Geometrically nonlinear theory of thin-walled composite box beams using shear-deformable beam theory

A general geometrically nonlinear model for thin-walled composite space beams with arbitrary lay-ups under various types of loadings is presented. This model is based on the first-order shear deformable beam theory, and accounts for all the structural coupling coming from both material anisotropy and geometric nonlinearity. The nonlinear governing equations are derived and solved by means of an incremental Newton-Raphson method. A displacement-based one-dimensional finite element model that accounts for the geometric nonlinearity in the von Kármán sense is developed. Numerical results are obtained for thin-walled composite box beams under vertical load to investigate the effects of shear deformation, geometric nonlinearity and fiber orientation on axial-flexural-torsional response.     

Exact dynamic analysis of composite beams with partial interaction

The partial differential equations and general solutions for the deflection and internal actions and the pertaining consistent boundary conditions are presented for composite Euler-Bernoulli members with interlayer slip subjected to general dynamic loading. Both free and forced vibrations are treated. The solutions are shown to be unique and complete under certain conditions, and valid for all so-called restricted admissible boundary conditions. Specifically, the exact eigenmode length coefficients are derived for the four Euler BC. They differ from those valid for ordinary, fully composite (solid) beams, except for the pinned-pinned case. The maximum deviation for beams with the other three Euler BC is shown to be less than 2-6% with respect to the eigenmode length coefficient and 3-10% with respect to the eigenfrequency, respectively, depending on the two non-dimensional parameters, composite action or shear connector stiffness and relative bending stiffness parameters. However, these deviations occur in a rather narrow range of the determining parameters, so for most practical cases the eigenmode length coefficients given for solid (fully composite) beams can approximately be used also for partially composite beams. The procedures of analysing beam vibrations are applied to a specific case. These solutions illustrate the effect of interlayer connection on the peak velocity of the beam vibrations. The proposed analytical theory is verified by tests and finite element calculations.     

Exact dynamic stiffness matrix of a Timoshenko three-beam system

An exact dynamic stiffness matrix is established for an elastically connected three-beam system, which is composed of three parallel beams of uniform properties with uniformly distributed-connecting springs among them. The formulation includes the effects of shear deformation and rotary inertia of the beams. The dynamic stiffness matrix is derived by rigorous use of the analytical solutions of the governing differential equations of motion of the three-beam system in free vibration. The use of the dynamic stiffness matrix to study the free vibration characteristics of the three-beam system is demonstrated by applying the Muller root search algorithm. Numerical results for the natural frequencies and mode shapes of the illustrative examples are discussed for 10 interesting boundary conditions and three different stiffness constants of springs.     

A finite thin circular beam element for out-of-plane vibration analysis of curved beams

A finite thin circular beam element for the out-of-plane vibration analysis of curved beams is presented in this paper. Its stiffness matrix and mass matrix are derived, respectively, from the strain energy and the kinetic energy by using the natural shape functions derived from an integration of the differential equations in static equilibrium. The matrices are formulated with respect to the local polar coordinate system or to the global Cartesian coordinate system in consideration of the effects of shear deformation and rotary inertias. Some numerical examples are analyzed to confirm the validity of the element. It is shown that this kind of finite element can describe quite efficiently and accurately the out-of-plane motion of thin curved beams. This paper was recommended for publication in revised form by Associate Editor Seockhyun Kim Chang-Boo Kim received his B.S. degree in Mechanical Engineering from Seoul University, Korea in 1973. He then received his D.E.A., Dr.-Ing. and Dr.-es-Science degrees from Nantes University, France in 1979, 1981 and 1984, respectively. Dr. Kim is currently a Professor at the School of Mechanical Engineering at Inha University in Incheon, Korea. His research interests are in the area of vibrations, structural dynamics, and MEMS.     

Lateral-torsional buckling analysis of thin-walled beams including shear and pre-buckling deformation effects

In this paper, lateral-torsional buckling behavior of open-section thin-walled beams is investigated based on a geometrically nonlinear formulation, which considers the effects of shear deformations. A finite element numerical solution along with an incremental-iterative solution procedure is adopted to trace the pre-buckling as well as the post-buckling equilibrium paths. Formulation is applicable to a general type of open-section and load position effects are also included. Numerical results are validated through comparisons with experimental results and those based on other formulations presented in the literature. Comparisons have also been made between the results based on fully nonlinear analysis and linearized buckling analysis in order to illustrate the effects of pre-buckling deformations as well as the shear deformations on the buckling load predictions. Examples illustrate the influence of beam slenderness and moment gradient on the effects of pre-buckling deformations in predicting bucking loads.     

Shear deformable doubly- and mono-symmetric composite I-beams

A shear deformable beam element is developed for the coupled flexural and torsional analyses of thin-walled composite I-beams with doubly- and mono-symmetric cross-sections. The present element includes the transverse shear and the restrained warping induced shear deformation by using the first-order shear deformation beam theory. Governing equations and force-displacement relations are derived from the principle of minimum total potential energy. Then the explicit expressions for displacement parameters are derived by applying the power series expansions of displacement components to simultaneous ordinary differential equations. Finally, the element stiffness matrix is determined using the force-displacement relations. In order to verify the accuracy and the superiority of the beam element developed herein, the numerical solutions are presented and compared with the results obtained from the isoparametric beam elements based on the Lagrangian interpolation polynomial, the detailed three-dimensional analysis results using the shell elements of ABAQUS, and the solutions by other researchers.     

Ductility requirements in connections of composite flexural structures

The provision of adequate shear connection between the tension and compression-resisting components of composite flexural members is essential to the robust performance of such structural members under load. If the combined capacity of all the connections in a given composite member is to be exploited at the ultimate load of the member, there is a requirement for the connections to possess some measure of ductility, because the shear force capacities of the connections will typically be activated before the member ultimate load is attained. In this paper, finite element (FE) analyses of a composite member comprising an I-section steel beam connected to a concrete slab are used to show that the required level of connection ductility is parasitic on the compliance of the connections. In order to clearly identify the nonlinear influence of plastification of the connections on overall member behaviour, the relative properties of the connections, the slab and the beam are such that the concrete and steel exhibit little and no nonlinearity up to the peak loads here considered. The analyses reveal that, when the ultimate load of the composite member is attained, the required ductility in the connections must increase as the compliance of the connections decreases. By contrast, it is seen that, en route to attaining the ultimate load, the connection ductility required to just achieve yield of all connections increases as connection compliance increases. The implications of the FE results for the performance of steel–concrete and timber–concrete composite members at the serviceability and ultimate limit states are discussed.     

Static and dynamic behaviour of composite riveted joints in tension

The tensile response and failure of composite riveted joints are studied experimentally in the present paper. Seven joint configurations for aircraft application are tested at quasi-static, 4 and 8 m/s nominal loading rates. Joint specimens are made of CFRP in a number of lay-ups of unidirectional tapes and woven fabrics. A dynamic tensile test method is designed to give reliable test results. It is shown that the variation of tensile strength with loading rate is negligible for the tested composite riveted joints. However, for most of the tested specimens, the average total energy absorption of the composite joint increases with increasing loading rate. Various failure modes are identified for various joint designs and it was found that joint failure modes can change with varying loading rates.     

Free vibration of laminated composite plates using two variable refined plate theory

Free vibration of laminated composite plates using two variable refined plate theory is presented in this paper. The theory accounts for parabolic distribution of the transverse shear strains through the plate thickness, and satisfies the zero traction boundary conditions on the surfaces of the plate without using shear correction factors. Equations of motion are derived from the Hamilton's principle. The Navier technique is employed to obtain the closed-form solutions of antisymmetric cross-ply and angle-ply laminates. Numerical results obtained using present theory are compared with three-dimensional elasticity solutions and those computed using the first-order and the other higher-order theories. It can be concluded that the proposed theory is not only accurate but also efficient in predicting the natural frequencies of laminated composite plates.     

铝合金E形截面轴压杆件屈曲分析方法的探讨

分别采用弹性理论公式法、ANSYS软件中的特征值屈曲分析法和非线性屈曲分析法计算两端简支的铝合金E形截面薄壁杆件在轴心受压时的弯扭屈曲临界载荷。计算结果表明,采用梁单元建模并用非线性法对E形截面薄壁杆件进行轴压屈曲分析,是一种既能满足一般工程设计要求又简单易行的计算方法。     

Three dimensional stress analysis of a composite patch using stress functions

A stress function-based analysis is proposed to provide a simple and efficient approximation method of three-dimensional (3D) state of stress that exists near the free edge of bonded composite patches. In order to apply plane strain assumption in a composite patch, a linear superposition of sliced section from a bonded patch is used. In addition, to describe the load transfer mechanism from the substrate to the composite patch, a simple shear lag model is introduced. The 3D stress behavior at the free edge of the composite patch is modeled by Lekhnitskii stress functions, and the governing equations of the given composite patch are obtained by applying the principle of complementary virtual work. After a suitable expansion of the functions, the governing equations are transformed into two coupled ordinary differential equations, and they are solved by a general eigenvalue solution procedure. As the number of base functions increases, the interlaminar stresses converge. The interlaminar stresses reach maximum at the free edge and decrease sharply at the inner part of the patch. The interlaminar stresses are concentrated at the interface between the layers because of the mismatch of material properties and the geometric singularity. Since the proposed method accurately predicts the 3D stresses in a composite patch bonded on the metal substrate, it can be used as a simple and efficient analytical tool for designing such structural components.     

Microstructural analysis of a FeAl/quasicrystal-based composite prepared using a focused ion beam miller

A composite consisting of a brittle multiphase matrix containing both an Al-based quasicrystalline phase (ψ) and an ordered body centred cubic phase (β) and a relatively ductile ordered body centred cubic intermetallic FeAl phase has been developed as an abrasive wear-resistant coating material. It is applied as a 500 μm thick layer onto stainless steel substrates through plasma spray processing. The microstructure of such materials can be readily examined by optical and scanning electron microscopy, but the inherent difficulty of preparing transmission electron microscope (TEM) samples has inhibited higher resolution studies. However, the relatively recent development of the focused ion beam (FIB) miller as a tool in materials science provides a method ideal for the preparation of TEM specimens of these materials. In this study a coating consisting of a mixture of an Al–Cu–Fe based quasicrystal and FeAl+Cr was deposited on to a 304 stainless steel substrate. TEM specimens were prepared using a FIB and subjected to detailed microstructural characterization. The structure consisted of elongated bands of a FeAl phase about 100 nm in width and several micrometres in length, which enclosed more equiaxed regions about 1 μm in diameter that consisted of fine mixtures of quasicrystal and two Al-Fe-Cu phases isostructurally related to FeAl.     

An exact solution for buckling of functionally graded circular plates based on higher order shear deformation plate theory under uniform radial compression

In this research, mechanical buckling of circular plates composed of functionally graded materials (FGMs) is considered. Equilibrium and stability equations of a FGM circular plate under uniform radial compression are derived, based on the higher order shear deformation plate theory (HSDT). Assuming that the material properties vary as a power form of the thickness coordinate variable z and using the variational method, the system of fundamental partial differential equations are established. A buckling analysis of a functionally graded circular plate (FGCP) under uniform radial compression is carried out and the results are given in closed-form solutions. The results are compared with the buckling loads of plates obtained for FGCP based on the first order shear deformation plate theory (FSDT) and classical plate theory (CPT) given in the literature. The study concludes that HSDT accurately predicts the behavior of FGCP, whereas the FSDT and CPT overestimates buckling loads.     

The shear buckling behaviour of thin composite plates with particular reference to the effects of bend–twist coupling

The effect of bend–twist coupling on the shear buckling behaviour of laminated composite plates is examined in this paper using a finite strip procedure. The complex buckled shapes which are associated with shear loading are duly accounted for in the analysis approach through the multi-term facility of the strip formulation employed and, of course, through the appropriate level of structural modelling. The degree of bend–twist coupling in the laminated composite plates is varied by changing the level of anisotropy in the plies and by altering the lay-up configuration of the plies in the laminated stack. Symmetric laminates of a balanced and unbalanced nature are given consideration. It is shown that, for a given degree of anisotropy in the plies of a laminate and for a given laminate thickness, the stacking sequence of the plies significantly alters the degree of bend–twist coupling. The shear buckling performance of composite plates having the same dimensions and being made from the same material are therefore shown in the paper to be quite different. The preclusion of the bend–twist coupling coefficients in the solution procedure of the finite strip method allows the shear buckling orthotropic solution to be determined. Comparisons between the coupled and orthotropic solutions are shown in the paper to be markedly different with respect to critical shear performance level and also buckled mode shape. For square plates or plates with a moderate aspect ratio the influence of bend–twist coupling on buckled mode shape is shown in the paper to be noticeable through increased distortion. For the larger aspect ratio plates it is shown that the presence of bend–twist coupling can cause a complete change in the mode shape from a symmetric to an antisymmetric nature or vice versa. Amplitude modulation is shown in the paper to be clearly evident in the shear buckling mode shapes of long plates.     

Dynamic analysis of composite beam subjected to harmonic moving load based on the third-order shear deformation theory

The response of an infinite Timoshenko beam subjected to a harmonic moving load based on the third-order shear deformation theory (TSDT) is studied. The beam is made of laminated composite, and located on a Pasternak viscoelastic foundation. By using the principle of total minimum potential energy, the governing partial differential equations of motion are obtained. The solution is directed to compute the deflection and bending moment distribution along the length of the beam. Also, the effects of two types of composite materials, stiffness and shear layer viscosity coefficients of foundation, velocity and frequency of the moving load over the beam response are studied. In order to demonstrate the accuracy of the present method, the results TSDT are compared with the previously obtained results based on first-order shear deformation theory, with which good agreements are observed.     

高速切削机床横梁的表态与动态分析

在机床设计的初期，利用有限元分析软件ANSYS，在材料和截面空间尺寸相似的情况下，对截面形状不同的几种结构的梁进行静力和模态分析，将强度较好的梁，用模态分析得到刚度更好的梁。通过结构的变形和一阶频率的振型研究比较，初步确定了较为合理的横梁结构。     

Vibration and buckling of cross-ply laminated composite circular cylindrical shells according to a global higher-order theory

Natural frequencies and buckling stresses of cross-ply laminated composite circular cylindrical shells are analyzed by taking into account the effects of higher-order deformations such as transverse shear and normal deformations, and rotatory inertia. By using the method of power series expansion of displacement components, a set of fundamental dynamic equations of a two-dimensional higher-order theory for laminated composite circular cylindrical shells made of elastic and orthotropic materials is derived through Hamilton's principle. Several sets of truncated approximate higher-order theories are applied to solve the vibration and buckling problems of laminated composite circular cylindrical shells subjected to axial stresses. The total number of unknowns does not depend on the number of layers in any multilayered shells. In order to assure the accuracy of the present theory, convergence properties of the first natural frequency and corresponding buckling stress for the fundamental mode r=s=1 are examined in detail. The internal and external works are calculated and compared to prove the numerical accuracy of solutions. Modal transverse shear and normal stresses can be calculated by integrating the three-dimensional equations of equilibrium in the thickness direction, and satisfying the continuity conditions at the interface between layers and stress boundary conditions at the external surfaces. It is noticed that the present global higher-order approximate theories can predict accurately the natural frequencies and buckling stresses of simply supported laminated composite circular cylindrical shells within small number of unknowns.     

Static and dynamic analysis of spur and bevel gears using FEM

This paper presents the findings of three-dimensional stress analysis of spur and bevel gear teeth by finite element method using cyclic symmetry concept. The displacement of a tooth is computed for each Fourier harmonic component of the contact line load and all the components are added to obtain the total displacement. This displacement is used in the calculation of static stress in the teeth. The natural frequencies and mode shapes are obtained using the submatrices elimination scheme.     

Kinematic and dynamic modeling of viscoelastic robotic manipulators using Timoshenko beam theory: theory and experiment

This paper presents an investigation into the development of modeling of n-viscoelastic robotic manipulators. The dynamic model of the system is derived using Gibbs-Appell formulation and assumed mode method. When the beam is short in length direction, shear deformation is a factor that may have significant effects on system dynamic. So, in modeling, the assumption of Timoshenko beam theory and associated mode shapes has been considered. Although including the effect of damping in continuous systems makes the formulations more complicated, two important damping mechanisms, namely, Kelvin-Voigt damping as internal damping and the viscous air damping as external damping have been considered. Based on derived formulation, a non-linear recursive algorithm is developed for deriving the inverse dynamic equation of motion, systematically. The performance of the proposed algorithm was assessed in terms of the required mathematical operations for deriving the kinematic and dynamic equations of the mechanical system. Finally, to validate the proposed formulation, a comparative assessment between the results achieved from experiment and simulation is presented in time and frequency domains.     

Coupled modification of natural frequencies and buckling loads of composite cylindrical panels

This paper proposes a new method for performing predefined simultaneous modification of natural frequencies and buckling loads of composite cylindrical panels. The method is based on the fact that both natural frequencies and buckling loads are eigenvalues of an algebraic system of simultaneous equations. First- and second-order derivatives of these eigenvalues are calculated and the first two terms in Taylor expansion are used for developing a modification procedure that is defined as an inverse eigenvalue problem. A four-layered composite cylindrical panel with an arbitrary angle-ply stacking sequence is considered as a case study and several simultaneous modifications for natural frequencies and buckling loads are carried out. It is shown that the proposed method can perform the predefined modification with an acceptable accuracy even for large perturbations in objective functions.