p version plate and curved shell element for geometrically non linear analysis this paper presents a p version geometrically non linear formulation based on the total lagrangian approach for a nine node three dimensional curved shell element the element geometry is defined by the coordinates of the nodes located on its middle surface and nodal vectors describing the bottom and top surfaces of the element the element displacement approximation can be of arbitrary and different polynomial orders in the plane of the element and in the transverse direction the element approximation functions and the corresponding nodal variables are derived from the lagrange family of interpolation functions the resulting approximation functions and the nodal variables are hierarchical and the element displacement approximation ensures c continuity the element properties are established using the principle of virtual work and the hierarchical element approximation in formulating the properties of the element complete three dimensional stresses and strains are considered hence the element is equally effective for very thin as well as extremely thick shells and plates incremental equations of equilibrium are derived and solved using the standard newton raphson method the total load is divided into increments and for each increment of load equilibrium iterations are performed until each component of the residuals is within a preset tolerance numerical examples are presented to show the accuracy efficiency and advantages of the present formulation the results obtained from the present formulation are compared with those available in the literature

modelling of superelements in mechanism analysis the paper deals with substructuring for dynamic analysis of flexible multibody systems three different techniques based on component synthesis are discussed corresponding respectively to fully consistent mass discretization lumped mass discretization and corotational approximation of inertia forces to simplify the computer implementation only the lumped mass and corotational approximations have been considered in detail and programmed both approaches are validated on simple examples of rotating beams for which a full elastic model is available using a fully non linear beam element the computational efficiency of the corotational inertia approach is also demonstrated on the deployment of a large flexible satellite antenna

an element free galerkin approach for rigidflexible coupling dynamics in 2d state based on an improved element free galerkin efg method and the geometric nonlinear elastic theory an element free numerical approach for rigidflexible coupling dynamics of a rotating hubbeam system is implemented using the hamilton principle the coupled nonlinear integral differential governing equations are derived in which the dynamic stiffening effect is expressed by the longitudinal shrinking of the beam induced by the transverse displacement by the efg method where the global interpolating moving least squares imls and generalized moving least squares igmls were used for discretizing the longitudinal and transverse deformation variables respectively the spatially element free discretized dynamic equations of the system are obtained and the newmark scheme was selected as the time integration method for the numerical computation the superiority of the global interpolating property makes the ease for imposing both displacement and derivative boundary conditions the transverse bending vibration and structural dynamics of the flexible beam in non inertial system are analyzed in the numerical simulations and influence parameters of the efg method are also fully discussed simulation results verify the feasibility of the improved efg approach for rigidflexible coupling dynamics

non linear substructure approach for dynamic analysis of rigid flexible multibody systems abstract this paper presents a substructure synthesis method ssm for non linear analysis of multibody systems the detailed derivation of the equation of motion which takes into account the geometric non linear effects of large rotation undergoing small strain elastic deformation is presented using the substructure synthesis approach the equation of motion of the systems can be simplified for rigid and flexible substructures for the flexible substructure the equation of motion is condensed through the boundary conditions at the interface between the flexible and rigid substructures as a result equations of motion for multi flexible body systems including the geometric non linear effects of large rotation are derived to demonstrate the applicability and accuracy of the proposed approach an example of a two link manipulator was chosen for this presentation the results using the linear and non linear models are presented to highlight the effects of geometric non linearities

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

large displacements of shells including material nonlinearities abstract the paper presents a finite element formulation of shells with large deflections including elastoplastic material behaviour the elements utilized are the so called degenerated shell elements with special emphasis on the simple 4 node quadrilateral both the total lagrangian and the updated lagrangian formulation are considered for the treatment of plastic behaviour the concept of a layered element model is proposed and investigated for both the tangential modulus method and the initial load method in the final section sample problems are presented and compared with reference solutions it is shown that the 4 node element is very well suited to the class of problems under consideration it is characterized by an easy applicability high accuracy and low rates of computer time in appendix a an analytical solution of a cantilever beam subjected to an end load including geometrical and material nonlinearities is presented

vibration analysis of 3 d composite beam elements including warping and shear deformation effects abstract in this paper the dynamic analysis of 3 d composite beam elements restrained at their edges by the most general boundary conditions and subjected in arbitrarily distributed dynamic loading is presented for the solution of the problem at hand a boundary element method is developed for the construction of the 14 14 stiffness matrix and the nodal load vector of a member of an arbitrarily shaped composite cross section taking into account both torsional warping and shear deformation effects which together with the corresponding mass and damping matrices lead to the formulation of the equation of motion to account for shear deformations the concept of shear deformation coefficients is used defining these factors using a strain energy approach eight boundary value problems with respect to the variable along the bar angle of twist to the primary warping function to a fictitious function to the beam transverse and longitudinal displacements and to two stress functions are formulated and solved employing a pure bem approach both free and forced vibrations are considered taking also into account effects of transverse longitudinal rotatory torsional and warping inertia and damping resistance numerical examples are presented to illustrate the method and demonstrate its efficiency and accuracy

non linear dynamic analysis of beams with variable stiffness abstract in this paper the analog equation method aem a bem based method is employed to the non linear dynamic analysis of a bernoulli euler beam with variable stiffness undergoing large deflections under general boundary conditions which maybe non linear as the cross sectional properties of the beam vary along its axis the coefficients of the differential equations governing the dynamic equilibrium of the beam are variable the formulation is in terms of the displacements the governing equations are derived in both deformed and undeformed configuration and the deviations of the two approaches are studied using the concept of the analog equation the two coupled non linear hyperbolic differential equations with variable coefficients are replaced by two uncoupled linear ones pertaining to the axial and transverse deformation of a substitute beam with unit axial and bending stiffness respectively under fictitious time dependent load distributions a significant advantage of this method is that the time history of the displacements as well as the stress resultants are computed at any cross section of the beam using the respective integral representations as mathematical formulae beams with constant and varying stiffness are analyzed under various boundary conditions and loadings to illustrate the merits of the method as well as its applicability efficiency and accuracy

accurate rigid body modes representation for a nonlinear curved thin shell element for certain highly curved shells such as bellows the formulation of a curved shell finite element with curvilinear displacement components may fail to properly model some rigid body modes even with either the explicit inclusion of rigid body terms or the use of high order displacement functions it is suggested in this paper that the rigid body modes can be properly included if the cartesian displacement components are used a 48 degree of freedom dof curved thin shell element is formulated and both the curvilinear and the cartesian forms are used for this investigation examples of the nonlinear analyses of a bellows shell and a spherical cap are given to demonstrate the advantage of using the cartesian formulation curved elements may also suffer from membrane locking which is caused by the inability of an element to bend without stretching numerical data are presented to show that the present element does not membrane lock some nonlinear examples are also presented to further demonstrate the versatility of this element

lyapunov characterization of input to state stability for semilinear control systems over banach spaces abstract we prove that input to state stability iss of nonlinear systems over banach spaces is equivalent to existence of a coercive lipschitz continuous iss lyapunov function for this system for linear infinite dimensional systems we show that iss is equivalent to existence of a non coercive iss lyapunov function and provide two simpler constructions of coercive and non coercive iss lyapunov functions for input to state stable linear systems

a rotation free shell formulation using nodal integration for static and dynamic analyses of structures summary this paper proposed a rotation free thin shell formulation with nodal integration for elastic static free vibration and explicit dynamic analyses of structures using three node triangular cells and linear interpolation functions the formulation is based on the classic kirchhoff plate theory in which only three translational displacements are treated as the filed variables based on each node the integration domains are further formed where the generalized gradient smoothing technique and green divergence theorem that can relax the continuity requirement for trial function are used to construct the curvature filed with the aid of strain smoothing operation and tensor transformation rule the smoothed strains in the integration domain can be finally expressed by constants the principle of virtual work is then used to establish the discretized system equations the translational boundary conditions are imposed same as the practice of standard finite element method while the rotational boundary conditions are constrained in the process of constructing the smoothed curvature filed to test the performance of the present formulation several numerical examples including both benchmark problems and practical engineering cases are studied the results demonstrate that the present method possesses better accuracy and higher efficiency for both static and dynamic problems copyright 2015 john wiley sons ltd

dynamics of flexible multibody systems using cartesian co ordinates and large displacement theory a formulation for the dynamic analysis of flexible systems composed of slender bodies that can be accurately modelled by beams is presented in this paper a new set of state variables composed of cartesian co ordinates of points and unit vectors is introduced to define the beam with respect to an inertial frame a non linear timoshenko beam finite element capable of handling finite displacements with small linear elastic strains is developed this allows relative displacements between material points of a single beam to be arbitrarily large since deformations are not explicit variables there is no need to define a moving reference frame attached to each flexible body instead deformations are obtained through a displacement deformation relation based on finite displacement beam theory the differential equations of motion are obtained using the lagrange equations a symmetric constant and sparse mass matrix is obtained in the inertial frame constraints are introduced with a penalty formulation and the resulting set of ordinary differential equations is integrated with newmark s family of methods the whole formulation is extremely simple and the results demonstrate the capabilities and efficiency of the proposed method for dynamic simulation even when relative displacements are finite in a single beam or coupling effects are significant

universal integral controllers for minimum phase nonlinear systems we consider a single input single output siso nonlinear system that has a well defined normal form with asymptotically stable zero dynamics using only knowledge of the relative degree and the sign of the high frequency gain we design an output feedback integral controller that asymptotically regulates the output to a bounded time varying reference signal with a constant limit we give regional as well as semi global results we also show that for relative degree one and two systems the proposed integral controller reduces to the classical pi and pid controllers respectively

dynamics of rectangular plates undergoing prescribed overall motion a set of linear equations of motion for rectangular plates undergoing prescribed overall motion is derived in this paper two in plane stretch variables with which the in plane strain energy of the plate can be expressed in an exact quadratic form are employed and approximated to derive the equations of motion the equations of motion include motion induced stiffness variation terms which are expressed as explicit functions of the prescribed overall motion the effects of the motion induced stiffness variation terms which are neglected in the conventional linear modelling method on the dynamic response of the plate are investigated the reliability and the accuracy of the equations of motion which are derived in the present work are examined through the numerical study

geometrically nonlinear formulation of a 48 d o f quadrilateral shell element with rational b spline geometry a geometrically nonlinear formulation for a 48 degrees of freedom d o f quadrilateral shell element is presented each of the three displacement functions of u v and w is based on the bicubic hermitian polynomial the surface of the element is modelled using linearized ratronal b spline functions which may be linked to the geometric data bases generated by the computer aided design system the displacement functions and the 48 d o f are expressed in both curvilinear and cartesian forms whereas the strain displacement equations are expressed in curvilinear co ordinates the use of cartesian displacement functions and degrees of freedom allow for the proper representation of the six rigid body motions even for the element with nonzero gaussian curvature such as a bellows two examples are demonstrated snap through buckling of a spherical cap and large deflection of a semi toroidal bellows shell results compare well with alternative solutions

a simple element for static and dynamic response of beams with material and geometric nonlinearities a unified simple 6 degrees of freedom beam finite element and the associated computational procedures have been developed for the fast and efficient solution of a wide class of static and dynamic response problems of the beam type with material and or geometrical nonlinearities the material nonlinearity is treated by including its effect in the governing equations by forming the stiffness matrix of each element using a two dimensional grid of gauss points and using the material properties at each point corresponding to the uniaxial strain at that point examples are provided for metal and reinforced concrete beams a powerful yet straightforward method for the solution of elastica problems of beams and frames using the beam element developed by the senior author has been extended for determining the dynamic response of beams undergoing large displacements including large rotations the solution procedure involves piecewise linearization of response equations and iterations at each incremental step to achieve equilibrium the solution procedure is simple and easy to apply a variety of problems is solved to determine the applicability of the proposed simple formulations excellent agreement with existing analytical solutions which employ higher order elements demonstrates the efficiency and versatility of the present simple beam element in nonlinear analysis

dynamic analysis of 3 d beam elements including warping and shear deformation effects abstract in this paper the dynamic analysis of 3 d beam elements restrained at their edges by the most general linear torsional transverse or longitudinal boundary conditions and subjected in arbitrarily distributed dynamic twisting bending transverse or longitudinal loading is presented for the solution of the problem at hand a boundary element method is developed for the construction of the 14 14 stiffness matrix and the corresponding nodal load vector of a member of an arbitrarily shaped simply or multiply connected cross section taking into account both warping and shear deformation effects which together with the respective mass and damping matrices lead to the formulation of the equation of motion to account for shear deformations the concept of shear deformation coefficients is used defining these factors using a strain energy approach eight boundary value problems with respect to the variable along the bar angle of twist to the primary warping function to a fictitious function to the beam transverse and longitudinal displacements and to two stress functions are formulated and solved employing a pure bem approach that is only boundary discretization is used both free and forced transverse longitudinal or torsional vibrations are considered taking also into account effects of transverse longitudinal rotatory torsional and warping inertia and damping resistance numerical examples are presented to illustrate the method and demonstrate its efficiency and accuracy the influence of the warping effect especially in members of open form cross section is analyzed through examples demonstrating the importance of the inclusion of the warping degrees of freedom in the dynamic analysis of a space frame moreover the discrepancy in the dynamic analysis of a member of a spatial structure arising from the ignorance of the shear deformation effect necessitates the inclusion of this additional effect especially in thick walled cross section members

generalized warping effect in the dynamic analysis of beams of arbitrary cross section abstract in this paper a general formulation for the nonuniform warping dynamic analysis of beams of arbitrary simply or multiply connected cross section under arbitrary external loading and general boundary conditions is presented taking into account the effects of rotary and warping inertia the nonuniform warping distributions are taken into account by employing four independent warping parameters multiplying a shear warping function in each direction and two torsional warping functions respectively which are obtained by solving the corresponding boundary value problems formulated exploiting the longitudinal local equilibrium equation a shear stress correction is also performed in order to improve the stress field arising from the employed kinematical considerations ten initial boundary value problems are formulated with respect to the displacement and rotation components as well as to the independent warping parameters and solved using the analog equation method a boundary element method based technique in combination with an appropriate time integration scheme the warping functions and the geometric constants including the additional ones due to warping are evaluated employing a pure bem approach

on peano s theorem in banach spaces abstract we show that if x is an infinite dimensional separable banach space or more generally a banach space with an infinite dimensional separable quotient then there is a continuous mapping f x x such that the autonomous differential equation x f x has no solution at any point

torsion constant for matrix analysis of structures including warping effect abstract in this research an effective torsion constant j eff for a wide flanged member with different warping restraint conditions at the ends is developed in order to derive j eff the boundary conditions for different warping restraint conditions at the ends as imposed by the use of different types of connections in steel structures are employed in the general equation of torsional rotation o this effective torsion constant can be used directly instead of the st venant torsion constant j in the conventional member stiffness matrix the use of j eff will account for the effect of warping when using the commercial computer programs which employ either a 6 x 6 member stiffness matrix for grid or a 12 x 12 member stiffness matrix for space frame a table for factor f which is the ratio of j eff to j is presented for different member properties and warping restraint conditions for the easy and rapid torsional analysis of structures composed of wide flanged members by the matrix method the solutions of a sample grid problem using j eff are compared with well known solutions to demonstrate its application

nonlinear aeroelastic study for folding wing structures doi 10 2514 1 44868 a folding wing structure consisting of three components a fuselage an inboard wing and an outboard wing is modeled computationally using a geometrically nonlinear structural dynamics theory based upon von karman strainsandathree dimensionalvortexlatticeaerodynamicmodelwithanexacttangent flowboundaryconditionand planar wake assumption the structural dynamic equations of motion are discretized in space using a discrete ritz basis derived from finite element analysis and component synthesis results from the computational model are comparedwiththosefromexperimentsdesignedandtestedinthedukeuniversitywindtunnelforthreefoldingwing configurations stablelimitcycleoscillationsat flowvelocitiesbeyondthelinear fluttervelocityaremeasuredinwindtunnel experiments and predicted using the computational model overall the limit cycle oscillation magnitude and dominant response frequency results from theory show good agreement with those measured in the experiment qualitatively both the experimental and theoretical limit cycle oscillation curves for the inboard wing show limited nonlinear stiffening with flow velocity for the range of velocities tested the theoretical model also predicts that the outboard wing limit cycle oscillation tip displacements for the folding wing configuration with the largest outboard folding angle is significantly higher than the two other configurations unlike the inboard wing for each configuration the outboard wing theoretical limit cycle oscillation curves do show a trend that is reminiscent of a stiffening nonlinearity

robust control for a nonlinear servomechanism problem this paper deals with the design of output feedback control to achieve asymptotic tracking and disturbance rejection for a class of nonlinear systems when the exogenous signals are generated by a known linear exosystem the system under consideration is single input single output input output linearizable minimum phase and modelled by an input output model of the form of an nth order differential equation we assume that at steady state the nonlinearities of the system can only introduce a finite number of harmonics of the original exosystem modes this assumption enables us to identify a linear servo compensator which is augmented with the original system moreover we augment a series of m integrators at the input side where m is the highest derivative of the input and then represent the augmented system by a state model the augmented system is stabilized via a separation approach in which a robust state feedback controller is designed first to ensure boundedness of all state variables and track

a procedure for analysing space frames with partial warping restraint stiffness matrices for three dimensional beam elements that include the effect of warping restraint on elastic torsional response have been derived by various investigators using one of the available stiffness matrices and assuming that the warping boundary conditions can be specified on a member by member basis an elastic warping support is introduced to represent conditions of partial warping restraint at the member ends the concept of a warping indicator is then introduced to facilitate use of warping springs following this static condensation is used to eliminate the restrained warping degrees of freedom the condensed stiffness matrices for the elements can then be assembled to yield a global stiffness matrix in the global matrix continuous warping degrees of freedom that is those internal to a member represented by several elements are expressed in local co ordinates the remainder are expressed in global co ordinates in the force recovery phase it is shown that an indirect method yields most accurate results for the bimoment and warping torsion when the twist function is represented by a cubic polynomial solutions to examples of linear elastic analysis are compared with well known analytical solutions to demonstrate the application of the method

nonlinear dynamic analysis with a 48 d o f curved thin shell element the developments of an existing 48 degrees of freedom d o f curved quadrilateral thin shell element for materially and geometrically nonlinear static analysis of shell structures are extended for the study of dynamic responses of nonlinear shells the variable order polynomial representations of the shell surface and the non axisymmetric definition of the shell boundaries allow the study of the dynamic behaviour of a class of shell structures more general than those treated by using flat plate elements and elements with assumptions of axisymmetry the equations of motion are based on a lagrangian frame of reference a combination of step by step and iterative procedures is used for the solution of nonlinear equations the incremental equations of motion are linearized for computation purposes and an algorithm for numerical integration based on newmark s generalized operator for dynamic analysis using optional iteration is adopted the flow theory of plasticity is used in the inelastic range and perfectly plastic or isotropic strain hardening materials are considered the spread of plastic zones in the thickness direction is treated by using a layered model numerical examples presented include the dynamic analyses of a square plate a circular annulus a cylindrical panel and a spherical cap comparisons with existing solutions demonstrate the validity and accuracy of the present developments

non uniform warping including the effects of torsion and shear forces part i a general beam theory this two part contribution presents a beam theory with a non uniform warping including the effects of torsion and shear forces and valid for any homogeneous cross section made of isotropic elastic material part i is devoted to the theoretical developments and part ii discusses analytical and numerical results obtained for torsion and shear bending of cantilever beams made of different kinds of cross section the theory is based on a kinematics assuming that the cross section maintains its shape and including three independent warping parameters associated to the three warping functions corresponding to torsion and shear forces starting from this displacement model and using the principle of virtual work the corresponding beam theory is derived for this theory closed form results are obtained for the cross sectional constants and the three dimensional expressions of the normal and shear stresses comparison with classical beam theories is carried out and additional effects due to the non uniformity of the warping are highlighted in particular the contributions of primary and secondary internal forces and the effect of the non symmetry of the cross section on the structural behavior of the beam are specified simplified versions of this theory wherein the number of degrees of freedom is reduced are also presented the analytical and numerical analyzes presented in part ii give responses on the quality of this non uniform beam theory and indicate also when its simplified versions could be applied

geometric non linear substructuring for dynamics of flexible mechanical systems a substructure synthesis formulation is presented that permits use of established flexible multibody dynamic analysis computer codes to account for structural geometric non linear effects large relative displacement is permitted between points within bodies that undergo small strain elastic deformation components are divided into substructures on each of which the theory of linear elasticity relative to a body reference frame is adequate to describe deformation and its coupling with system motion normal vibration and static correction deformation modes are used to account for elastic deformation within each substructure compatibility conditions are derived and imposed as constraint equations at boundary points between substructures system equations of motion that include geometric non linear effects of large rotation in terms of generalized co ordinates of a reference frame for each substructure and a set of deformation modes that are defined within the substructure are assembled the method is implemented in an industry standard flexible multibody dynamics code with minimal modification use of the formulation is illustrated on the classical problem of a spinning beam with geometric stiffening and on a space structure that experiences large deformation

nonlinear postbuckling analysis of plates and shells by four noded strain element this paper deals with the nonlinear postbuckling analysis of plates and shells by the finite element method the four noded c strain element for nonlinear plate anaysis developed by the authors is first extended to the nonlinear shell analysis and then used for the nonlinear postbuckling analysis of plates and shallow shells the element tangent stiffness matrix presented here is given explicitly i e without any numerical integration consequently this c strain element is much more computationally economical and efficient than the widely used elements obtained from numerical integration the efficiency and accuracy of the present four noded strain element for postbuckling analysis are demonstrated by five numerical examples of various plates and shells

geometrically nonlinear formulation for the curved shell elements this paper presents a geometrically nonlinear formulation using total lagrangian approach for the three dimensional curved shell elements the basic element geometry is constructed using the coordinates of the middle surface nodes and the mid surface nodal point normals the element displacement field is described using three translations of the mid surface nodes and the two rotations about the local axes the existing shell element formulations are restricted to small nodal rotations between two successive load increments the element formulation presented here removes such restrictions this is accomplished by retaining nonlinear nodal rotation terms in the definition of the displacement field and the consistent derivation of the element properties the formulation presented here is very general and yet can be made specific by selecting proper nonlinear functions representing the effects of nodal rotations the element properties are derived and presented in detail numerical examples are also presented to demonstrate the behaviour and the accuracy of the elements

a curved quadrilateral element for static analysis of shells with geometric and material nonlinearities a 48 degrees of freedom quadrilateral element including the effect of both material and geometric nonlinearities is formulated and appropriate numerical procedures are adopted for the development of a systematic and efficient approach for the static nonlinear analysis of general shell structures the element surface is described by a variable order polynomial in curvilinear co ordinates the displacement functions are described by bicubic hermitian polynomials in curvilinear co ordinates without being confined to the assumption of axisymmetry this formulation allows for the treatment of shells with a more general shape and with a complex spread of plastic zones in the formulation for geometric nonlinearity the total lagrangian approach is adopted only small strains and small rotations are allowed in the formulation for plastic deformation the concept of a layered element model is used in the inelastic range the material is assumed to obey the von mises yield criterion and the prandtl reuss flow rule a tangential stiffness formulation is combined with the modified newton raphson iteration method for the solution of nonlinear problems a systematic choice of examples ranging from fiat plates to cylindrical panels and to spherical caps is solved and compared with available solutions to evaluate the recommended formulations and procedures in terms of their accuracy and efficiency

a separation principle for a class of non uco systems this paper introduces a new approach to output feedback stabilization of single input single output systems which unlike other techniques found in the literature does not use quasilinear high gain observers and control input saturation to achieve separation between the state feedback and observer designs rather we show that by using nonlinear high gain observers working in state coordinates together with a dynamic projection algorithm the same kind of separation principle is achieved for a larger class of systems which are not uniformly completely observable by working in state coordinates this approach avoids using knowledge of the inverse of the observability mapping to estimate the state of the plant which is otherwise needed when using high gain observers to estimate the output time derivatives

deformation modes in the finite element absolute nodal coordinate formulation abstract the objective of this study is to provide interpretation of the deformation modes in the finite element absolute nodal coordinate formulation using several strain definitions in this finite element formulation the nodal coordinates consist of absolute position coordinates and gradients that can be used to define a unique rotation and deformation fields within the element as well as at the nodal points the results obtained in this study clearly show cross section deformation modes eliminated when the number of the finite element nodal coordinates is systematically and consistently reduced using the procedure discussed in this paper one can obtain a reduced order dynamic model eliminate position vector gradients that introduce high frequencies to the solution of some problems achieve the continuity of the remaining gradients at the nodal points and obtain a formulation that automatically satisfies the principle of work and energy furthermore the resulting dynamic model unlike large rotation finite element formulations leads to a unique rotation field and as a consequence the obtained formulation does not suffer from the problem of coordinate redundancy that characterizes existing large deformation finite element formulations in order to accurately define strain components that can have easy physical interpretation a material coordinate system is introduced to define the material element rotation and deformation using the material coordinate system the timoshenko reissner and euler bernoulli beam models can be systematically obtained as special cases of the absolute nodal coordinate formulation beam models while a constraint approach is used in this study to eliminate the cross section deformation modes it is important to point out as mentioned in this paper that lower order finite elements some of which already presented in previous investigations can be efficiently used in thin and stiff structure applications

on ω limit sets of ordinary differential equations in banach spaces abstract let x be an infinite dimensional real banach space we classify limit sets of autonomous ordinary differential equations x f x x 0 x 0 where f x x is lipschitz as being of three types i iii we denote by s x the class of all sets in x which are limit sets of a solution to 1 for some lipschitz vector field f and some initial condition x 0 x we say that s s x is of type i if there exists a lipschitz function f and a solution x such that s x and x t t 0 s we say that s s x is of type ii if it has non empty interior we say that s s x is of type iii if it has empty interior and for every solution x of eq 1 where f is lipschitz such that s x it holds x t t 0 s our main results are the following s is a type i set in s x if and only if s is a closed and separable subset of the topological boundary of an open and connected set u x suppose that there exists an open separable and connected set u x such that s u then s is a type ii set in s x every separable banach space with a schauder basis contains a type iii set moreover in all these results we show that in addition f may be chosen c k smooth whenever the underlying banach space is c k smooth

cross sections of solution funnels abstract let x be a separable infinite dimensional real banach space we denote by f x the class of continuous functions f r x x such that the ode u f t u u t 0 x t 0 r x x has a global solution for any initial condition our main result states that a x is the cross section of a solution funnel of the ode u f t u u 0 0 for some f f x if and only if a is an analytic set

nonlinear dynamic finite element analysis of composite cylindrical shells considering large rotations a new nonlinear finite element formulation is developed for the nonlinear dynamics of shell structures using a vectorial approach the kinematics that can be used to describe very large displacements and large rotations are derived green strain measures and second piola kirchhoff stress measures are used in the determination of the total potential a displacement based eight noded cylindrical shell element with a total of 36 degrees of freedom is developed several numerical examples are dynamically analyzed to observe the characteristics of large displacements and large rotations a convergence study was carried out to establish the numerical accuracy of the model the most efficient and accurate model was used he nonlinear vibration analysis of shells has been the focus of research for the past few years thin shells subjected to dynamic loads could encounter deflections of the order of the thick ness of the shell dynamic response of thin shells also could lead to the phenomena of dynamic snapping or dynamic buckling be cause these kinds of responses cannot be determined accurately using small displacement and small rotation theories large defor mation and large rotation theories are required the complex nature of these theories requires solving numerous simultaneous nonlin ear differential equations even with simplifying assumptions these equations remain complex and extensive as background a few relevant past efforts are reviewed earlier work regarding the nonlinear vibrations for isotropic shell structures can be attributed to carr 1 yeh 2 clough and wilson 3 belytschko and marchertas 4 and belytschko and tsay 5 these researchers used flat plate elements saigal and yang6 developed a curved shell element for isotropic shells for composite shell structures simitses7 provided an elegant analytical solution of thin laminated shells subjected to sudden loads he ignored through the thickness shear effects and used donnell type kinematic relations raouf and palazotto8 9 developed a perturbation procedure to derive a set of asymptotically consistent nonlinear equations of motion for an arbi trary laminated composite cylindrical shell in cylindrical bending they also neglected transverse shear effects simo and tarnow10 de veloped an energy and momentum conservating algorithm for shell analysis to analyze shells undergoing large rigid body motions palazotto and dennis11 presented the simplified large rotation slr theory to analyze shells experiencing moderately large ro tations the slr theory determines the equilibrium path of or thotropic shells using a total lagrangian approach and includes a parabolic transverse shear stress distribution this approach cap tures the appropriate kinematics through displacement polynomi als green strain displacement relations are used and all of the final displacement functions are carried into the expression for the total potential without making any attempt at separating the rigid body movement using this approach the features classically pre sented for including through the thickness shear for example can be exploited 12 smith and palazotto13 discussed eight higher order shear theories to the nonlinear finite element analysis of compos ite shells they also used the green lagrange strains and second piola kirchhoff stresses these theories were successful for large displacements and moderately large rotations a reason for the fail ure of these theories in the modeling of large rotation can be at tributed to the approximations used in the kinematics gummadi and palazotto14 modified the kinematics incorporated in the slr theory and successfully carried out the solutions to problems ex hibiting the characteristics of very large displacements and rota tions in their work a vectorial approach was followed to derive the appropriate kinematics that can capture the characteristics of large displacements and large rotations using appropriate assumptions the kinematics for the slr theory can be obtained as a special case the large rotation kinematics was introduced through the use of sine and cosine functions a 36 degree of freedom composite shell element was developed based on this theory based on the slr theory tsai and palazotto15 formulated a nonlinear dynamic finite element analysis procedure for composite cylindrical shells in their work a linear mass matrix was incorpo rated along with the nonlinear stiffness matrix that was originally developed in slr theory this theory again has the same drawbacks as the slr theory in terms of realizing the large displacements and large rotations in the present paper a theory that can capture the large displacement and large rotations is discussed the present work is an extension of the authors earlier work on large rotation theory for static analysis a new mass matrix is generated using hamilton equations the mass matrix thus generated is a nonlin ear mass matrix a fi m method15 is used to solve the nonlinear algebraic equations resulting from the finite element technique se lected numerical examples are solved to determine the validity of the developed theory

an inertia capacitance beam substructure formulation based on the bond graph method with application to rotating beams in this paper a novel inertia capacitance ic beam substructure formulation based on the ic field presentation from the bond graph method is developed the ic beam provides a modular systematic and graphical approach to beam modeling these features allow the modeler to focus more on the modeling and less on the mathematics as such the ic beam is proposed as an alternative to the many existing types of beam models available in the literature the ic beam is formulated in the center of mass body fixed coordinate system allowing for easy interfacing in a multibody system setting this floating frame approach is also computationally cheap elastic deformations in the ic beam are assumed to be small and described by modal superposition the formulation couples rigid body and elastic deformations in a nonlinear fashion the formulation is also compact and efficient detailed derivations for a two dimensional planar ic beam with bending modes are presented a modal acceleration method based on the decoupling of bending modes is proposed for use in the ic beam the rotating beam spin up maneuver problem is solved the karnopp margolis method is applied to ensure complete integral causality for an efficient numerical system geometric substructuring technique is applied to model large deflections the ic beam is shown to be capable of solving the rotating beam problem accurately and efficiently

a geometrically non linear tensorial formulation of a skewed quadrilateral thin shell finite element a 48 degree of freedom d o f skewed quadrilateral thin shell finite element including the effect of geometrical non linearity is formulated and appropriate numerical procedures are adopted for the development of an efficient approach for the static and dynamic analysis of general thin shell structures the element surface is described by a variable order polynomial in curvilinear co ordinates the displacement functions are described by bicubic hermitian polynomials in curvilinear co ordinates the directions of the curvilinear co ordinates at each nodal point are uniquely defined to coincide with the directions of the boundaries of the element in the present case of a skewed quadrilateral with non orthogonal curvilinear coordinates the coupling terms of the metric tensor and curvature tensor of the surface no longer vanish such as in the case of orthogonal co ordinates the tensor form is used in the setup of the shape functions geometric derivatives stiffness matrix and computer code this allows for the treatment of shells with irregular shapes and variable curvatures to evaluate the efficiency and accuracy of this formulation a systematic list of examples is chosen i linear and non linear static analysis of square and rhombic plates cylindrical and spherical shells ii linear vibrations of trapezoidal flat and curved plates iii large amplitude vibrations of a rhombic plate for the square plate and cylindrical and spherical shell shewed element meshes with various distortion angles are used to study the effect of the distortion angles on the accuracy of the results and to demonstrate the versatility of the present element all results are compared with alternative available solutions including those obtained using regular rectangular meshes pinched thin cylindrical and spherical shells are studied using different skewed meshes and various gauss integration meshes and no membrane locking phenomenon is observed

a two dimensional shear deformable beam element based on the absolute nodal coordinate formulation in this study a new two dimensional shear deformable beam element is proposed for large deformation problems the kinematics of the beam are defined using an exact displacement field where the rotation angles of the cross section caused by bending and shear deformations are described separately cubic interpolation is used for determining the curvature of the beam due to bending while linear interpolation polynomials are used for the shear strain the absolute nodal coordinate formulation in which global displacements and slopes are used as the nodal coordinates is employed for the finite element discretization of the beam the capability of the element to predict static deformation is studied using numerical examples the results imply that the element is free of a phenomenon called shear locking the capability of the element to model highly nonlinear behaviour is established using a bending test where the cantilever is bent into a full circle using only four elements a flexible pendulum and a spin up manoeuvre are modelled in order to study the behaviour of the element in dynamical problems the proposed element is also compared with an existing shear deformable beam element based on the absolute nodal coordinate formulation finally the simple linearization of the beam curvature based on the assumption of small strain will be discussed

geometrically nonlinear transient analysis of laminated composite shells using the finite element method abstract the nonlinear transient response of composite shells with without cutouts and initial geometric imperfection is investigated using the finite element method the present formulation considers doubly curved shells incorporating von karman type nonlinear strains into the first order shear deformation theory the analysis is carried out using quadratic c0 eight noded isoparametric element the governing nonlinear equations are solved by using the newmark average acceleration method in the time integration in conjunction with modified newton raphson iteration scheme the validity of the model is demonstrated by comparing the present results with those available in the literature parametric studies are carried out varying the radius of curvature to width ratio and amplitude of initial geometric imperfection of laminated composite cylindrical spherical and hyperbolic paraboloid shells with without cutouts