power series and a is a square matrix we use a well known explicit formula for the resolvent of a and show that f ta is the hadamard product of f t and the function i ta 1 which is easily obtained from the resolvent

local shimura correspondence it splits over the maximal compact subgroup let t be the corresponding lift of i the iwahori subgroup of g now fix a faithful character of n f let r be the category of smooth representations of which are generated by its t fixed vectors and such that n f acts via also let h be the hecke algebra of i biinvariant compactly supported functions on satisfying f gq f g for z v obj r let v be the space of i fixed vectors then f f l v is a representation of h t according to bernstein and borel 2 this gives the equivalence of r and the category of representations of h in particular this is the case for g whose hecke algebra will be denoted by h g and category by ri g in this paper we describe h in terms of generators and relations as a consequence in the case of simple group for example we find a group g related to g such that h t h g in particular we get the equivalence of r t and