conservation of angular momentum and energy in the integration of non linear dynamic equations the analysis and implementation of a step by step algorithm conceived to preserve scalar invariants of motion i e angular momentum and energy of a rigid body in the integration of non linear dynamic equations is presented here the considered rigid body is subjected to generic translational and rotational motions with large displacements and finite rotations the algorithm is implemented in a new efficient c f e m code which allows an easy performance of several numerical applications

chow rings of fine quiver moduli are tautologically presented a result of a king and c walter asserts that the chow ring of a fine quiver moduli space is generated by the chern classes of universal bundles if the quiver is acyclic we will show that defining relations between these chern classes arise geometrically as degeneracy loci associated to the universal representation

bracket formulations and energy and helicity preserving numerical methods for the three dimensional vorticity equation abstract the vorticity equation for three dimensional viscous incompressible fluid flows is formulated within different bracket formalisms using the poisson or nambu bracket together with a dissipative bracket the budgets of kinetic energy helicity and enstrophy derived from the bracket formulations are properly inherited by the finite difference equations obtained by invoking the discrete variational derivative method combined with the mimetic finite difference method in particular energy and helicity are conserved precisely in inviscid flow computations the energy and enstrophy dissipate properly owing to viscosity in viscous flow computations and the enstrophy is appropriately produced by the vortex stretching effect in both inviscid and viscous flow computations the relationships between the stream function velocity and vorticity as well as the solenoidal conditions on the velocity and vorticity fields are also inherited numerical experiments on a periodic array of rolls that permits analytical solutions have been done to examine the properties and usefulness of the proposed method

corotational nonlinear dynamic analysis of thin shell structures with finite rotations a new formulation for corotational nonlinear dynamic analysis of thin shell structures involving large displacements and finite rotations has been presented in this paper by introducing the kinematic description of the geometrically exact quasi static shell model to describe the motion of an arbitrary material point in a triangular shell element the new expressions for the inertial force vector and tangent inertia matrix were derived systematically the elastic deformation was handled by using the consistent symmetrizable equilibrated corotational formulation which is independent with respect to the local finite element modeling an energy momentum conserving algorithm and an energy decaying momentum conserving algorithm were developed for nonlinear dynamic analysis by applying the generalized energy momentum method in the corotational formulation three classic numerical examples including the dynamic response free motion and dynamic buckling of thin shell structures were computed to verify the ac

on a stress resultant geometrically exact shell model part vii shell intersections with dof finite element formulations abstract if the mid surface of a shell is smooth the classical theory describes the orientation of the director field attached to the mid surface by two independent rotational degrees of freedom at a shell intersection where this smoothness assumption no longer holds it is shown that the director field in the full nonlinear continuum shell equations must be necessarily described by three degrees of freedom this added degree of freedom however is totally unrelated to the so called drill rotation widely used as a means of tackling the shell intersection problem a computational procedure involving a trivial modification of the global singularity free update procedure described in part iii of this work is described which completely resolves the shell intersection problem without introducing drill springs or related ad hoc devices the proposed approach leaves unchanged standard finite element formulations in terms of 5 dof node affects only the global update formulae and exhibits excellent performance as illustrated by representative numerical simulations

integrating finite rotations abstract we study the integration of problems of evolution in the rotation group instead of attacking the problem in the nonlinear differential manifold so 3 pure rotational dynamics as is usually done we derive equations for the complete problem of motion translational and rotational dynamics on an extended manifold we develop a generalization of runge kutta methods that by design ensures that the solution will remain on the manifold for any choice of the tableau this is obtained through configuration updates performed via the exponential map we show how certain terms can be approximated while retaining the order of accuracy of the scheme and how the method conserves the total momentum of the system within this framework we develop two nonlinearly unconditionally stable time integration schemes that are associated with discrete laws of conservation dissipation of the total energy the dissipating algorithm generalizes to the nonlinear case the high frequency damping characteristics provided by some well known conventional methods we present numerical results to support our analysis and we develop a complete application of this methodology to the nonlinear dynamics of three dimensional rods undergoing large displacements and finite rotations under the assumption of small strains

monotonic convergence of iterative learning control systems with variable pass length abstracta growing number of researchers consider iterative learning control ilc a promising tool for numerous control problems in biomedical application systems we will briefly discuss why classical ilc theory is technically too restrictive for some of these applications subsequently we will extend the classical ilc design in the lifted systems framework to the class of repetitive trajectory tracking tasks with variable pass length we will analyse the closed loop dynamics for two standard learning laws and we will discuss in which sense the tracking error can be reduced by which controller design strategies necessary and sufficient conditions for monotonic convergence will be derived we then summarise all results in a set of practical controller design guidelines finally a simulation study is presented which demonstrates the usefulness of these guidelines and illustrates the special dynamics that occur in variable pass length learning

on the moduli scheme of stable sheaves supported on cubic space curves we investigate the geometry of the simpson moduli space m p inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i of stable sheaves with hilbert polynomial p m 3 m 1 it consists of two smooth rational components m 0 and m 1 of dimensions 12 and 13 intersecting each other transversally along an 11 dimensional smooth rational subvariety the component m 0 is isomorphic to the closure of the space of twisted cubics in the hilbert scheme hilb p inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 02i and m 1 is isomorphic to the incidence variety of the relative hilbert scheme of cubic curves contained in planes in order to obtain the result and to classify the sheaves we characterize mp inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 03i as geometric quotient of a certain matrix parameter space by a nonreductive group we also compute the betti numbers of the chow groups of the moduli space

bdf like methods for nonlinear dynamic analysis we present several time integration algorithms of second order accuracy that are numerically simple and effective for nonlinear elastodynamic problems these algorithms are based on a general four step scheme that has a resemblance to the backward differentiation formulas we also present an extension to the composite strategy of the bathe method appropriate values for the algorithmic parameters are determined based on considerations of stability and dissipativity and less dissipative members of each algorithm have been identified we demonstrate the convergence characteristics of the proposed algorithms with a nonlinear dynamic problem having analytic solutions and test these algorithms with several three dimensional nonlinear elastodynamic problems involving large deformations and rotations employing st venant kirchhoff and compressible neo hookean hyperelastic material models these tests show that stable computations are obtained with the proposed algorithms in nonlinear situations where the trapezoidal rule encounters a well known instability

the abelian nonabelian correspondence and frobenius manifolds we propose an approach via frobenius manifolds to the study began in bck2 of the relation between rational gromov witten invariants of nonabelian quotients x g and those of the corresponding abelianized quotients x t for t a maximal torus in g the ensuing conjecture expresses the gromov witten potential of x g in terms of the potential of x t we prove this conjecture when the nonabelian quotients are partial flag manifolds

a four node corotational quadrilateral elastoplastic shell element using vectorial rotational variables four node corotational quadrilateral elastoplastic shell element summary a four node corotational quadrilateral elastoplastic shell element is presented the local coordinate system of the element is defined by the two bisectors of the diagonal vectors generated from the four corner nodes and their cross product this local coordinate system rotates rigidly with the element but does not deform with the element as a result the element rigid body rotations are excluded in calculating the local nodal variables from the global nodal variables the two smallest components of each nodal orientation vector are defined as rotational variables leading to the desired additive property for all nodal variables in a nonlinear incremental solution procedure different from other existing corotational finite element formulations the resulting element tangent stiffness matrix is symmetric owing to the commutativity of the local nodal variables in calculating the second derivative of strains with respect to these variables for elastoplastic analyses the maxwell huber hencky von mises yield criterion is employed together with the backward euler return mapping method for the evaluation of the elastoplastic stress state the consistent tangent modulus matrix is derived to eliminate locking problems we use the assumed strain method several elastic patch tests and elastoplastic plate shell problems undergoing large deformation are solved to demonstrate the computational efficiency and accuracy of the proposed formulation copyright 2013 john wiley sons ltd

a new energy and momentum conserving algorithm for the non linear dynamics of shells a numerical time integration scheme for the dynamics of non linear elastic shells is presented that simultaneously and independent of the time step size inherits exactly the conservation laws of total linear total angular momentum as well as total energy the proposed technique generalizes to non linear shells recent work of the authors on non linear elastodynamics and is ideally suited for long term large scale simulations the algorithm is second order accurate and can be immediately extended with no modification to a fourth order accurate scheme the property of exact energy conservation induces a strong notion of non linear numerical stability which manifests itself in actual simulations

non linear dynamics of three dimensional rods exact energy and momentum conserving algorithms the long term dynamic response of non linear geometrically exact rods under going finite extension shear and bending accompanied by large overall motions is addressed in detail the central objective is the design of unconditionally stable time stepping algorithms which exactly preserve fundamental constants of the motion such as the total linear momentum the total angular momentum and for the hamiltonian case the total energy this objective is accomplished in two steps first a class of algorithms is introduced which conserves linear and angular momentum this result holds independently of the definition of the algorithmic stress resultants second an algorithmic counterpart of the elastic constitutive equations is developed such that the law of conservation of total energy is exactly preserved conventional schemes exhibiting no numerical dissipation symplectic algorithms in particular are shown to lead to unstable solutions when the high frequencies are not resolved compared to conventional schemes there is little if any additional computational cost involved in the proposed class of energy momentum methods the excellent performance of the new algorithm in comparison to other standard schemes is demonstrated in several numerical simulations

robust iterative learning control for linear systems with multiple time invariant parametric uncertainties this article presents a novel robust iterative learning control algorithm ilc for linear systems in the presence of multiple time invariant parametric uncertainties the robust design problem is formulated as a min max problem with a quadratic performance criterion subject to constraints of the iterative control input update then we propose a new methodology to find a sub optimal solution of the min max problem by finding an upper bound of the worst case performance the min max problem is relaxed to be a minimisation problem applying lagrangian duality to this minimisation problem leads to a dual problem which can be reformulated as a convex optimisation problem over linear matrix inequalities lmis an lmi based ilc algorithm is given afterward and the convergence of the control input as well as the system error are proved finally we apply the proposed ilc to a generic example and a distillation column the numerical results reveal the effectiveness of the lmi based algorithm

dynamic analysis of beam structures considering geometric and constitutive nonlinearity abstract a fully geometric and constitutive nonlinear model for the description of the dynamic behavior of beam structures is developed the proposed formulation is based on the geometrically exact formulation for beams due to simo but in this article an intermediate curved reference configuration is considered the resulting deformation map belongs to a nonlinear differential manifold and therefore an appropriated version of newmark s scheme is used in updating the kinematics variables each material point of the cross section is assumed to be composed of several simple materials with their own constitutive laws the mixing rule is used to describe the resulting composite an explicit expression for the objective measure of the strain rate acting on each material point is deduced in this article details about its numerical implementation in the time stepping scheme are also addressed viscosity is included at the constitutive level by means of a thermodynamically consistent visco damage model developed in terms of the material description of the first piola kirchhoff stress vector the constitutive part of the tangent tensor is deduced including the effect of rate dependent inelasticity finally several numerical examples validating the proposed formulation are given

robust iterative learning control design is straightforward for uncertain lti systems satisfying the robust performance condition this note demonstrates that the design of a robust iterative learning control is straightforward for uncertain linear time invariant systems satisfying the robust performance condition it is shown that once a controller is designed to satisfy the well known robust performance condition a convergent updating rule involving the performance weighting function can be directly obtained it is also shown that for a particular choice of this weighting function one can achieve a perfect tracking in the case where this choice is not allowable a sufficient condition ensuring that the least upper bound of the spl lscr sub 2 norm of the final tracking error is less than the least upper bound of the spl lscr sub 2 norm of the initial tracking error is provided this sufficient condition also guarantees that the infinity norm of the final tracking error is less than the infinity norm of the initial tracking error

an easily implementable fourth order method for the time integration of wave problems abstract we are concerned with the time integration of systems of ordinary differential equations arising from the space discretization of partial differential wave equations with smooth solutions a method is suggested that while being as easily implementable as the standard implicit mid point rule is fourth order accurate the new method is symplectic so that it is very well suited for long time integrations of problems with a hamiltonian structure numerical experiments are reported that refer to a fourth order galerkin space discretization of the korteweg de vries equation and to a pseudospectral space discretization of the same equation

technical communique a robust approach to iterative learning control design for uncertain systems this note proposes a frequency domain design method to achieve an iterative learning controller for uncertain feedback control systems for a linear time invariant plant with multiplicative perturbations and a feedback controller we derive a sufficient condition for the iterative process to converge for all admissible plant uncertainties based on the derived sufficient condition we show that the iterative learning control design problem can be reformulated as a general robust control problem setup consequently the iterative learning controller under plant uncertainty can be systematically designed by wellestablished robust control design procedures

how to render second order accurate time stepping algorithms fourth order accurate while retaining the stability and conservation properties abstract for a fairly general class of second order accurate algorithms a sub stepping procedure is described which achieves fourth order accuracy while retaining the stability conservation properties and implementation of the underlying second order method two features render the proposed approach especially attractive from a computational perspective over conventional fourth order methods first the improved fourth order accuracy is attained merely by two additional residual evaluations with no changes in the implementation of the underlying second order method in particular no additional storage or extra computations of high order gradients are required second for hamiltonian systems the stability properties and possible conservation properties of the underlying second order method such as energy momentum and symplectic character are preserved the new technique is applied to a number of standard algorithms for elastodynamics structural and rigid body dynamics in particular when applied to the recently proposed second order accurate energy momentum method this approach results in a fourth order accurate energy linear and angular momentum conserving algorithm for general hamiltonian systems

an iterative learning control theory for a class of nonlinear dynamic systems abstract an iterative learning control scheme is presented for a class of nonlinear dynamic systems which includes holonomic systems as its subset the control scheme is composed of two types of control methodology a linear feedback mechanism and a feedforward learning strategy at each iteration the linear feedback provides stability of the system and keeps its state errors within uniform bounds the iterative learning rule on the other hand tracks the entire span of a reference input over a sequence of iterations the proposed learning control scheme takes into account the dominant system dynamics in its update algorithm in the form of scaled feedback errors in contrast to many other learning control techniques the proposed learning algorithm neither uses derivative terms of feedback errors nor assumes external input perturbations as a prerequisite the convergence proof of the proposed learning scheme is given under minor conditions on the system parameters

on a stress resultant geometrically exact shell model part vi conserving algorithms for non linear dynamics in parts i to v of the present work the formulation and finite element implementation of a non linear stress resultant shell model are considered in detail this paper is concerned with the extension of these results to incorporate completely general non linear dynamic response of special interest here is the dynamics of very flexible shells undergoing large overall motion which conserves the total linear and angular momentum and for the hamiltonian case the total energy a main goal of this paper is the design of non linear time stepping algorithms and the construction of finite element interpolations which preserve exactly these fundamental constants of motion it is shown that only a very special class of algorithms namely a formulation of the mid point rule in conservation form exactly preserves the total linear and angular momentum for the hamiltonian case a somewhat surprising result is proved regardless of the degree of non linearity in the stored energy function a generalized mid point rule algorithm always exists which exactly conserves energy the conservation properties of a time stepping algorithm need not and in general will not be preserved by the spatial discretization precise conditions which ensure preservation of these conservation properties are derived a number of numerical simulations are presented which illustrate the exact conservation properties of the proposed methodology

on shear correction factors in the non linear theory of elastic shells abstract theoretical values of two correction factors s 5 6 and t 7 10 are established for the respective transverse shear stress resultants and stress couples within the general dynamically and kinematically exact six field theory of elastic shells these values do not depend on the shell material symmetry geometry of the base surface the shell thickness or any kind of kinematic and or dynamic constraints the analysis is based on the complementary energy density following from the transverse shear stresses acting only on the shell cross section the appropriate quadratic and cubic distributions of the stresses across the thickness allow one to derive the consistent constitutive equations for the transverse shear stress resultants and stress couples with s and t as the respective correction factors four numerical examples of highly non linear shell structures illustrate the influence of different values of s and t on the results in particular some influence of t is noticed on the placement of bifurcation points in dynamic problem of flight of three intersecting plates analysed with newmark type temporal algorithm the value of t influences the moment at which the relative error of total energy of the system begins to grow indefinitely leading to the solution failure

unconditionally stable algorithms for rigid body dynamics that exactly preserve energy and momentum we show that for rigid body dynamics the mid point rule formulated in body co ordinates exactly conserves energy and the norm of the angular momentum for incremental force free motions but fails to conserve the direction of the angular momentum vector further we show that the mid point rule formulated in the spatial representation is in general physically and geometrically meaningless an alternative algorithm is developed which exactly preserves energy and the total spatial angular momentum in incremental force free motions the implicit version of this algorithm is unconditionally stable and second order accurate the explicit version conserves exactly angular momentum in incremental force free motions numerical simulations are presented which illustrate the excellent performance of the proposed procedure even for incremental rotations over 65 degrees the procedure is directly applicable to transient dynamic calculations of geometrically exact rods and shells