improving stability by change of representation in time stepping analysis of non linear beams dynamics in this paper we propose a change in the representation of the discrete motion equations in structural non linear dynamics to obtain an improvement in the stability of time numerical integrations in particular natural local state variables are indicated for a finite element approach to beam problems the results relative to newmark approximations for the variations in the displacement and velocity vectors show a significant increase in the range of stability of the time integration process and a reduction in the number of newton iterations required in the time integration steps the proposed method further preserves energy as well as the linear and angular momentum of the dynamical system copyright 2006 john wiley sons ltd

brief exponential stabilization of nonholonomic dynamic systems by smooth time varying control a general dynamic model is proposed for describing a large class of nonholonomic systems including extended chained systems extended power systems underactuated surface vessel systems etc by introducing an assistant state variable and a time varying state transformation based on the concept of minimal dilation degree this class of nonholonomic systems is transformed into linear time varying control systems and the asymptotic exponential stability is thus achieved by using a smooth time varying feedback control law the existence and uniqueness of the minimal dilation degree for the discussed systems are also proved under certain conditions

nonlinear dynamic analysis of shells with the triangular element tric abstract tric is a facet triangular shell element which is based on the natural mode method it has been shown that the tric shell element satisfies the individual element test and in the framework of the nonconsistent formulation the convergence requirements are fulfilled while it has been proved to be very efficient in linear and nonlinear static problems moreover another major advantage in the formulation of this element is the incorporation of the transverse shear deformations in a way that defies the shear locking phenomenon in this work the derivation of the consistent and lumped mass matrices of the tric element is presented so that it can be used in linear and nonlinear dynamic problems both translational and rotational inertia are included in the consistent mass matrix which is conceived using kinematical and geometrical arguments consistent with the assumed natural rigid body and straining modes of the element all the kinematical and geometrical arguments that are invoked for the derivation of the consistent mass matrix are briefly presented moreover two formulations of the lumped mass matrix of tric are derived the first formulation is based entirely on geometrical considerations whereas the second is based on lumping the consistent mass matrix of tric finally the element s robustness and accuracy will be shown by applying it to properly selected benchmark examples of nonlinear shell dynamics while its computational efficiency will be demonstrated by comparing the cpu performance of the element with the other available shell elements

switched mode feedback control laws for nonholonomic systems in extended power form abstract a class of nonholonomic control systems in extended power form is studied it is demonstrated that under appropriate assumptions lagrange s equations including classical nonholonomic constraints can be transformed into the extended power form a switched mode feedback controller is used to obtain global convergence of the states of the extended power form to the origin this feedback controller can be interpreted as a hybrid system consisting of a high level discrete event supervisor and a family of low level feedback controllers the closed loop system exhibits finite time responses

formulation and analysis of conserving algorithms for frictionless dynamic contact impact problems this paper presents the formulation of conserving time stepping algorithms for frictionless dynamic contact of solids a new class of finite element methods is proposed for the solution of these problems that exhibit the same conservation laws as the underlying continuum dynamical system the proposed methods are based on a penalty regularization of the constrained contact problem and lead to full conservation of the total energy of the system including the regularization penalty potential during persistent contact and restoration of the original energy upon release both linear and angular momenta are conserved by the scheme furthermore the newly developed methods have the ability to enforce the associated constraints in the velocity besides the impenetrability constraint in the displacements while preserving the conservation restoration properties of the final numerical scheme a modification of these schemes is described that assures positive energy dissipation if desired even in the highly nonlinear setting of contact impact problems leading to contact schemes with high frequency energy dissipation representative numerical simulations are presented illustrating the performance of the proposed numerical schemes

nonholonomic motion planning steering using sinusoids methods for steering systems with nonholonomic c onstraints between arbitrary configurations are investigated suboptimal trajectories are derived for systems that are not in canonical form systems in which it takes more than one level of bracketing to achieve controllability are considered the trajectories use sinusoids at integrally related frequencies to achieve motion at a given bracketing level a class of systems that can be steered using sinusoids claimed systems is defined conditions under which a class of two input systems can be converted into this form are given

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

finite time controllers continuous finite time differential equations are introduced as fast accurate controllers for dynamical systems these have qualities superior to controllers which are currently in use in such appl

conservation properties of a time fe method part i time stepping schemes forn body problems in the present paper one step implicit integration algorithms for the n body problem are developed the time stepping schemes are based on a petrov galerkin finite element method applied to the hamiltonian formulation of the n body problem the approach furnishes algorithmic energy conservation in a natural way the proposed time finite element method facilitates a systematic implementation of a family of time stepping schemes a particular algorithm is specified by the associated quadrature rule employed for the evaluation of time integrals the influence of various standard as well as non standard quadrature formulas on algorithmic energy conservation and conservation of angular momentum is examined in detail for linear and quadratic time elements copyright 2000 john wiley sons ltd

explicit design of time varying stabilizing control laws for a class of controllable systems without drift abstract this paper gives a systematic way to design time variant feedback control laws for a class of controllable nonlinear systems this class contains a lot of systems which cannot be stabilized via a time invariant feedback control law the interest of this work lies in the design method since a general existence results is already available the techniques employed here are basic they mainly involve classical lyapunov analysis

a unified set of single step algorithms part 1 general formulation and applications a general algorithm for a single step time marching scheme for use in dynamic or diffusion equations is presented this algorithm is easily programmed in its universal form for all orders of approximation and covers most of the currently used schemes as well as presenting many new possibilities in many cases it presents a computationally advantageous form over conventional procedures this is particularly so when compared with the newmark algorighm and its variants

nonregular feedback linearization a nonsmooth approach in this note we address the problem of exact linearization via nonsmooth nonregular feedback a criterion of nonregular static state feedback linearizability is presented for a class of nonlinear affine systems with two control inputs and its application to nonholonomic systems is briefly discussed

energy conserving and decaying algorithms in non linear structural dynamics a generalized formulation of the energy momentum methodwill be developed within the framework of the generalizedmethodwhich allows at the same time guaranteed conservation or decay of total energy and controllable numerical dissipation of unwanted high frequency response furthermore the latter algorithm will be extended by the consistently integrated constraints of energy and momentum conservation originally derived for the constraint energy momentum algorithm the goal of this general approach of implicit energyconserving and decaying time integration schemes is to compare these algorithms on the basis of an equivalent notation by the means of an overall algorithmic design and hence to investigate their numerical properties numerical stability and controllable numerical dissipation of high frequencies will be studied in application to non linear structural dynamics among the methods considered will be the newmark method the classical methods the energy momentum methodwith and without numerical dissipation the constraint energymomentum algorithm and the constraint energy method copyright 1999 john wiley sons ltd

constraint energy momentum algorithm and its application to non linear dynamics of shells abstract a modified time integration method is developed for non linear structural dynamics combining controllable algorithmic dissipation of higher modes and at the same time conservation of energy as well as linear and angular momentum although these features seem to be actually inconsistent numerical stability with large time steps for dynamic buckling and snap through problems as well as for dynamical systems with smooth solutions is guaranteed arbitrary implicit one step time integration schemes with newmark approximations are suitable for use as basic algorithms for the proposed method the desired conservation attributes are obtained if the basic algorithm is augmented by energy and momentum constraints the potential of the suggested algorithm is demonstrated by selected applications to non linear dynamics of shell structures

generalized energy momentum method for non linear adaptive shell dynamics in the present study a generalization of the energy momentum method denoted by generalized energy momentum method applied to the non linear dynamics of shells will be developed within the framework of the generalized a method this algorithmic environment contains the unconditionally stable energy momentum method and its numerically damped version as well as the classical newmark and a methods as special cases in order to control the size of the time steps of the integration scheme with respect to accuracy and eaciency an adaptive time stepping procedure based on local a posteriori error estimation will be improved for non linear dynamical systems and applied to the proposed class of algorithms the spatial discretization is realized by an eight noded finite shell element of reissner mindlin type including an extensible shell director field permitting the application of three dimensional material laws the original formulation of this finite element will be developed for non linear dynamic analysis and adapted for the employment within the introduced energy conserving decaying time integration scheme 1999 elsevier science s a all rights reserved

control and stabilization of nonholonomic dynamic systems a class of inherently nonlinear control problems has been identified the nonlinear features arising directly from physical assumptions about constraints on the motion of a mechanical system models are presented for mechanical systems with nonholonomic constraints represented both by differential algebraic equations and by reduced state equations control issues for this class of systems are studied and a number of fundamental results are derived although a single equilibrium solution cannot be asymptotically stabilized using continuous state feedback a general procedure for constructing a piecewise analytic state feedback which achieves the desired result is suggested

finite rotation analysis and consistent linearization using projectors abstract a systematic procedure is presented that may be used to extend the capabilities of an existing linear finite element to accomodate finite rotation analysis this procedure is a generalization of the work presented in computers and structures volume 30 pp 257 267 the basis of our approach is the element independent co rotational algorithm where the element rigid body motion translations and rotations is separated from the deformational part of its total motion the variation of this co rotational relation results in a projector matrix with the property that a consistent internal force vector is invariant under its action the consistent tangent stiffness matrix is shown to depend on this invariance condition through the derivative of the projector this results in an unsymmetric tangent matrix whose anti symmetric part depends on the out of balance force vector in this paper we prove that using the symmetric part of the tangent matrix the newton iteration retains its quadratic rate of convergence this approach has been used to solve a number of large rotation test example problems the results demonstrate that it is possible to analyze structures undergoing large rotations within a general co rotational framework using simple and economical finite elements the resulting improvements in the performance of these simple elements are brought about through the use of convenient software utilities as pre and post processors to the element routines

global stabilizing near optimal control design for nonholonomic chained systems it is well known that a nonlinear optimal control requires the solution to a two point boundary value problem or to a nonlinear partial differential equation and that such a solution can only be obtained off line by numerical iteration in this paper a new and near optimal control design framework is proposed for controlling any nonholonomic system in the chained form the proposed design is based upon thorough study of uniform complete controllability of the corresponding linear time varying nominal system it is shown that no matter whether the first component u1d t of reference input vector is uniformly nonvanishing or simply nonconvergent to zero or vanishing or identically zero uniform complete controllability of the nominal system can be recovered by employing the proposed time folding unfolding technique upon establishing the common property of uniform complete controllability the proposed framework can be used to design both trajectory tracking control and regulation control in a systematic and unified manner using duality uniform complete observability can also be established a closed form and exponentially convergent observer can be synthesized and the controls designed using the proposed framework can be either state feedback or output feedback the tracking controls are designed using the same three step process that is design of the proposed controls starts with optimal control solutions to two linear nominal subsystems one time invariant and the other time varying the two solutions combined together render a globally stabilizing suboptimal control for the overall system then the optimality condition is invoked to determine the distance between the suboptimal control and the optimal one consequently an improved control can be obtained by introducing a nonlinear additive control term in such a way that the distance aforementioned is minimized as much as possible in closed form an example is used to show that regulation control can be designed similarly all the controls designed are in simple closed forms and hence real time implementable they are time varying and smooth globally and exponentially asymptotically stabilizing and they are near optimal since their closeness to the optimal control attainable only offline can be measured monitored on line and has been minimized

co rotational flat facet triangular elements for shell instability analyses abstract this paper investigates the formulation of co rotational flat facet triangular elements for the numerical analysis of instability phenomena in shell structures the elements have three nodes with six degrees of freedom at each node the term co rotational relates here to the provision of a local system that continuously rotates and translates with the element following mainly nour omid and rankin b nour omid and c c rankin finite rotation analysis and consistent linearization using projectors comput methods appl mech engrg 93 1991 353 384 the definition of an element resorts to a change of variables from the local frame to the global one this is done through the use of a projector matrix which relates the variations of the local displacements to the variations of the global ones by extracting the rigid body modes from the latter the main difference from the original formulation lies in the parameterization of 3d finite rotations in contrast to the paper by nour omid and rankin a parameterization based on the rotational vector is here adopted and thus an additional change of variables has to be performed as a result the rotational variables become additive and the necessity of a special updating procedure is avoided the main feature of the adopted formulation is its independence of the local assumptions used to derive the internal forces and tangent stiffness in local coordinates for a certain class of elements i e elements with the same number of nodes and degrees of freedom the main co rotational framework is the same using this property three types of local formulations are considered a set of carefully chosen test problems is used in order to assess the performances of the three element types

zeta function continuation and the casimir energy on odd and even dimensional spheres the zeta function continuation method is applied to compute the casimir energy on spheressn both odd and even dimensional spheres are studied for the appropriate conformally modified laplacian the casimir energy is shown to be finite for all dimensions even though generically it should diverge in odd dimensions due to the presence of a pole in the associated zeta function s the residue of this pole is computed and shown to vanish in our case an explicit analytic continuation of s is constructed for all values ofn this enables us to calculate exactly and we find that the casimir energy vanishes in all even dimensions for odd dimensions is never zero but alternates in sign asn increases through odd values some results are also derived for the casimir energy of other operators of laplacian type