an asymptotic analysis of composite beams with kinematically corrected end effects a finite element based beam analysis for anisotropic beams with arbitrary shaped cross sections is developed with the aid of a formal asymptotic expansion method from the equilibrium equations of the linear three dimensional 3d elasticity a set of the microscopic 2d and macroscopic 1d equations are systematically derived by introducing the virtual work concept displacements at each order are split into two parts such as fundamental and warping solutions first we seek the warping solutions via the microscopic 2d cross sectional analyses that will be smeared into the macroscopic 1d beam equations the variations of fundamental solutions enable us to formulate the macroscopic 1d beam problems by introducing the orthogonality of asymptotic displacements to six beam fundamental solutions the end effects of a clamped boundary are kinematically corrected without applying the sophisticated decay analysis method the boundary conditions obtained herein are applied to composite beams with solid and thin walled cross sections in order to demonstrate the efficiency and accuracy of the formal asymptotic method based beam analysis famba presented in this paper the numerical results are compared to those reported in literature as well as 3d fem solutions

a mixed variational formulation based on exact intrinsic equations for dynamics of moving beams abstract a nonlinear intrinsic formulation for the dynamics of initially curved and twisted beams in a moving frame is presented the equations are written in a compact matrix form without any approximations to the geometry of the deformed beam reference line or to the orientation of the intrinsic cross section frame in accordance with previously published work when effects of warping on the dynamics and local constraints on the cross sectional deformation are ignorable the in and out of plane st venant warping displacements which are fully coupled for nonhomogeneous anisotropic beams need only be included explicitly in the determination of a suitable elastic law a two dimensional problem and need not be considered explicitly in the one dimensional equations governing global deformation in this paper it is presupposed that such an elastic law is given as a one dimensional strain energy function thus the present equations which are based on only six generalized strain variables are valid for beams with closed cross sections and for which warping is unrestrained when simplified for various special cases they agree with similar intrinsic equations in the literature although the resulting equations are newtonian in structure closely resembling euler s dynamical equations for a rigid body the formulation adheres to a variational approach throughout thus providing a link between newtonian and energy based methods in particular the present development provides substantial insight into the relationships among variational formulations in which different displacement and rotational variables are used as well as between these formulations and newtonian ones for computational purposes a compact and complete mixed variational formulation is presented that is ideally suited for development of finite element analyses finally a specialized version of the intrinsic equations is developed in which shear deformations is suppressed

an enhancement of constraint feasibility in bpn based approximate optimization back propagation neural networks bpn have been extensively used as global approximation tools in the context of approximate optimization a traditional bpn is normally trained by minimizing the absolute difference between target outputs and approximate outputs when bpn is used as a meta model for inequality constraint function approximate optimal solutions are sometimes actually infeasible in a case where they are active at the constraint boundary the paper explores the development of the efficient bpn based meta model that enhances the constraint feasibility of approximate optimal solution the bpn based meta model is optimized via exterior penalty method to optimally determine interconnection weights between layers in the network the proposed approach is verified through a simple mathematical function and a ten bar planar truss problem for constrained approximate optimization design of rotor blade is conducted to support the proposed strategies

variational asymptotic method for unit cell homogenization of periodically heterogeneous materials a new micromechanics model namely the variational asymptotic method for unit cell homogenization vamuch is developed to predict the effective properties of periodically heterogeneous materials and recover the local fields considering the periodicity as a small parameter we can formulate a variational statement of the unit cell through an asymptotic expansion of the energy functional it is shown that the governing differential equations and periodic boundary conditions of mathematical homogenization theories mht can be reproduced from this variational statement in comparison to other approaches vamuch does not rely on ad hoc assumptions has the same rigor as mht has a straightforward numerical implementation and can calculate the complete set of properties simultaneously without using multiple loadings this theory is implemented using the finite element method and an engineering program vamuch is developed for micromechanical analysis of unit cells many examples of binary composites fiber reinforced composites and particle reinforced composites are used to demonstrate the application power and accuracy of the theory and the code of vamuch

on the asymptotic boundary conditions of an anisotropic beam via virtual work principle in this research an efficient and effective method is proposed to derive the boundary conditions of an anisotropic beam in the asymptotic sense we first set up the constrained virtual work by introducing the lagrange multiplier on the displacement prescribed boundary the macroscopic beam and microscopic cross section equations with the boundary conditions are simultaneously obtained by taking the asymptotic expansion on the displacement vector in this way the three dimensional characteristics of the beam are asymptotically smeared into the macroscopic beam equations and the beam boundary conditions the boundary conditions obtained are then compared to those from the decay analysis method the beam bending slope boundary condition obtained in the frame work of variational principle is different from the well known average condition this new boundary condition is more accurate than the average one for a sandwich beam this is further demonstrated and discussed via the examples of a cantilever beam loaded at the end

cross sectional analysis of nonhomogeneous anisotropic active slender structures a general formulation for the reduction of the three dimensional problem of electrothermoelasticity in slender solids to an arbitrarily defined reference line is presented the dimensional reduction is based on a variationalasymptotic formulation using the slenderness ratio as small parameter in the proposed scheme the coupled linear electroelastic equations are solved at the cross sectional level using the finite element method furthermore modal components of the displacement field are added to introduce arbitrary deformation shapes into the onedimensional analysis and arbitrary electric modes are used to define applied electric fields at the cross section this results in a general definition of a coupled electroelastic stiffness which can be used in virtually all composite and active beam formulations as well as in the development of new low order high accuracy reduced models for active structures finally the formulation also yields recovery relations for the elastic and electric fields in the original three dimensional solid once the one dimensional problem is solved the method has been implemented in a computer program um vabs and numerical results are presented for active anisotropic beam cross sections of simple geometries which are shown to compare very well with three dimensional finite element analysis

cross sectional analysis of composite beams including large initial twist and curvature effects an asymptotically exact methodology based on geometrically nonlinear three dimensional elasticity is presented for cross sectional analysis of initially curved and twisted nonhomogeneous anisotropic beams the analysis is subject only to the restrictions that the strain is small relative to unity and that the maximum dimension of the cross section is small relative to the wavelength of the deformation and to the minimum radius of curvature and or twist the final one dimensional strain energy per unit length exhibits asymptotically correct second order dependence of the initial curvature and twist parameters cross sectional constants of the one dimensional theory are obtained via finite element discretization over the cross sectional plane numerical results obtained for both isotropic and composite beams are compared with published results from special purpose analyses for initially twisted straight beams as well as initially curved untwisted beams the agreement with previously published results is excellent

an asymptotically correct model for initially curved and twisted thin walled composite beams abstract the variational asymptotic method has been applied to develop an asymptotically correct model for initially curved and twisted thin walled composite beams of arbitrary cross sectional shapes and arbitrary anisotropic materials in a two step asymptotic reduction procedure the three dimensional strain energy is asymptotically reduced first to a two dimensional shell strain energy and then to a one dimensional beam strain energy this is a new attempt where initially curved and twisted thin walled composite beams with open or closed sections have been modeled in an asymptotically correct unified framework

on some solvable systems of difference equations abstract we show that the following systems of difference equations x n 1 u n 1 v n y n 1 w n 1 s n n n 0 where u n v n w n s n are some of the sequences x n or y n with real initial values x 0 and y 0 are solvable in fourteen out of sixteen possible cases two cases are left unsolved probably the most interesting is the result in the case u n x n v n x n w n x n s n y n where a fascinating formula is obtained in an elegant way by using some ad hoc ideas

on the relative position of twist and shear centres in the orthotropic and fiberwise homogeneous saint venant beam theory abstract the relationship between twist and shear centres in an orthotropic s aint v enant beam with fiberwise homogeneous elastic moduli and constant poisson ratios is investigated arbitrary cross sections are considered as a new result the relative position of these points is expressed in terms of the scalar potential whose gradient is the rotated field of twist tangential stresses its evaluation requires the solution of n 1 boundary value problems being n 0 the number of holes in the cross section in an isotropic and homogeneous beam the potential is p randtl stress function and known formulae providing the relative position of twist and shear centres are recovered explicit expressions of sliding torsional compliance blocks for t imoshenko beams defined by an energy condition of equivalence with the orthotropic and fiberwise homogeneous s aint v enant theory are provided coincidence of twist centre and t imoshenko shear centre is proven numerical computations on homogeneous and composite orthotropic l sections are performed

quasi static and dynamic response of viscoelastic helical rods in this study the dynamic behaviour of cylindrical helical rods made of linear viscoelastic materials are investigated in the laplace domain the governing equations for naturally twisted and curved spatial rods obtained using the timoshenko beam theory are rewritten for cylindrical helical rods the curvature of the rod axis effect of rotary inertia and shear and axial deformations are considered in the formulation the material of the rod is assumed to be homogeneous isotropic and linear viscoelastic in the viscoelastic material case according to the correspondence principle the material constants are replaced with their complex counterparts in the laplace domain ordinary differential equations in scalar form obtained in the laplace domain are solved numerically using the complementary functions method to calculate the dynamic stiffness matrix of the problem in the solutions the kelvin model is employed the solutions obtained are transformed to the real space using the durbin s numerical inverse laplace transform method numerical results for quasi static and dynamic response of viscoelastic models are presented in the form of graphics

on asymptotically correct timoshenko like anisotropic beam theory abstract this paper presents a finite element cross sectional beam analysis capable of capturing transverse shear effects the approach uses the variational asymptotic method and can handle beams of general cross sectional shape and arbitrary anisotropic material the work builds on previous works which deal with development of the classical beam theory which includes only extension torsion and bending a timoshenko like formulation is sought to achieve a refined theory with simple boundary conditions apart from some simple special cases it is shown that this problem is overdetermined however it is possible to obtain the best possible solution using the least squares minimization technique the geometrical meaning of the shear variable for this formulation is also derived results are found to be in good agreement with published results for the shear stiffness coefficients for both isotropic and anisotropic beams

on the positive solutions of the system of rational difference equations xn 1 1 yn k yn 1 yn xn myn m k abstract our aim in this paper is to investigate the periodic nature of solutions of the system of rational difference equations x n 1 1 y n k y n 1 y n x n m y n m k n 0 1 where k is a nonnegative integer m is a positive integer and the initial values x m x m 1 x 0 y m k y m k 1 y 0 are positive real numbers

best strip beam properties derivable from classical lamination theory this paper presents a simple method to extract classical beam properties for composite strips with general anisotropy from an asymptotically correct classical lamination theory derived using the variational asymptotic method none of the ad hoc approximations common in the literature of beam theory are used rather this approach discovers the necessary and su cient engineering assumptions for obtaining the correct cross sectional constants and stress recovery relations for a strip numerical examples are provided to illustrate that the resulting theory resulting elastic constants agree well with those from well established methods of calculating cross sectional constants and the accuracy deteriorates as the strip thickness to width ratio increases

stability analysis of columns with imperfection in this paper geometrically exact fully intrinsic equations and variational asymptotic beam sections are used to study the buckling and postbuckling of a column under self weight initial curvature effects both generalized one dimensional beam equations and the cross sectional stiffness properties the effects of initial curvature have been studied on buckling and postbuckling in this paper this problem is a valuable test case for the utility of the fully intrinsic equations and variational asymptotic beam sections

analysis of a beam cross section under coupled actions including transversal shear abstract an efficient finite elements fe based method of cross sectional analysis of a longitudinally homogeneous beam with an arbitrary cross section and material model assumed submitted to tension compression bending torsion and shear is developed a new formulation of this classical problem is done as a special case of the homogenization theory it takes into account 3d strain and stress state fulfilling equilibrium compatibility and constitutive equations at any point stress free conditions on lateral surfaces but preserves control by cross sectional stress resultant forces and corresponding generalized strains a source of problems caused by the presence of a shear force is explained and a way of overcoming it is shown in the paper both variational formulation of the problem and its 2d fe solution are given benchmark cases including shear of a square a composite l section an orthotropic square and an elasto plastic analysis of shearing of a square section show correctness of the method finally two practical cases of application of the method to an analysis of reinforced concrete beam sections are shown

on timoshenko like modeling of initially curved and twisted composite beams abstract a generalized finite element based cross sectional analysis for nonhomogenous initially curved and twisted anistropic beams is formulated from geometrically nonlinear three dimensional 3 d elasticity the 3 d strain field is formulated based on the concept of decomposition of the rotation tensor and is given in terms of one dimensional 1 d generalized strains and a 3 d warping displacement that is obtained from the formulation not assumed the warping is found in terms of the 1 d strains via the variational asymptotic method vam in this paper a timoshenko like model is presupposed for a beam with cross sectional characteristic length h wavelength of deformation given by l and the magnitude of the radius of initial curvature and or twist is taken to be of the order r first a solution for the asymptotically correct refinement of classical anisotropic beam theory for initially curved and twisted beams through o h2 r2 is obtained next the o h2 l2 correction is computed it is known that timoshenko like theory is not capable of capturing all the o h2 l2 corrections for generally anisotropic beams however if all the o h2 l2 terms are known then the corresponding timoshenko like theory is uniquely defined numerical results are presented to illustrate the trends of the various classical extension twist bending twist and extension bending and nonclassical couplings extension shear bending shear and shear torsion as the initial twist and curvatures are varied

sensitivity analysis of flexible multibody systems using composite materials components in this paper a general formulation for the computation of the first order analytical sensitivities based on the direct method using automatic differentiation of flexible multibody systems is presented the direct method for sensitivity calculation is obtained by differentiating the equations that define the response of the flexible multibody systems of composite materials with respect to the design variables which are the ply orientations of the laminated in order to appraise the benefits of the approach suggested and to highlight the risks of the procedure the analytical sensitivities are compared with the numerical results obtained by using the finite difference method for the beam composite material elements the section properties and their sensitivities are found using an asymptotic procedure that involves a two dimensional 2 d finite element analysis of their cross section the equations of the sensitivities are obtained by automatic differentiation and integrated in time simultaneously with the equations of motion of the multibody systems the equations of motion and the sensitivities of the flexible multibody system are solved and the accelerations velocities and the sensitivities of accelerations and velocities are integrated in time using a multi step multi order integration algorithm through the application of the methodology to two simple flexible multibody systems the difficulties and benefits of the procedure with respect to finite difference approaches or to the direct implementation of the analytic sensitivities are discussed copyright 2008 john wiley sons ltd

on some systems of difference equations abstract in this note we show that the following systems of difference equations u n 1 v n 1 v n v n 1 u n 1 u n u n 1 v n 1 u n v n 1 u n 1 v n u n 1 u n 1 v n v n 1 v n 1 u n with n n 0 and complex initial values u 0 and v 0 are solvable explicitly by means of riccati equations and based on the formulae for the general solutions we present the behaviour of their solutions as n while the result is natural for the first system it is a bit surprising for the other two systems

validation of the variational asymptotic beam sectional analysis the computer program vabs variational asymptotic beam section analysis uses the variational asymptotic method to split a three dimensional nonlinear elasticity problem into a twodimensional linear cross sectional analysis and a one dimensional nonlinear beam problem this is accomplished by taking advantage of certain small parameters inherent to beam like structures vabs is able to calculate the one dimensional cross sectional stiffness constants with transverse shear and vlasov refinements for initially twisted and curved beams with arbitrary geometry and material properties several validation cases are presented first an elliptic bar is modeled with transverse shear refinement using the variational asymptotic method and the solution is shown to be identical to that obtained from the theory of elasticity the shear center locations calculated by vabs for various cross sections agree well with those obtained from common engineering analyses comparisons with other composite beam theories prove that it is unnecessary to introduce ad hoc kinematic assumptions to build an accurate beam model for numerical validation values of the one dimensional variables are extracted from an abaqus model and compared with results from a one dimensional beam analysis using cross sectional constants from vabs furthermore point wise three dimensional stress and strain fields are recovered using vabs and the correlation with the three dimensional results from abaqus is excellent finally classical theory is shown to be insufficient for general purpose beam modeling appropriate refined theories are recommended for some classes of problems

variational asymptotic micromechanics modeling of heterogeneous porous materials abstract this paper presents a numerical technique to predict the effective elastic properties of heterogeneous fluid filled porous media where the heterogeneity may result from dissimilar solid and fluid phase properties or due to mismatch in porous microstructure the technique is based on the variational asymptotic method of homogenization where finite element method is employed for discretization biot s theory of poroelasticity is used to describe porous media where both solid and fluid phase motions u u formulation are considered with associated strain measures the method estimates the poroelastic constitutive law in single analysis which makes it very efficient compared to other finite element based homogenization techniques the method is also general enough to compute all 28 elements of an anisotropic constitutive matrix other than estimating the effective properties the micro stress strain distribution is also obtained at no additional cost the method is successfully applied for homogenization of porous media fluid filled cavity and finally for effective property estimation of bone lamella in absence of any other direct method of porous media homogenization the present technique is compared with classical homogenization methods with fluid approximated as solid of very high poisson s ratio the suitability of this approximation and various other alternatives are also discussed it is shown that the present homogenization method can be an efficient tool for bone property estimation where fluid filled porous hierarchical micro nanostructure must be respected at all steps

on the theory of porous elastic rods we consider the direct approach to the theory of rods in which the thin body is modelled as a deformable curve with a triad of rigidly rotating orthonormal vectors attached to every material point in this context we employ the theory of elastic materials with voids to describe the mechanical behavior of porous rods first we derive the dynamical nonlinear field equations of the model then in the framework of linear theory we prove the uniqueness of the solution to the associated boundary initial value problem we identify the relevant field quantities from the theory of directed curves by comparison with the three dimensional equations of straight porous rods finally for orthotropic and homogeneous rods we determine the constitutive coefficients in terms of the three dimensional elasticity constants by solving several problems in the two different approaches

long term stable time integration scheme for dynamic analysis of planar geometrically exact timoshenko beams abstract in this paper an energy momentum method for geometrically exact timoshenko type beam is proposed the classical time integration schemes in dynamics are known to exhibit instability in the non linear regime the so called timoshenko type beam with the use of rotational degree of freedom leads to simpler strain relations and simpler expressions of the inertial terms as compared to the well known bernoulli type model the treatment of the bernoulli model has been recently addressed by the authors in this present work we extend our approach of using the strain rates to define the strain fields to in plane geometrically exact timoshenko type beams the large rotational degrees of freedom are exactly computed the well known enhanced strain method is used to avoid locking phenomena conservation of energy momentum and angular momentum is proved formally and numerically the excellent performance of the formulation will be demonstrated through a range of examples

on the rational difference equation y n 1 a y n y n k we find conditions for the global asymptotic stability of the unique negative equilibrium y 1 a of the equation yn 1 a yn yn k where y k y k 1 y0 a r and k 1 2 3 4

on the system of two difference equations xn 1 i 0kai yn ipi yn 1 i 0kbi xn iqi abstract in this paper we study the system of two difference equations of the form x n 1 i 0 k a i y n i p i y n 1 i 0 k b i x n i q i where a i b i i 0 1 k x i y i i k k 1 0 are positive numbers and p i q i i 0 k are positive constants more precisely we investigate the boundedness the persistence of the positive solutions the existence of a unique positive equilibrium and the global asymptotic stability of the positive equilibrium of the above system finally we find solutions of the system which do not oscillate about the positive equilibrium

analytical formulation and evaluation for free vibration of naturally curved and twisted beams abstract an analytical study for free vibration of naturally curved and twisted beams with uniform cross sectional shapes is carried out using spatial curved beam theory based on the washizu s static model in the governing equations of motion of the beams all displacement functions and the generalized warping coordinate are defined at the centroid axis and also the effects of rotary inertia transverse shear deformations and torsion related warping are included in the proposed model explicit analytical expressions are derived for the vibrating mode shapes of a curved bending torsional shearing coupled beam under clamped clamped boundary condition with the help of symbolic computing package mathematica and a process of searching is used to determine the natural frequencies comparisons of the present results with the fem results using beam elements in ansys code show good accuracy in computation and validity of the model further the present model is used for cylindrical helical springs with circular cross section fixed at both ends and the results indicate that the natural frequencies agree well with the theoretical and experimental results available

geometrically exact intrinsic theory for dynamics of curved and twisted anisotropic beams a formulation is presented for the nonlinear dynamics of initially curved and twisted anisotropic beams when the applied loads at the ends of and distributed along the beam are independent of the deformation neither displacement nor rotation variables appear an intrinsic formulation like well known special cases of these equations governing nonlinear dynamics of rigid bodies and nonlinear statics of beams the complete set of intrinsic equations has a maximum degree of nonlinearity equal to two advantages of such a formulation are demonstrated with a simple example when the initial curvature and twist are constant along the beam two space time conservation laws are shown to exist one being a work energy relation and the other a generalized impulse momentum relation these laws can be used for example as benchmarks to check the accuracy of any proposed solution including time marching and finite element schemes the structure of the intrinsic equations suggests parallel approaches to spatial and temporal discretization a particularly simple spatial discretization scheme is presented for the special case of the nonlinear static behavior of end loaded beams that by virtue of the kirchhoff analogy leads to a time marching scheme for the dynamics of a pivoted rigid body in a gravity field this time marching scheme conserves both the angular momentum about a vertical line passing through the pivot and total mechanical energy whereas the analogous spatial discretization scheme for the nonlinear static behavior of end loaded beams satisfies analogous integrals of deformation along the beam span remarkably a straightforward generalization of these discretization schemes is shown to satisfy both space time conservation laws for the nonlinear dynamics of beams when the applied loads are constant within a space time element

kinematically exact curved and twisted strain based beam the paper presents a formulation of the geometrically exact three dimensional beam theory where the shape functions of three dimensional rotations are obtained from strains by the analytical solution of kinematic equations in general it is very demanding to obtain rotations from known rotational strains in the paper we limit our studies to the constant strain field along the element the relation between the total three dimensional rotations and the rotational strains is complicated even when a constant strain field is assumed the analytical solution for the rotation matrix is for constant rotational strains expressed by the matrix exponential despite the analytical relationship between rotations and rotational strains the governing equations of the beam are in general too demanding to be solved analytically a finite element strain based formulation is presented in which numerical integration in governing equations and their variations is completely omitted and replaced by analytical integrals some interesting connections between quantities and non linear expressions of the beam are revealed these relations can also serve as useful guidelines in the development of new finite elements especially in the choice of suitable shape functions

an asymptotically correct classical model for smart beams an asymptotically correct classical beam model has been developed for smart slender structures using the variational asymptotic method taking advantage of the slenderness of the structure we asymptotically split the original three dimensional electromechanical problem into a two dimensional electromechanical cross sectional analysis and a one dimensional beam analysis the one dimensional beam analysis could be geometrically nonlinear or linear depending whether the original three dimensional analysis is geometrically nonlinear or linear the cross sectional analysis implemented using the finite element method provides an asymptotically correct one dimensional constitutive model for smart slender structures without a priori assumptions regarding the geometry of the cross section the distribution of the electric field and the location of smart materials such as embedded or surface mounted several examples are used to validate the accuracy of the present theory with available results in the literature and three dimensional commercial finite element packages

boundedness character of a class of difference equations abstract a complete picture regarding the boundedness character of positive solutions to the following difference equation x n max a x n 1 p x n k p n n 0 where k 2 and the parameters a and p are positive real numbers is given in particular for the case p k 1 0 k k k 1 k 1 we prove that all solutions to the equation are bounded we also present corresponding results concerning the following closely related difference equation x n a x n 1 p x n k p n n 0

global behavior of the nonlinear difference equation xn 1 f xn s xn t abstract in this note we consider a nonlinear difference equation of the form x n 1 f x n s x n t n 0 1 under some certain assumptions where s t 0 1 2 with s t and the initial values x t x t 1 x 0 0 we prove that the length of its finite semicycle is less than or equal to t and give sufficient conditions under which every positive solution of this equation converges to the positive equilibrium some known results are included and improved

on the system of rational difference equations xn a yn 3 yn byn 3 xn qyn q abstract in this paper we investigate the behaviour of the positive solutions of the system of rational difference equation x n a y n 3 y n by n 3 x n q y n q n 1 2 where q 3 is a positive integer with 3 q a and b are positive constants and the initial values x q 1 x q 2 x 0 y q 1 y q 2 y 0 are positive real numbers

a semi analytic meshfree method for almansi michell problems of piezoelectric cylinders abstract saint venant s problem almansi michell problems meshfree methods piezoelectricity we present a semi analytical method for analyzing prismatic nonhomogeneous piezoelectric cylinders with arbitrary cross sectional geometry the prescribed loads considered in this study include axial forces torques moments and voltage resultants prescribed at the cylinder s ends as well as body forces lateral surface shears voltages and pressures as long as they can be represented by a power series in the axial coordinate this problem can be considered as an extension of saint venant and almansi michell problems for elastic bodies to piezoelectric bodies in this computationally efficient method the cross sectional plane is discretized with a meshfree approach and the solution is obtained analytically with respect to the axial coordinate a number of examples are provided to demonstrate the veracity and utility of the proposed method

non prismatic beams a simple and effective timoshenko like model abstract the present paper discusses simple compatibility equilibrium and constitutive equations for a non prismatic planar beam specifically the proposed model is based on standard timoshenko kinematics i e planar cross section remain planar in consequence of a deformation but can rotate with respect to the beam center line an initial discussion of a 2d elastic problem highlights that the boundary equilibrium deeply influences the cross section stress distribution and all unknown fields are represented with respect to global cartesian coordinates a simple beam model i e a set of ordinary differential equations odes is derived describing accurately the effects of non prismatic geometry on the beam behavior and motivating equation s terms with both physical and mathematical arguments finally several analytical and numerical solutions are compared with results existing in literature the main conclusions can be summarized as follows i the stress distribution within the cross section is not trivial as in prismatic beams in particular the shear stress distribution depends on all generalized stresses and on the beam geometry ii the derivation of simplified constitutive relations highlights a strong dependence of each generalized deformation on all the generalized stresses iii axial and shear bending problems are strictly coupled iv the beam model is naturally expressed as an explicit system of six first order odes v the odes solution can be obtained through the iterative integration of the right hand side term of each equation vi the proposed simple model predicts the real behavior of non prismatic beams with a good accuracy reasonable for the most of practical applications

a homogenization based theory for anisotropic beams with accurate through section stress and strain prediction this paper presents a homogenization based theory for three dimensional anisotropic beams the proposed beam theory uses a hierarchy of solutions to carefully chosen beam problems that are referred to as the fundamental states the stress and strain distribution in the beam is expressed as a linear combination of the fundamental state solutions and stress and strain residuals that capture the parts of the solution not accounted for by the fundamental states this decomposition plays an important role in the homogenization process and provides a consistent method to reconstruct the stress and strain distribution in the beam in a post processing calculation a nite element method is presented to calculate the fundamental state solutions results are presented demonstrating that the stress and strain reconstruction achieves accuracy comparable with full three dimensional nite element computations away from the ends of the beam the computational cost of the proposed approach is three orders of magnitude less than the computational cost of full three dimensional calculations for the cases presented here for isotropic beams with symmetric cross sections the proposed theory takes the form of classical timoshenko beam theory with cowper s shear correction factor and additional load dependent corrections the proposed approach provides an extension of timoshenko s beam theory that handles sections with anisotropic construction

isogeometric analysis of composite beams with arbitrary cross section using dimensional reduction method abstract a novel isogeometric based cross sectional analysis of composite beams with arbitrary cross section geometry and a one dimensional composite beam model is presented via the concept of dimensional reduction method in dimensional reduction method three dimensional beam problem is decomposed into a two dimensional beam cross sectional analysis and a one dimensional beam problem to achieve this goal warping displacements should be computed by solving a cross sectional eigenvalue problem the cross sectional analysis is accomplished by spline basis functions to describe unknown warping fields as well as beam cross section geometry in an isogeometric framework the present method benefits from the exact geometric definition of beam cross section greatly simplifying mesh refinement and better convergence in contrast to classical finite element method the proposed beam cross sectional analysis is applied to a variety of beam cross section configurations with isotropic and anisotropic materials which show good correlation with the available results in the literature

on asymptotic behaviour of the difference equation xn 1 α xn kxn in this paper we investigate the global stability and the periodic character of positive solutions of the difference equationx n email protected x n kx nunder specified conditions

on a nonlinear generalized max type difference equation abstract the boundedness character of positive solutions of the following max type difference equation x n max a x n 1 p x n k r n n 0 where k n 1 the parameters a and r are positive and p is a nonnegative real number is studied in this paper our main results considerably improve results appearing in the literature

geometrically exact intrinsic theory for dynamics of moving composite plates a geometrically exact and fully intrinsic theory is presented for dynamics of composite plates undergoing large deformation to say that the formulation is intrinsic means that it is without displacement and rotation variables although the equations are geometrically exact the highest degree nonlinearities are quadratic there are no singularities associated with finite rotation methods for posing problems in this framework along with advantages of the formulation are discussed

dynamics of a family of two dimensional difference systems the boundedness and global asymptotic behavior of positive solutions of the nonlinear two dimensional difference systems x n f x n t 1 y n s 1 y n j y n s 2 x n t 2 where t 1 s 1 s 2 t 2 are all positive integers are investigated some sufficient conditions are established such that the positive solutions converge to the unique equilibrium finally some examples are given to illustrate our results

comment on an asymptotic analysis of composite beams with kinematically corrected end effects by jun sik kim maenghyo cho and edward c smith int j solids struct 45 2008 1954 1977 abstract in their paper kim et al 2008 kim cho and smith presented predictions that exhibited significant differences in bending shear coupling for the cus box beam from their own analysis famba vis a vis from vabs yu et al 2002 2012 the actual differences between results obtained from vabs yu et al 2002 2012 and famba when executed properly are shown herein to be very minor indeed both stiffness models yield very acceptable results for a static analysis specifically vabs does not significantly deviate qualitatively or quantitatively from 3d fem predictions in contrast to results presented in kim et al 2008

a hopf theorem for non constant mean curvature and a conjecture of a d alexandrov we prove a uniqueness theorem for immersed spheres of prescribed non constant mean curvature in homogeneous three manifolds in particular this uniqueness theorem proves a conjecture by a d alexandrov about immersed spheres of prescribed weingarten curvature in mathbb r 3 for the special but important case of prescribed mean curvature as a consequence we extend the classical hopf uniqueness theorem for constant mean curvature spheres to the case of immersed spheres of prescribed antipodally symmetric mean curvature in mathbb r 3

a coupled timoshenko model for smart slender structures abstract in this paper a generalized timoshenko model has been developed for prismatic beam like slender structures with embedded or surface mounted piezoelectric type smart materials starting from a geometrically exact formulation of the original three dimensional electromechanical problem we apply the variational asymptotic method to carry out a systematic dimensional reduction in the process the three dimensional electromechanical enthalpy functional is approximated asymptotically using the slenderness as the small parameter to find out an equivalent one dimensional electromechanical enthalpy functional for timoshenko like refinement over the euler bernoulli beam model terms up to the second order of the slenderness are kept in the enthalpy expression as an unified analysis tool the present model can analyze embedded or surface mounted active layer with arbitrary cross sectional geometry as two cases of a general one no special assumptions or modifications need to be made for these two separate types of active inclusions