low rank perturbation of regular matrix polynomials abstract let a be a complex regular matrix polynomial of degree l with g elementary divisors corresponding to the finite eigenvalue 0 we show that for most complex matrix polynomials b with degree at most l satisfying rank b 0 g the perturbed polynomial a b has exactly g rank b 0 elementary divisors corresponding to 0 and we determine their degrees if rank b 0 rank b b 0 does not exceed the number of 0 elementary divisors of a with degree greater than 1 then the 0 elementary divisors of a b are the g rank b 0 rank b b 0 elementary divisors of a corresponding to 0 with smallest degree together with rank b b 0 linear 0 elementary divisors otherwise the degree of all the 0 elementary divisors of a b is one this behavior happens for any matrix polynomial b except those in a proper algebraic submanifold in the set of matrix polynomials of degree at most l if a has an infinite eigenvalue the corresponding result follows from considering the zero eigenvalue of the perturbed dual polynomial

explicit solution of the row completion problem for matrix pencils in this paper we give new explicit and simplified conditions for the problem of determining the possible strict equivalence class of a pencil with prescribed rows columns this improves the result from 1 and solves an important particular case of the challenge problem posed by loiseau et al 7 all results that we present are obtained over arbitrary fields

isogeometric kirchhoff love shell formulations for general hyperelastic materials abstract we present formulations for compressible and incompressible hyperelastic thin shells which can use general 3d constitutive models the necessary plane stress condition is enforced analytically for incompressible materials and iteratively for compressible materials the thickness stretch is statically condensed and the shell kinematics are completely described by the first and second fundamental forms of the midsurface we use c 1 continuous isogeometric discretizations to build the numerical models numerical tests including structural dynamics simulations of a bioprosthetic heart valve show the good performance and applicability of the presented methods

an isogeometric implicit g1 mixed finite element for kirchhoff space rods abstract in the paper we present a multi patch isogeometric mixed element with implicit geometric continuity at the ends for the analysis of non polar kirchhoff space rods rotations are introduced at the ends of the element analogously to the hermitian interpolation performing a change of basis for the configuration space a mixed method in which the internal forces are interpolated by means of an l 2 projection leading to a b formulation is used to cope with the membrane flexural locking that affects the solution the efficiency of the method in avoiding locking and instabilities is investigated the formulation adopted has the advantage with respect to other formulations that a non full global stiffness matrix is obtained this approach appears very appealing for efficient analyses of general assemblies of 3d non polar elements

isogeometric analysis of high order partial differential equations on surfaces we consider the numerical approximation of high order partial differential equations pdes defined on surfaces in the three dimensional space with particular emphasis on closed surfaces we consider computational domains that can be represented by b splines or nurbs as for example the sphere and we spatially discretize the pdes by means of nurbs based isogeometric analysis in the framework of the standard galerkin method we numerically solve benchmark laplace beltrami problems of the fourth and sixth order as well as the corresponding eigenvalue problems with the goal of analyzing the role of the continuity of the nurbs basis functions on closed surfaces in this respect we show that the use of globally high order continuous basis functions as allowed by the construction of periodic nurbs leads to the efficient solution of the high order pdes finally we consider the numerical solution of high order phase field problems on closed surfaces namely the cahn hilliard and crystal equations

feedback invariants of matrices with prescribed rows abstract let a f n n b f n m where f is an arbitrary field in this paper we solve the problem of the existence of the matrix a b when its feedback invariants and some rows are prescribed

nonlinear isogeometric spatial bernoulli beam abstract a new element formulation of a geometrically nonlinear spatial curved beam assuming bernoulli theory including torsion without warping is proposed the element formulation is derived directly from the 3d continuum by means of nonlinear kinematics thus accounting for large displacements the geometric description of the proposed element is adapted from the spatial rod of greco and cuomo 2013 and extended to a nonlinear element formulation the proposed formulation can handle arbitrary orientations of the cross section along the beam in this publication nurbs are used as basis functions for discretization since they can easily provide the required c 1 continuity between elements the presented element formulation has four degrees of freedom three for displacements and one for the rotation around the center line in order to prove the accuracy of the developed spatial bernoulli beam several numerical examples are presented and compared to analytic solutions and other element formulations

resource allocation with time intervals we study a resource allocation problem where jobs have the following characteristic each job consumes some quantity of a bounded resource during a certain time interval and induces a given profit we aim to select a subset of jobs with maximal total profit such that the total resource consumed at any point in time remains bounded by the given resource capacity while this case is trivially np hard in general and polynomially solvable for uniform resource consumptions our main result shows the np hardness for the case of general resource consumptions but uniform profit values i e for the case of maximizing the number of performed jobs this result applies even for proper time intervals we also give a deterministic 1 email protected approximation algorithm for the general problem on proper intervals improving upon the currently known 1 3 ratio for general intervals finally we study the worst case performance ratio of a simple greedy algorithm

a fully locking free isogeometric approach for plane linear elasticity problems a stream function formulation in this paper we study plane incompressible elastic problems by means of a stream function formulation such that a divergence free displacement field can be computed from a scalar potential the numerical scheme is constructed within the framework of nurbs based isogeometric analysis and we take advantage of the high continuity guaranteed by nurbs basis functions in order to obtain the displacement field from the potential differentiation as a consequence the obtained numerical scheme is automatically locking free in the presence of the incompressibility constraint a discontinuous galerkin approach is proposed to deal with multiple mapped possibly multiply connected domains extensive numerical results are provided to show the method capabilities 2007 elsevier b v all rights reserved

floquet bloch decomposition for the computation of dispersion of two dimensional periodic damped mechanical systems floquet bloch theorem is widely applied for computing the dispersion properties of periodic structures and for estimating their wave modes and group velocities the theorem allows reducing computational costs through modeling of a representative cell while providing a rigorous and well posed spectral problem representing wave dispersion in undamped media most studies employ the floquet bloch approach for the analysis of undamped systems or for systems with simple damping models such as viscous or proportional damping in this paper an alternative formulation is proposed whereby wave heading and frequency are used to scan the k space and estimate the dispersion properties the considered approach lends itself to the analysis of periodic structures with complex damping configurations resulting for example from active control schemes the presence of damping materials or the use of shunted piezoelectric patches examples on waveguides with various levels of damping illustrate the performance and the characteristics of the proposed approach and provide insights into the properties of the obtained eigensolutions

enumeration and interactive selection of efficient paths in a multiple criteria graph for scheduling an earth observing satellite we consider a satellite following orbits around the earth in order to take shots corresponding to images requested by various customers the daily operations of such a satellite consist of defining a feasible and satisfactory shot sequence this problem involves both combinatorial and multiple criteria difficulties indeed the number of feasible shot sequences grows significantly with the number of images asked for and the evaluation of a shot sequence is based on several conflicting criteria we propose to formulate this problem as the selection of a multiple criteria path in a graph without circuit our approach for solving this problem involves two stages generation of efficient paths and selection of a satisfactory path using a multiple criteria interactive procedure

the rank distance problem for pairs of matrices and a completion of quasi regular matrix pencils abstract in this paper we give a complete description of the possible feedback invariants of a pair of matrices submitted to an additive perturbation of low rank also we describe the possible kronecker invariants of a quasi regular matrix pencil with a prescribed quasi regular subpencil all the results are valid over arbitrary fields

an implicit multi patch b spline interpolation for kirchhoff love space rod abstract the paper presents a novel formulation for the isogeometric analysis of assemblies of kirchhoff love space rod elements introducing a multi patch implicit g 1 formulation so that an automatic non singular stiffness operator is obtained without the need of adding continuity conditions the goal is achieved using a polar decomposition of the deformation of the first and last segments of the control polygon that allows to introduce directly the end rotations as degrees of freedom both parametric and geometric continuity can be obtained in this way we use bezier and b spline interpolations and we show that they are able to attain very good accuracy for developing a 3d exact curve element with geometric torsion pre twisted rod in the paper the performance of the multi patch elements is examined comparing the rates of convergence of the l 2 error norm for the multi patch and single patch formulations it is shown that the rate of convergence remains the same although in certain cases the accuracy is lower for the multi patch solutions

finite element prediction of wave motion in structural waveguides a method is presented by which the wavenumbers for a one dimensional waveguide can be predicted from a finite element fe model the method involves postprocessing a conventional but low order fe model the mass and stiffness matrices of which are typically found using a conventional fe package this is in contrast to the most popular previous waveguide fe approach sometimes termed the spectral finite element approach which requires new spectral element matrices to be developed in the approach described here a section of the waveguide is modeled using conventional fe software and the dynamic stiffness matrix formed a periodicity condition is applied the wavenumbers following from the eigensolution of the resulting transfer matrix the method is described estimation of wavenumbers energy and group velocity discussed and numerical examples presented these concern wave propagation in a beam and a simply supported plate strip for which analytical solutions exist and the more complex case of a viscoelastic laminate which involves postprocessing an ansys fe model the method is seen to yield accurate results for the wavenumbers and group velocities of both propagating and evanescent waves

treatment of reissner mindlin shells with kinks without the need for drilling rotation stabilization in an isogeometric framework this work presents a framework for the computation of complex geometries containing intersections of multiple patches with reissner mindlin shell elements the main objective is to provide an isogeometric finite element implementation which neither requires drilling rotation stabilization nor user interaction to quantify the number of rotational degrees of freedom for every node for this purpose the following set of methods is presented control points with corresponding physical location are assigned to one common node for the finite element solution a nodal basis system in every control point is defined which ensures an exact interpolation of the director vector throughout the whole domain a distinction criterion for the automatic quantification of rotational degrees of freedom for every node is presented an isogeometric reissner mindlin shell formulation is enhanced to handle geometries with kinks and allowing for arbitrary intersections of patches the parametrization of adjacent patches along the interface has to be conforming the shell formulation is derived from the continuum theory and uses a rotational update scheme for the current director vector the nonlinear kinematic allows the computation of large deformations and large rotations two concepts for the description of rotations are presented the first one uses an interpolation which is commonly used in standard lagrange based shell element formulations the second scheme uses a more elaborate concept proposed by the authors in prior work which increases the accuracy for arbitrary curved geometries numerical examples show the high accuracy and robustness of both concepts the applicability of the proposed framework is demonstrated

the change of feedback invariants under one row perturbation in this paper we completely characterize possible feedback invariants of a rectangular matrix under small additive perturbations on one of its rows

wave propagation in two dimensional periodic lattices plane wave propagation in infinite two dimensional periodic lattices is investigated using floquet bloch principles frequency bandgaps and spatial filtering phenomena are examined in four representative planar lattice topologies hexagonal honeycomb kagome lattice triangular honeycomb and the square honeycomb these topologies exhibit dramatic differences in their long wavelength deformation properties long wavelength asymptotes to the dispersion curves based on homogenization theory are in good agreement with the numerical results for each of the four lattices the slenderness ratio of the constituent beams of the lattice or relative density has a significant influence on the band structure the techniques developed in this work can be used to design lattices with a desired band structure the observed spatial filtering effects due to anisotropy at high frequencies short wavelengths of wave propagation are consistent with the lattice symmetries

b spline interpolation of kirchhoff love space rods the paper deals with the isogeometric analysis via b splines of space rods under kirchhoff love hypotheses the approach was used by gontier and vollmer 12 for developing a plane curve element within the framework of the timoshenko rod model but they adopted only one patch to represent entirely the geometry of the rod furthermore the authors developed their theory only for plane elements in this work we develop an isogeometric approach for the numerical analysis of the 3d kirchhoff love rod theory we use b splines and bezier interpolations and we show that they are able to attain very good accuracy for rod structures particularly for developing a 3d exact curve element with geometric torsion the paper presents an original parametrization of the geometric torsion that proves to be very effective the use of b splines allows to avoid discontinuities on the geometrical quantities and particularly on the normal fields so that even relatively low order interpolation functions are able to yield accurate results

blended isogeometric shells abstract we propose a new isogeometric shell formulation that blends kirchhoff love theory with reissner mindlin theory this enables us to reduce the size of equation systems by eliminating rotational degrees of freedom while simultaneously providing a general and effective treatment of kinematic constraints engendered by shell intersections folds boundary conditions the merging of nurbs patches etc we illustrate the blended theory s performance on a series of test problems

rank one perturbations of matrix pencils abstract we solve the problem of characterizing the kronecker structure of a matrix pencil obtained by a rank one perturbation of another matrix pencil the results hold over arbitrary fields

isogeometric mortar methods the application of mortar methods in the framework of isogeometric analysis is investigated theoretically as well as numerically for the lagrange multiplier two choices of uniformly stable spaces are presented both of them are spline spaces but of a different degree in one case we consider an equal order pairing for which a cross point modification based on a local degree reduction is required in the other case the degree of the dual space is reduced by two compared to the primal this pairing is proven to be inf sup stable without any necessary cross point modification several numerical examples confirm the theoretical results and illustrate additional aspects

a new method of analyzing wave propagation in periodic structures applications to periodic timoshenko beams and stiffened plates a response function is found for an infinite uniform one dimensional structure which is subjected to an array of harmonic forces or moments spaced equidistantly and which have a constant phase or ratio between any adjacent pair receptance functions are derived for these phased arrays they are used to set up a general determinantal equation for the propagation constants of the infinite structure when it is made periodic by the addition of an infinite set of regular constraints they are also used to set up equations for the response of the structure to a convected harmonic pressure field the method enables the equations for the propagation constants and for the response to convected loading to be set up with much greater facility than by earlier methods it only requires a knowledge of the response function of the infinite uninterrupted structure under a single point harmonic force or moment the general equation for the propagation constants is used to study a a simply supported periodic timoshenko beam and b a parallel plate with periodic beam type stiffeners some calculated propagation constants are presented and discussed the periodic plate results are relevant to integrally stiffened skins of the type used in aeroplanes

the fixed job schedule problem with working time constraints we consider a generalization of the fixed job schedule problem where a bound is imposed on the total working time of each processor it is shown that the problem is np hard but polynomially solvable in the preemptive case we introduce several lower bounds one is determined through definition of a special class of graphs for which the maximum clique problem is shown to be polynomial lower bounds and dominance criteria are exploited in a branch and bound algorithm for optimal solution of the problem the effectiveness of the algorithm is analyzed through computational experiments

isogeometric analysis of the cahn hilliard phase field model abstract the cahn hilliard equation involves fourth order spatial derivatives finite element solutions are not common because primal variational formulations of fourth order operators are only well defined and integrable if the finite element basis functions are piecewise smooth and globally c 1 continuous there are a very limited number of two dimensional finite elements possessing c 1 continuity applicable to complex geometries but none in three dimensions we propose isogeometric analysis as a technology that possesses a unique combination of attributes for complex problems involving higher order differential operators namely higher order accuracy robustness two and three dimensional geometric flexibility compact support and most importantly the possibility of c 1 and higher order continuity a nurbs based variational formulation for the cahn hilliard equation was tested on two and three dimensional problems we present steady state solutions in two dimensions and for the first time in three dimensions to achieve these results an adaptive time stepping method is introduced we also present a technique for desensitizing calculations to dependence on mesh refinement this enables the calculation of topologically correct solutions on coarse meshes opening the way to practical engineering applications of phase field methodology

studies of refinement and continuity in isogeometric structural analysis we investigate the effects of smoothness of basis functions on solution accuracy within the isogeometric analysis framework we consider two simple one dimensional structural eigenvalue problems and two static shell boundary value problems modeled with trivariate nurbs solids we also develop a local refinement strategy that we utilize in one of the shell analyses we find that increased smoothness that is the k method leads to a significant increase in accuracy for the problems of structural vibrations over the classical c0c0 continuous p method whereas a judicious insertion of c0c0 continuous surfaces about singularities in a mesh otherwise generated by the k method usually outperforms a mesh in which all basis functions attain their maximum level of smoothness we conclude that the potential for the k method is high but smoothness is an issue that is not well understood due to the historical dominance of c0c0 continuous finite elements and therefore further studies are warranted

bloch theorem for isogeometric analysis of periodic problems governed by high order partial differential equations abstract with the emergence of isogeometric analysis iga numerical rotation free solutions to high order partial differential equations pdes are facilitated indeed iga allows the use of high order continuous basis functions through the domain for periodic systems the bloch theorem is useful for analyzing wave propagation restricting the analysis to a single unit cell and applying periodic boundary conditions however in the literature boundary conditions are only accounting for c 0 continuity and we propose in the present paper to enforce the g 1 continuity as well or to maintain the angle in case of unit cells meeting at kinks while g 1 continuity is enforced by maintaining the collinearity between adjacent control points in the presence of kinks variations of the field derived with respect to opposite in plane edge normals are linked by the rodrigues rotation matrix this method applied at collocation points belonging to the unit cell edges can be viewed as a novel approach of coupling multi patch geometries with kinks avoiding the use of nonlinear multipliers or additional bending strip elements both transfer matrix and indirect methods of the bloch theorem are investigated for respectively quasi one and quasi two dimensional wave propagation in periodic structures discretized by nurbs based iga dispersion curves of a set of numerical problems treating isogeometric rotation free extensible elastica beams and kirchhoff love shells are then analyzed

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

bloch theorem with revised boundary conditions applied to glide screw and rotational symmetric structures abstract wave propagation in complex periodic systems is often addressed with the bloch theorem and consists in applying periodic boundary conditions to a discretized unit cell while this method has been developed for structures periodic by translation in a recent work for quasi one dimensional wave propagation it has been shown that screw translation plus rotation and glide translation plus reflection periodicities can be accounted for as well keeping the cartesian coordinate system but revisiting the periodic boundary conditions the goal of the present paper is to generalize this concept to quasi two dimensional wave propagation two dimensional waves propagating in three dimensional structures dispersion relations for a set of reduced problems are then compared to results from the classical method when available by considering a smaller periodicity the computational cost is decreased and the number of folding curves and non interacting intersecting curves is reduced improving their interpretability while the size of a unit cell is divided by a factor two when glide symmetries are considered this ratio is significantly increased for screw or rotational symmetries moreover the proposed revisited bloch method is applicable to screw symmetric structures that do not possess purely translational symmetries and for which the classical method cannot be used e g chiral nanotubes longitudinally wrinkled helicoids

maximizing the value of a space mission abstract the problem of selecting and scheduling projects to maximize the scientific military or commercial value of a space mission has been the subject of ongoing studies for several years the typical outcome of such studies even after many man years of effort is a heuristic solution with no comparison to optimality we depart from the traditional knowledge based systems approach and describe a machine scheduling model for the problem the problem which is similar to a longest path problem with time windows is np complete in the strong sense a number of heuristic methods are described and computational tests reveal that they routinely deliver very close to optimal solutions we describe two upper bounding procedures based upon a preemptive relaxation of the problem and upon the use of lagragean relaxation the heuristics and bounding procedures are incorporated into a dynamic programming algorithm which can solve to optimality randomly generated problem instances with one hundred or more projects we further demonstrate how if problems are too large to be solved optimally a limited enumeration version of this algorithm can be used to provide very accurate heuristic solutions we also examine some special cases and variants of the problem

matrix pencils completion problems ii in this paper we give new simple and explicit necessary and sufficient conditions for the existence of a matrix pencil with prescribed kronecker invariants and a regular subpencil moreover we explicitly solve the problem of describing the possible kronecker invariants of a pencil with a prescribed subpencil in the case of the existence of an intermediate regular pencil all the results are obtained over algebraically closed fields

a new rotation free isogeometric thin shell formulation and a corresponding continuity constraint for patch boundaries abstract this paper presents a general non linear computational formulation for rotation free thin shells based on isogeometric finite elements it is a displacement based formulation that admits general material models the formulation allows for a wide range of constitutive laws including both shell models that are extracted from existing 3d continua using numerical integration and those that are directly formulated in 2d manifold form like the koiter canham and helfrich models further a unified approach to enforce the g 1 continuity between patches fix the angle between surface folds enforce symmetry conditions and prescribe rotational dirichlet boundary conditions is presented using penalty and lagrange multiplier methods the formulation is fully described in the natural curvilinear coordinate system of the finite element description which facilitates an efficient computational implementation it contains existing isogeometric thin shell formulations as special cases several classical numerical benchmark examples are considered to demonstrate the robustness and accuracy of the proposed formulation the presented constitutive models in particular the simple mixed koiter model that does not require any thickness integration show excellent performance even for large deformations

feedback invariants of restrictions a polynomial approach the possible feedback invariants of a linear time invariant dynamical system represented by a pair of matrices a b are studied when the only information about the system is that it has an a b invariant subspace s whose restriction is an autonomous system and the quotient is controllable this problem is shown to be related to the problem of designing a control matrix b 1 for a series connected system to have prescribed feedback invariants

reissner mindlin shell implementation and energy conserving isogeometric multi patch coupling summary a shear flexible isogeometric reissner mindlin shell formulation using non uniform rational b splines basis functions is introduced which is used for the demonstration of a coupling approach for multiple non conforming patches the six degrees of freedom formulation uses the exact surface normal vectors and curvature the shell formulation is implemented in an isogeometric analysis framework for computation of structures composed of multiple geometric entities to enable local model refinement as well as non matching domains coupling a conservative multi patch approach using lagrange multipliers for structured non uniform rational b splines patches is presented here an additional border frame mesh is used to couple geometries during structural analyses this frame interface approach avoids the problem of excessive constraints when multiple patches are coupled at one point first the shell formulation is verified with several reference cases then the influence of the frame interface discretization and frame penalty stiffness on the smoothness of the results is investigated the effects of the perturbed lagrangian method in combination with the frame interface approach is shown in addition results of models with t joint interface connections and perpendicular stiffener patches are presented copyright 2016 john wiley sons ltd

embedding a regular subpencil into a general linear pencil abstract we study the possible strictly equivalence classes of a pencil when a regular subpencil is prescribed we also study the possible invariant polynomials and the possible characteristic polynomials of a by xc xdy when x and y vary

exact wave based bloch analysis procedure for investigating wave propagation in two dimensional periodic lattices abstract this paper presents an exact wave based approach for determining bloch waves in two dimensional periodic lattices this is in contrast to existing methods which employ approximate approaches e g finite difference ritz finite element or plane wave expansion methods to compute bloch waves in general two dimensional lattices the analysis combines the recently introduced wave based vibration analysis technique with specialized bloch boundary conditions developed herein timoshenko beams with axial extension are used in modeling the lattice members the bloch boundary conditions incorporate a propagation constant capturing bloch wave propagation in a single direction but applied to all wave directions propagating in the lattice members this results in a unique and properly posed bloch analysis results are generated for the simple problem of a periodic bi material beam and then for the more complex examples of square diamond and hexagonal honeycomb lattices the bi material beam clearly introduces the concepts but also allows the bloch wave mode to be explored using insight from the technique the square diamond and hexagonal honeycomb lattices illustrate application of the developed technique to two dimensional periodic lattices and allow comparison to a finite element approach differences are noted in the predicted dispersion curves and therefore band gaps which are attributed to the exact procedure more faithfully modeling the finite nature of lattice connection points the exact method also differs from approximate methods in that the same number of solution degrees of freedom is needed to resolve low frequency and arbitrarily high frequency dispersion branches these advantageous features may make the method attractive to researchers studying dispersion characteristics band gap behavior and energy propagation in two dimensional periodic lattices

finite element and nurbs approximations of eigenvalue boundary value and initial value problems abstract we study the spectral approximation properties of finite element and nurbs spaces from a global perspective we focus on eigenfunction approximations and discover that the l 2 norm errors for finite element eigenfunctions exhibit pronounced spikes about the transition points between branches of the eigenvalue spectrum this pathology is absent in nurbs approximations by way of the pythagorean eigenvalue error theorem we determine that the squares of the energy norm errors of the eigenfunctions are the sums of the eigenvalue errors and the squares of the l 2 norm eigenfunction errors the spurious behavior of the higher eigenvalues for standard finite elements is well known and therefore inherited by the energy norm errors along with the spikes in the l 2 norm of the eigenfunction errors the eigenvalue pathology is absent for nurbs the implications of these results to the corresponding elliptic boundary value problem and parabolic and hyperbolic initial value problems are discussed

completion of quasi regular matrix pencils abstract in this paper we give solutions for two important particular cases of the general completion problem involving quasi regular matrix pencil we describe the possible kronecker invariants of a quasi regular pencil whose subpencil is prescribed in the case when the prescribed subpencil is without nontrivial homogeneous invariant factors also we solve the dual problem by describing the possible kronecker invariants of a pencil without nontrivial homogeneous invariant factors when a quasi regular subpencil is prescribed these two results are expected to be the crucial steps toward a solution of the general completion problem the results are given over algebraically closed fields

the algebraic structure of pencils and block toeplitz matrices abstract we restate several results on the kronecker structure obtainable after a given matrix pencil is affected by an arbitrarily small perturbation and state some new results on the kronecker structure after a new row is appended or a column deleted the results are simple consequences of a theory of majorization for semi infinite integer sequences the bounds after a new row is appended correspond to bounding the controllability indices after adding a single input to a linear time invariant dynamical system we illustrate the known relations between the kronecker indices the segre characteristics and the nullities of certain block toeplitz matrices constructed from the original pencils and discuss how those nullities change when the pencil is affected by a perturbation or a new row

fixed rank perturbations of regular matrix pencils abstract a characterization of the structure of a regular matrix pencil obtained by a bounded rank perturbation of another regular matrix pencil has been recently obtained the result generalizes the solution for the bounded rank perturbation problem of a square constant matrix when comparing the fixed rank perturbation problem of a constant matrix with the bounded rank perturbation problem we realize that both problems are of different nature the first one is more restrictive in this paper we characterize the structure of a regular matrix pencil obtained by a fixed rank perturbation of another regular matrix pencil we apply the result to find necessary and sufficient conditions for the existence of a fixed rank perturbation such that the perturbed pencil has a prescribed determinant the results hold over fields with sufficient number of elements

isogeometric reissner mindlin shell analysis with exactly calculated director vectors abstract an isogeometric reissner mindlin shell derived from the continuum theory is presented the geometry is described by nurbs surfaces the kinematic description of the employed shell theory requires the interpolation of the director vector and of a local basis system hence the definition of nodal basis systems at the control points is necessary for the proposed formulation the control points are in general not located on the shell reference surface and thus several choices for the nodal values are possible the proposed new method uses the higher continuity of the geometrical description to calculate nodal basis system and director vectors which lead to geometrical exact interpolated values thereof thus the initial director vector coincides with the normal vector even for the coarsest mesh in addition to that a more accurate interpolation of the current director and its variation is proposed instead of the interpolation of nodal director vectors the new approach interpolates nodal rotations account is taken for the discrepancy between interpolated basis systems and the individual nodal basis systems with an additional transformation the exact evaluation of the initial director vector along with the interpolation of the nodal rotations lead to a shell formulation which yields precise results even for coarse meshes the convergence behavior is shown to be correct for k refinement allowing the use of coarse meshes with high orders of nurbs basis functions this is potentially advantageous for applications with high numerical effort per integration point the geometrically nonlinear formulation accounts for large rotations the consistent tangent matrix is derived various standard benchmark examples show the superior accuracy of the presented shell formulation a new benchmark designed to test the convergence behavior for free form surfaces is presented despite the higher numerical effort per integration point the improved accuracy yields considerable savings in computation cost for a predefined error bound

on the direct solution of wave propagation for repetitive structures abstract the direct method of solving the wave constants for a repetitive structure with given frequency is developed in this paper the analogy between structural mechanics and optimal control theory is applied the dynamic stiffness matrix approach is used to solve for the eigensolutions of wave propagation the weighted adjoint symplectic orthonormality relationship and the eigenvector expansion theorem are also established for this approach the symplectic eigenproblem is derived for skew symmetric matrices a cell triangular decomposition for skew symmetric matrices is introduced to reduce the generalized eigenproblem and the symplectic householder transformation is introduced to cell tri diagonalize the skew symmetric matrix to solve the eigenequation the problem of a wave impinging on the boundary is considered by the eigenvector expansion method which could also be applied to a wave scattering when passing over an abnormal part numerical examples show that resonance will occur for the localized vibration case

superconvergent isogeometric free vibration analysis of euler bernoulli beams and kirchhoff plates with new higher order mass matrices abstract a superconvergent isogeometric free vibration analysis is presented for euler bernoulli beams and kirchhoff plates this method is featured by new higher order mass matrices for the 1d euler bernoulli beam problem it is shown that a new higher order mass matrix can be directly established by optimizing a reduced bandwidth mass matrix the reduced bandwidth mass matrix is designed based upon the consistent mass matrix and it contains adjustable parameters to be determined via maximizing the order of accuracy of the vibration frequency as a result 4th and 6th orders of accuracy are observed for the proposed quadratic and cubic higher order mass matrices while their corresponding consistent mass matrices are 2nd and 4th order accurate respectively thus the higher order beam mass matrices have more superior frequency accuracy simultaneously with smaller bandwidth compared with their corresponding consistent mass matrices while for the 2d kirchhoff plate problem in order to compute arbitrary frequency in a superconvergent fashion a mixed mass matrix is formulated through a linear combination of the consistent mass matrix and the reduced bandwidth mass matrix then by introducing the wave propagation angle the higher order plate mass matrix can be rationally derived from the mixed mass matrix it is proved that the optimal combination parameter for higher order mass matrix depends on the wave propagation angle consequently a particular higher order mass matrix can always be set up for a superconvergent computation of arbitrary vibration frequency it is shown that the quadratic and cubic higher order mass matrices possess 4th and 6th orders of accuracy which are two orders higher than those of the consistent plate mass matrices the construction of higher order mass matrices and the analytical results for vibration frequencies are systematically demonstrated by a set of numerical examples

isogeometric analysis for second order partial differential equations on surfaces we consider the numerical solution of second order partial differential equations pdes on lower dimensional manifolds specifically on surfaces in three dimensional spaces for the spatial approximation we consider isogeometric analysis which facilitates the encapsulation of the exact geometrical description of the manifold in the analysis when this is represented by b splines or nurbs our analysis addresses linear nonlinear time dependent and eigenvalues problems involving the laplace beltrami operator on surfaces moreover we propose a priori error estimates under h refinement in the general case of second order pdes on the lower dimensional manifolds we highlight the accuracy and efficiency of isogeometric analysis with respect to the exactness of the geometrical representations of the surfaces

an extended isogeometric thin shell analysis based on kirchhoff love theory abstract an extended isogeometric element formulation xiga for analysis of through the thickness cracks in thin shell structures is developed the discretization is based on non uniform rational b splines nurbs the proposed xiga formulation can reproduce the singular field near the crack tip and the discontinuities across the crack it is based on the kirchhoff love theory where c 1 continuity of the displacement field is required this condition is satisfied by the nurbs basis functions hence the formulation eliminates the need of rotational degrees of freedom or the discretization of the director field facilitating the enrichment strategy the performance and validity of the formulation is tested by several benchmark examples

unified theorems on completions of matrix pencils abstract we generalize and unify some theorems concerned with the existence of a pencil with a prescribed subpencil and prescribed strict equivalence class

completion up to a matrix pencil with column minimal indices as the only nontrivial kronecker invariants abstract in this paper we give explicit necessary and sufficient conditions for a completion of an arbitrary matrix pencil up to a pencil with a prescribed set of kronecker invariants in the case when the only nontrivial invariants of the resulting pencil are its column row minimal indices the result is given over arbitrary fields

dual and approximate dual basis functions for b splines and nurbs comparison and application for an efficient coupling of patches with the isogeometric mortar method abstract this contribution defines and compares different methods for the computation of dual basis functions for b splines and non uniform rational b splines nurbs they are intended to be used as test functions for the isogeometric mortar method but other fields of application are possible too three different concepts are presented and compared the first concept is the explicit formula for the computation of dual basis functions for nurbs proposed in the work of carl de boor these dual basis functions entail minimal support i e the support of the dual basis functions is equal to the support of the corresponding b spline basis functions in the second concept dual basis functions are derived from the inversion of the gram matrix these dual basis functions have global support along the interface the third concept is the use of approximate dual basis functions which were initially proposed for the use in harmonic analysis the support of these functions is local but larger than the support of the associated b spline basis functions we propose an extension of the approximate dual basis functions for nurbs basis functions after providing the general formulas we elaborate explicit expressions for several degrees of spline basis functions all three approaches are applied in the frame of the mortar method for the coupling of non conforming nurbs patches a method which allows complex discretizations with multiple intersecting interfaces is presented numerical examples show that the explicitly defined dual basis functions with minimal support severely deteriorate the global stress convergence behavior of the mechanical analysis this fact is in accordance with mathematical findings in literature which state that the optimal reproduction degree of arbitrary functions is not possible without extending the support of the dual basis functions the dual basis functions computed from the inverse of the gram matrix yield accurate numerical results but the global support yields significantly higher computational costs in comparison to computations of conforming meshes only the approximate dual basis functions yield accurate and efficient computations where neither accuracy nor efficiency is significantly deteriorated in comparison to computations of conforming meshes all basic cases of t intersections and star intersections are studied furthermore an example which combines all basic cases in a complex discretization is given the applicability of the presented method for the nonlinear case and for shell formulations is shown with the help of one numerical example

an isogeometric indirect boundary element method for solving acoustic problems in open boundary domains abstract this work introduces an indirect boundary element method bem within a nurbs based isogeometric framework for solving three dimensional acoustic problems in the frequency domain developments of isogeometric boundary elements so far have focused on the direct bem yet a multitude of common problems in acoustics involves open boundary surfaces which require a more involved indirect boundary element formulation the current work presents an indirect variational bem which makes use of nurbs shape functions additionally a novel technique for coupling strongly non conforming patches is introduced to allow the analysis of more complex geometries the proposed isogeometric indirect boundary element method is verified against analytical solutions and benchmarked against the conventional polynomial based indirect bem also two open boundary problems are studied including analyses over wider frequency ranges and one industrial type complex geometry containing multiple non conforming patches the proposed method is found to be not only significantly more efficient than its polynomial based counterpart but also very robust against strong non conformities in the nurbs descriptions

the weak substitution method an application of the mortar method for patch coupling in nurbs based isogeometric analysis in this contribution a mortar type method for the coupling of non conforming nurbs surface patches is proposed the connection of non conforming patches with shared degrees of freedom requires mutual refinement which propagates throughout the whole patch due to the tensor product structure of nurbs surfaces thus methods to handle non conforming meshes are essential in nurbs based isogeometric analysis the main objective of this work is to provide a simple and efficient way to couple the individual patches of complex geometrical models without altering the variational formulation the deformations of the interface control points of adjacent patches are interrelated with a master slave relation this relation is established numerically using the weak form of the equality of mutual deformations along the interface with the help of this relation the interface degrees of freedom of the slave patch can be condensated out of the system a natural connection of the patches is attained without additional terms in the weak form the proposed method is also applicable for nonlinear computations without further measures linear and geometrical nonlinear examples show the high accuracy and robustness of the new method a comparison to reference results and to computations with the lagrange multiplier method is given

isogeometric collocation for kirchhoff love plates and shells abstract with the emergence of isogeometric analysis iga the galerkin rotation free discretization of kirchhoff love shells is facilitated enabling more efficient thin shell structural analysis high order shape functions used in iga also allow the collocation of partial differential equations avoiding the time consuming numerical integration of the galerkin technique the goal of the present work is to apply this method to nurbs based isogeometric kirchhoff love plates and shells under the assumption of small deformations since kirchhoff love plate theory yields a fourth order formulation two boundary conditions are required at each location on the contour generating some conflicts at the corners where there are more equations than needed to remedy this overdetermination we provide priority and averaging rules that cover all the possible combinations of adjacent edge boundary conditions i e the clamped simply supported symmetric and free supports greville and alternative superconvergent points are used for nurbs basis of even and odd degrees respectively for square circular and annular flat plates convergence orders are found to be in agreement with a priori error estimates the proposed isogeometric collocation method is then validated and benchmarked against a galerkin implementation by studying a set of problems involving kirchhoff love shells

assigning the kronecker invariants of a matrix pencil by row or column completions abstract the challenge consists in describing the relationships between the kronecker invariants of a matrix pencil and one of its subpencils for a given subpencil an algorithm for constructing a matrix pencil with prescribed kronecker invariants should also be proposed