an exact finite rotation shell theory its mixed variational formulation and its finite element implementation a non linear shell theory including transverse shear strains with exact description of the kinematical fields is developed the strain measures are derived via the polar decomposition theorem allowing for an explicit use of a three parametric rotation tensor thus in plane rotations also called drilling degrees of freedom are included in a natural way various alternatives of the theory are derived for a special version of the theory with altogether six kinematical fields different mixed variational principles are given a hybrid finite element formulation which does not exhibit locking phenomena is developed numerical examples of shell deformation at finite rotations with excellent element performance are presented comparison with results reported in the literature demonstrates the features of the theory as well as the proposed finite element formulation

on the stabilization of a flexible beam with a tip mass we study the stability of a flexible beam that is clamped at one end and free at the other a mass is also attached to the free end of the beam to stabilize this system we apply a boundary control force at the free end of the beam we prove that the closed loop system is well posed and is exponentially stable we then analyze the spectrum of the system for a special case and prove that the spectrum determines the exponential decay rate for the considered case

meshless implementation of the geometrically exact kirchhoff love shell theory summary in the present paper a meshless generalized multiple fixed least squares implementation of the geometrically exact kirchhoff love shell theory is described the material time derivative of the deformation gradient and the first piola kirchhoff stress tensor are considered as basic conjugate quantities to evaluate the internal power the shell s initial geometry is reproduced exactly by the predefined mapping from a reference plane configuration as a constitutive model a neo hookean material whose functional is altered in compliance with the plane stress condition is chosen the augmented weak form suitable for both interpolative and non interpolative approximations thanks to the imposition of the essential boundary conditions through lagrange multipliers is consistently linearized and the resultant bilinear form proved to be symmetric the appearance of the corner reactions related to the jumps of the pseudo torsion boundary moment requires the inclusion of additional pointwise displacement constraints at the essential boundary corners the importance of these quantities is demonstrated in the numerical tests revealing its positive influence on the displacements and particularly their derivatives up to 3rd order in both linear and nonlinear problems the possibility of incorporation of drilling boundary moment for nonlinear problems was successfully assessed copyright 2014 john wiley sons ltd

stabilization and disturbance rejection for the beam equation we consider a system described by the one dimensional linear wave equation in a bounded domain with appropriate boundary conditions to stabilize the system we propose a dynamic boundary controller applied at the free end of the system the transfer function of the proposed controller is a proper rational function of the complex variable and may contain a single pole at the origin and a pair of complex conjugate poles on the imaginary axis provided that the residues corresponding to these poles are nonnegative the rest of the transfer function is required to be a strictly positive real function we then show that depending on the location of the pole on the imaginary axis the closed loop system is asymptotically stable we also consider the case where the output of the controller is corrupted by a disturbance and show that it may be possible to attenuate the effect of the disturbance at the output if we choose the controller transfer function appropriately we also present some numerical simulation results which support this argument

a 4 node finite shell element for the implementation of general hyperelastic 3d elasticity at finite strains abstract in this paper a finite shell element for large deformations is presented based on extensible director kinematics the essential feature is an interface to arbitrary three dimensional material laws the non linear lagrangian formulation is based on the three field variational principle parametrized with the displacement vector enhanced green lagrangian strain tensor and second piola kirchhoff stress tensor the developed quadrilateral shell element is characterized by a course mesh accuracy and distortion insensitivity compared with bilinear displacement approaches furthermore plane stress response is approximately recovered in the asymptotic case of vanishing thickness a number of example problems investigating large deformation as well as finite strain applications are presented compressible and incompressible hyperelastic materials of the st venant kirchhoff neo hookean and mooney rivlin type are particularly used

interconnection and damping assignment passivity based control of port controlled hamiltonian systems passivity based control pbc is a well established technique that has shown to be very powerful to design robust controllers for physical systems described by euler lagrange el equations of motion for regulation problems of mechanical systems which can be stabilized shaping only the potential energy pbc preserves the el structure and furthermore assigns a closed loop energy function equal to the difference between the energy of the system and the energy supplied by the controller thus we say that stabilization is achieved via energy balancing unfortunately these nice properties of el pbc are lost when used in other applications which require shaping of the total energy for instance in electrical or electromechanical systems or even some underactuated mechanical devices our main objective in this paper is to develop a new pbc theory which extends to a broader class of systems the aforementioned energy balancing stabilization mechanism and the structure invariance towards this end we depart from the el description of the systems and consider instead port controlled hamiltonian models which result from the network modelling of energy conserving lumped parameter physical systems with independent storage elements and strictly contain the class of el models

uniform stabilization of a hybrid system of elasticity the problem of boundary feedback stabilization of a euler bernoulli beam with an endmass is considered using a method of compact perturbation the lack of uniform stabilization is proved in the case of a clamped beam with the usual boundary feedbacks applied to the end with the mass next the uniform stabilization when the usual boundary feedbacks are applied to the end without the mass is proved also the uniform decay of energy by means of higher order feedbacks applied to the end with the mass is established

the cosserat surface as a shell model theory and finite element formulation abstract relying on the concept of a cosserat continuum the reduction of the three dimensional equations of a shell body to two dimensions is carried out in a direct manner by considering the cosserat continuum to be a two dimensional surface by that a non linear shell theory including transverse shear strains with exact description of the kinematical fields is derived the strain measures are taken to be the first and the second cosserat deformation tensors allowing for an explicit use of a three parametric rotation tensor thus inplane rotations also called drilling degrees of freedom are included in a natural way the structure of the configuration space is discussed and two possible definitions of it are given equipped once with a killing metric and once with an euclidean one a partially mixed variational principle is proposed on the base of which an efficient hybrid finite element formulation which does not exhibit locking phenomena is developed various numerical examples of shell deformations at finite rotations with excellent element performance are presented

a unified finite strain theory for membranes and ropes abstract the finite strain theory is reformulated in the frame of the tangential differential calculus tdc resulting in a unification in a threefold sense firstly ropes membranes and three dimensional continua are treated with one set of governing equations secondly the reformulated boundary value problem applies to parametrized and implicit geometries therefore the formulation is more general than classical ones as it does not rely on parametrizations implying curvilinear coordinate systems and the concept of co and contravariant base vectors this leads to the third unification tdc based models are applicable to two fundamentally different numerical approaches on the one hand one may use the classical surface fem where the geometry is discretized by curved one dimensional elements for ropes and two dimensional surface elements for membranes on the other hand it also applies to recent trace fem approaches where the geometry is immersed in a higher dimensional background mesh then the shape functions of the background mesh are evaluated on the trace of the immersed geometry and used for the approximation as such the trace fem is a fictitious domain method for partial differential equations on manifolds the numerical results show that the proposed finite strain theory yields higher order convergence rates independent of the numerical methodology the dimension of the manifold and the geometric representation type

genuinely resultant shell finite elements accounting for geometric and material non linearity the underlying theory is statically and geometrically exact and it naturally includes small strain and finite strain problems of thin as well as thick shells this paper examines the development of computational procedures employing the newton kantorovich linearization process and the galerkin type discretization method the treatment of finite rotations through an arbitrary parametrization of the rotation group the interpolation procedure of so 3 valued functions underlying the construction of finite element basis

relative entropy collaborative fuzzy clustering method the main task of clustering methods especially fuzzy methods is to find whether natural grouping exists in data and to impose identity on them in some situations data are stored in several data sites and to discover the global structures clustering methods have to be aware of dependencies in all data sites collaborative fuzzy clustering methods have been proposed and widely studied to answer such need in this paper a novel collaborative fuzzy clustering method is proposed in this method relative entropy concept is used as the communication method a new approach is applied to calculate the interaction coefficient between data sites and horizontal and vertical modes of the proposed method are discussed performance of the proposed method is evaluated using several experiments and the results show that it has the highest quality of collaboration and could classify data more efficiently in many clustering methods it is assumed that the data are stored in one data site ways of communication between data sites effects the clustering results a new communication method based on relative entropy is proposed it minimizes the divergence of membership degrees of kth data in ith cluster in all data sites recfc and its two modes could efficiently classify data stored in several data sites

exponential stability of a class of boundary control systems we study a class of partial differential equations with variable coefficients on a one dimensional spatial domain with control and observation at the boundary for this class of systems we provide simple tools to check exponential stability this class is general enough to include models of flexible structures traveling waves heat exchangers and bioreactors among others the result is based on the use of a generating function the energy for physical systems and an inequality condition at the boundary furthermore based on the port hamiltonian approach we give a constructive method to reduce this inequality to a simple matrix inequality

exponential stabilization of port hamiltonian boundary control systems via energy shaping this article is concerned with the exponential stabilization of a class of linear boundary control systems bcss in port hamiltonian form through energy shaping starting from a first feedback loop that is in charge of modifying the hamiltonian function of the plant a second control loop that guarantees exponential convergence to the equilibrium is designed in this way a major limitation of standard energy shaping plus damping injection control laws applied to linear port hamiltonian bcss namely the fact that only asymptotic convergence is assured has been removed

thin shells with finite rotations formulated in biot stresses theory and finite element formulation a bending theory for thin shells undergoing finite rotations is presented and its associated finite element model is described the kinematic assumption is based on a shear elastic reissner mindlin theory the starting point for the derivation of the strain measures are the resultant equilibrium equations and the associated principle of virtual work within this formulation the polar decomposition of the shell material deformation gradient leads to symmetric strain measures the associated work conjugate stress resultants and stress couples are integrals of the biot stress tensor this tensor is invariant with respect to rigid body motions and therefore appropriate for the formulation of constitutive equations finite rotations are introduced via eulerian angles the finite element discretization of arbitrary shells is based on the isoparametric concept formulated with respect to a plane reference configuration the numerical model is applied to different non linear plate and shell problems and compared with existing formulations due to a consistent linearization the step size of a load increment is only limited by the local convergence behaviour of newton s method

a continuum based shell theory for non linear applications the paper introduces a non linear shell theory which provides a complete three dimensional state of stress since the theory is derived from simple three dimensional continuum mechanics it is very easy to understand as an example the theory is applied to quadrilateral shell elements which provide only displacement degrees of freedom located at nodes on the outer surfaces and one degree of freedom at the middle surface it is proposed to eliminate this degree of freedom on element level so that the elements have the same layout as the equivalent brick elements but have a better behaviour in bending have stress resultants and are cheaper with respect to computational effort the advantages with respect to implementation in a finite element program as well as in special applications are obvious however well known conditioning problems in thin shell applications must be expected therefore emphasis is put on this issue in the example problems it is shown that the elements can give acceptable answers in engineering applications and offer a potential for material non linear applications which will be considered in a forthcoming paper

on the boundary conditions of the geometrically nonlinear kirchhoff love shell theory abstract the present paper addresses the problem of establishing the boundary conditions of a geometrically nonlinear thin shell model especially the kinematic ones our model is consistently derived from general 3d continuum mechanics statements generalized cross sectional strains and stresses are based on the deformation gradient and the first piola kirchhoff stress tensor since only the bending deformation is included in this model no special technique needs to be adopted in order to avoid shear locking the theory is derived in such a way that any material model can be considered as a constitutive relation once the zero transverse normal stress assumption is properly taken into account special attention is given to the question of devising the appropriate shell boundary conditions several parameters are proposed to characterize the boundary rotation for an arbitrary spatial shell configuration the appearance of corner concentrated forces related to jumps of torsion moments is captured and justified a weak form of the equilibrium is presented which is suitable for implementation by means of any numerical technique that provides c 1 continuity approximation it is prone to be used with both interpolative like the finite element method and non interpolative methods like the element free galerkin method the latter is used to exemplify the proposed approach

generalization of the c1 tuba plate finite elements to the geometrically exact kirchhoff love shell model abstract the finite element implementation of a geometrically exact thin shell model is reported in the present paper the shell kinematics is based on the kirchhoff love assumption and is characterized by the deformation gradient which yielded the generalized cross section strain measures stretches and curvatures written in terms of first and second order derivatives of displacements the energetically conjugate quantity the first piola kirchhoff stress tensor is used to define the generalized stresses the shell s initial geometry is exactly represented using a mapping from a reference configuration a neo hookean material functional supplemented by the plane stress condition is incorporated in the constitutive level of the model both configuration dependent and independent forces are considered for the domain and boundary loading the consistent linearization of the rendered weak form is addressed the tuba family of plate finite elements is adopted for the discretization of the displacement vector field these triangular elements with necessarily straight sides in the reference configuration provide c 1 continuous approximations a sine qua non property for a consistent discretization of the kirchhoff love model the family contains 3 pairs of elements primary and reduced which provide polynomial approximants of degrees k 5 6 and 7 respectively the reduced elements have a simpler structure and a smaller number of nodes but still guarantee c 1 continuity the boundary normal derivative of the approximation in these elements is constrained such that its order is reduced by one unit from k 1 at the primary elements to k 2 due to complexity of the elements degrees of freedom which are the function value its normal first and second order derivatives the imposition of the essential boundary conditions requires some preliminary analysis of the boundary behavior such study is presented for the most common practical cases six benchmark examples are presented to demonstrate the model usefulness and efficiency

exponential stabilization of boundary controlled port hamiltonian systems with dynamic feedback it is shown that a strictly input passive linear finite dimensional controller exponentially stabilizes a large class of partial differential equations actuated at the boundary of a one dimensional spatial domain this follows since the controller imposes exponential dissipation of the total energy the result can by use for control synthesis and for the stability analysis of complex systems modeled by sets of coupled pde s and ode s the result is specialized to port hamiltonian control systems and a simplified dna manipulation process is used to illustrate the result

riesz basis property and exponential stability of controlled euler bernoulli beam equations with variable coefficients this paper studies the basis property and the stability of a distributed system described by a nonuniform euler bernoulli beam equation under linear boundary feedback control it is shown that there is a sequence of generalized eigenfunctions of the system which forms a riesz basis for the state hilbert space the asymptotic distribution of eigenvalues the spectrum determined growth condition and the exponential stability are concluded the results are applied to a nonuniform beam equation with viscous damping of variable coefficient as a generalization of existing results for the uniform beam

stability of an euler bernoulli beam with a nonlinear dynamic feedback system this paper is concerned with the stability analysis of a lossless euler bernoulli beam that carries a tip payload which is coupled to a finite dimensional nonlinear dynamic feedback system the latter comprises dynamic systems satisfying the nonlinear kyp lemma which may represent the closed loop dynamics of subordinate controlled actuators as well as the interaction with a nonlinear passive environment global in time wellposedness and asymptotic stability is rigorously proven for the resulting closed loop partial differential equation ordinary differential equation pde ode system the analysis is based on semigroup theory for the corresponding first order evolution problem for the large time analysis precompactness of the trajectories is shown by deriving uniform in time bounds on the solution and its time derivatives

shell curvature as an initial deformation a geometrically exact finite element approach an alternative approach for the analysis of arbitrarily curved shells is developed in this paper based on the idea of initial deformations by alternative we mean that neither differential geometry nor the concept of degeneration is invoked here to describe the shell surface we begin with a flat reference configuration for the shell mid surface after which the initial curved geometry is mapped as a stress free deformation from the plane position the actual motion of the shell takes place only after this initial mapping in contrast to classical works in the literature this strategy enables the use of only orthogonal frames within the theory and therefore objects such as christoffel symbols the second fundamental form or three dimensional degenerated solids do not enter the formulation furthermore the issue of physical components of tensors does not appear another important aspect but not exclusive of our scheme is the possibility to describe exactly the initial geometry the model is kinematically exact encompasses finite strains in a totally consistent manner and is here discretized under the light of the finite element method although implementation via mesh free techniques is also possible assessment is made by means of several numerical simulations copyright 2009 john wiley sons ltd

stress resultant plasticity for shells revisited in this work we revisit the stress resultant elastoplastic geometrically exact shell finite element formulation that is based on the ilyushin shapiro two surface yield function with isotropic and kinematic hardening the main focus is on implicit projection algorithms for computation of updated values of internal variables for stress resultant shell elastoplasticity four different algorithms are derived and compared three of them yield practically identical final results yet they differ considerably in computational efficiency and implementation complexity since they solve different sets of equations and they use different procedures that choose active yield surfaces one algorithm does not provide acceptable accuracy it turns out that the most simple and straightforward algorithm performs surprisingly well and efficiently several numerical examples are presented to illustrate the ilyushin shapiro stress resultant shell formulation and the numerical performance of the presented integration algorithms