Deformation of short composite beam using refined theories

High-order flexural theories for short laminated composite beams subjected to mechanical and thermal loading are presented. The formulation allows for warping of the cross-section of the beam and eliminates the need for using arbitrary shear correction coefficients as in other theories. Based on higher-order shear deformation theories, the governing equations are obtained using the principle of virtual work (PVW). The justification for use of higher-order shear deformation theories is established for short and composite beams where cross-sectional warping is predominant.     

Finite element dynamic analysis of unsymmetric composite laminated beams with shear effect and rotary inertia under the action of moving loads

The finite element dynamic response of an unsymmetric composite laminated orthotropic beam, subjected to moving loads, has been studied. One-dimensional finite element based on classical lamination theory, first-order shear deformation theory, and higher-order shear deformation theory having 16, 20 and 24 degrees of freedom, respectively, are developed to study the effects of extension, bending, and transverse shear deformation. The theories also account for the Poisson effect, thus, the lateral strains and curvatures can be expressed in terms of the axial and transverse strains and curvatures and the characteristic couplings (bend–stretch, shear–stretch and bend–twist couplings) are not lost. The dynamic response of symmetric cross-ply and unsymmetric angle-ply laminated beams under the action of a moving load have been compared to the results of an isotropic simple beam. The formulation also has been applied to the static and free vibration analysis.     

Two new hyperbolic shear displacement models for orthotropic laminated composite plates

Two hyperbolic displacement models, HPSDT1 and HPSDT2, are developed for a bending analysis of orthotropic laminated composite plates. These models take into account the parabolic distribution of transverse shear stresses and satisfy the condition of zero shear stresses on the top and bottom surfaces of the plates. The accuracy of the analysis presented is demonstrated by comparing the results with solutions derived from other higher-order models and with data found in the literature. It is established that the HPSDT1 model is more accurate than some theories of laminates developed previously, and therefore the analysis can be expanded to laminated composite shells.     

A vibration analysis of composite laminated plates

A finite element formulation of the equations governing laminated anisotropic plates using Reddy's higher-order theory is presented. This simple higher-order shear deformable theory takes into account the parabolic distribution of the transverse shear deformation through the thickness of the plate and contains the same unknowns as in the first-order shear deformation theory. Finite element solutions are presented for rectangular plates of different layups, such as cross-ply, antisymmetric angle-ply, and sandwich plates with various material properties, boundaries, and plate aspect ratios. The numerical results are compared with the available closed-form results, the 3-D linear elasticity theory results, and the other available numerical results. A comparison is also made with test data from a laminated cantilever plate.     

Buckling and free vibration analyses of laminated composite plates by using two new hyperbolic shear-deformation theories

Two new hyperbolic displacement models, HPSDT1 and HPSDT2, are used for the buckling and free vibration analyses of simply supported orthotropic laminated composite plates. The models contain hyperbolic expressions to account for the parabolic distributions of transverse shear stresses and to satisfy the zero shear-stress conditions at the top and bottom surfaces of the plates. The equation of motion for thick laminated rectangular plates subjected to in-plane loads is deduced through the use of Hamilton’s principle. Closed-form solutions are obtained by using the Navier technique, and then the buckling loads and the fundamental frequencies are found by solving eigenvalue problems. The accuracy of the models presented is demonstrated by comparing the results obtained with solutions of other higher-order models given in the literature. It is found that the theories proposed can predict the fundamental frequencies and buckling loads of cross-ply laminated composite plates rather accurately. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 2, pp. 217–230, March–April, 2008.     

Frequency response analysis of laminated composite beams

Conclusions The modeling of laminated composite beams has been derived systematically from the three-dimensional elasticity relations. The correctness of the solution found by using the present finite element model is verified by comparison with the results obtained by analytical solutions and other results presented in the literature. Numerical results indicate that the present technique can given accurate results for frequency response analysis for laminated composite beams. Loss factors of structures obtained by the method of complex eigenvalues and the direct frequency response method exhibit very good agreement. Optimum design of a laminated composite beam by the finite element method and the method of experiment planning has been successfully presented.Published in Mekhanika Kompozitnykh Materialov, Vol. 30, No. 5, pp. 664–674, September–October, 1994.     

Multi-dimensional deformation tests of sandwich plates

Sandwich-type plates are widely used in present technical structures. A variety of special sandwich theories and composite laminated plate theories (CLT, FSDT, HSDT) are available for calculating plate deflections. Since the problem of assessing these theories still exists, a new test apparatus for multilayered composite and sandwich plates was developed. Different types of sandwich plates were used in quasistatic multidimensional deformation tests. Deflections and thickness reductions are compared with the theoretical results obtained by sandwich theories, CLT-, FSDT-, HSDT-, and 3D-solutions.Submitted to the 10th International Conference on Mechanics of Composite Materials, Riga, April 20–23, 1998.Published in Mekhanika Kompozitnykh Materialov, Vol. 33, No. 5, pp. 612–625, September–October, 1997.     

An Iterative Analytical Theory in the Mechanics of Layered Composite Systems

An iterative analytical theory in the mechanics of layered composite systems is developed. The prehistory of the nonclassical theory of layered systems is presented. The division of this theory into two principal directions - discrete-structural and continuous-structural - is mentioned. The basic iterative Ambartsumyan theory, which belongs to the second direction, is described. The formation of the generalized iteration theory of first approximation is shown. In this theory, the disagreement between the kinematic and static models is removed, i.e., a generalization of these models is realized. The theory of second approximation is described. An iterative principle is presented for the formation of a higher-approximation nonclassical theory. Based on this principle, theories of anisotropic composite shallow shells, plates, and beams are formulated. Comparative calculation results for different layered composite systems are presented.     

Strength Analyses of Laminated Composite Structures Based on Different Theories

Modern materials, such as composite ones, slowly replace conventional materials in structures of different kind and their growing popularity is caused by their multiple advantages. Through selection of parameters, such as number of layers, thickness of layers, direction of arranging fibers, or material from which internal and outside layers are made, it is possible to control properties of a structure. In the result, structures made of composite materials have high ratio of flexural stiffness to weight. The goal of this paper is to compare three theories of laminated composite plates and shells with the help of the multilayered rectangular plate model subjected to crosswise pressure perpendicular to the surface of a plate. Comparison was made for the classical laminated theory (CLT), first-order laminated theory and third-order laminated theory (TSDT). In all these theories, the number of parameters describing the displacement doesn't depend on the number of layers. For each of these theories strains and displacements were determined. Additionally, the computations time for every method were compared. Obtained results are presented in the form of tables. The analysis of the obtained solutions will be used as the base in choosing the best theory in multicriteria optimization process of composite thin-walled structures. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

夹芯梁的精确解法

夹芯梁与普通梁的本质区别在于剪切引起芯层横截面严重的而又不均匀的翘曲变形,其应力分布已远非初等理论所能描述,而正在广泛应用的经典夹层理论却都建立在平面假设基础上,尤其不能正确反映弱芯的轻质夹层结构的行为,本文放弃了不合理的假设,将夹芯梁视为一般层状弹性体,严格按弹性理论导出了既满足控制方程又同时满足全部边界条件、层间的应力及位移的连续条件的封闭解.它可确切地反映夹芯梁的位移形态和应力分布,并从不同角度,包括多种实验和FEM数值解,验证了它的正确性.     

Nonlinear vibration of moderately thick laminated beams using finite element method

A finite element model is developed to study the large-amplitude free vibrations of generally-layered laminated composite beams. The Poisson effect, which is often neglected, is included in the laminated beam constitutive equation. The large deformation is accounted for by using von Karman strains and the transverse shear deformation is incorporated using a higher order theory. The beam element has eight degrees of freedom with the inplane displacement, transverse displacement, bending slope and bending rotation as the variables at each node. The direct iteration method is used to solve the nonlinear equations which are evaluated at the point of reversal of motion. The influence of boundary conditions, beam geometries, Poisson effect, and ply orientations on the nonlinear frequencies and mode shapes are demonstrated.     

关于一阶剪切板的Kármán型精化理论

依据Mindlin_Reissner理论 ,着重研究一阶剪切板的K rm n型精化理论 ,并推导出仅以挠度和应力函数为未知变量的广义K rm n型大挠度方程 ,适用于复合材料上复合构造剪切板的非线性分析·　在当前板的精化理论中 ,消去的两个转角以隐含形式作用于板的整体变形·　这一工程理论适用于各种计及横向剪切复合材料板、正交各向异性中厚板和夹层板等的线性和非线性分析·　容易发现 ,针对具体的工程应用 ,由该方程可直接获得相应的退化形式 ,并且与文献所载的一致·     

A higher order finite element including transverse normal strain for linear elastic composite plates with general lamination configurations

This paper describes a higher-order global-local theory for thermal/mechanical response of moderately thick laminated composites with general lamination configurations. In-plane displacement fields are constructed by superimposing the third-order local displacement field to the global cubic displacement field. To eliminate layer-dependent variables, interlaminar shear stress compatibility conditions have been employed, so that the number of variables involved in the proposed model is independent of the number of layers of laminates. Imposing shear stress free condition at the top and the bottom surfaces, derivatives of transverse displacement are eliminated from the displacement field, so that C⁰ interpolation functions are only required for the finite element implementation. To assess the proposed model, the quadratic six-node C⁰ triangular element is employed for the interpolation of all the displacement parameters defined at each nodal point on the composite plate. Comparing to various existing laminated plate models, it is found that simple C⁰ finite elements with non-zero normal strain could produce more accurate displacement and stresses for thick multilayer composite plates subjected to thermal and mechanical loads. Finally, it is remarked that the proposed model is quite robust, such that the finite element results are not sensitive to the mesh configuration and can rapidly converge to 3-D elasticity solutions using regular or irregular meshes.     

Formulation and evaluation of a finite element model for the linear analysis of stiffened composite cylindrical panels

A finite element model for linear static and free vibration analysis of composite cylindrical panels with composite stiffeners is presented. The proposed model is based on a cylindrical shell finite element, which uses a first-roder shear deformation theory. The stiffeners are curved beam elements based on Timoshenko and Saint-Venant assumptions for bending and torsion respectively. The two elements are developed in a cylindrical coordinate system and their stiffness matrices result from a hybrid-mixed formulation where the element assumed stress field is such that exact equilibrium equations are satisfied. The elements are free of membrane and shear locking with correct satisfaction of rigid body motions. Several examples dealing with stiffened isotropic and laminated plates and shells with eccentric as well as concentric stiffeners are analyzed showing the validity of the models.     

Analysis of laminated composite plates using higher-order shear deformation plate theory and node-based smoothed discrete shear gap method

This paper presents a novel finite element formulation for static, free vibration and buckling analyses of laminated composite plates. The idea relies on a combination of node-based smoothing discrete shear gap method with the higher-order shear deformation plate theory (HSDT) to give a so-called NS-DSG3 element. The higher-order shear deformation plate theory (HSDT) is introduced in the present method to remove the shear correction factors and improve the accuracy of transverse shear stresses. The formulation uses only linear approximations and its implementation into finite element programs is quite simple and efficient. The numerical examples demonstrated that the present element is free of shear locking and shows high reliability and accuracy compared to other published solutions in the literature.     

Análise de vigas laminadas utilizando o natural neighbour radial point interpolation method

In this work, a meshless method, “natural neighbour radial point interpolation method” (NNRPIM), is applied to the one‐dimensional analysis of laminated beams, considering the theory of Timoshenko.The NNRPIM combines the mathematical concept of natural neighbours with the radial point interpolation. Voronoï diagrams allows to impose the nodal connectivity and the construction of a background mesh for integration purposes, via influence cells. The construction of the NNRPIM interpolation functions is shown, and, for this, it is used the multiquadratic radial basis function. The generated interpolation functions possess infinite continuity and the delta Kronecker property, which facilitates the enforcement of boundary conditions, since these can be directly imposed, as in the finite element method (FEM).In order to obtain the displacements and the deformation fields, it is considered the Timoshenko theory for beams under transverse efforts. Several numerical examples of isotropic beams and laminated beams are presented in order to demonstrate the convergence and accuracy of the proposed application. The results obtained are compared with analytical solutions available in the literature.     

Static and dynamic analysis of smart cylindrical shell

Shell type components and structures are very common in many mechanical and structural systems. In smart structural applications, piezolaminated plates and shells are commonly used. In this paper a finite element formulation is presented to model the static and dynamic response of laminated composite shells containing integrated piezoelectric sensors and actuators subjected to electrical, mechanical and thermal loadings. The formulation is based on the first order shear deformation theory and Hamilton's principle. In this formulation, the mass and stiffness of the piezo-layers have been taken into account. A nine-noded degenerated shell element is implemented for the analysis. The model is validated by comparing with existing results documented in the literature. A simple negative velocity feedback control algorithm coupling the direct and converse piezoelectric effects is used to actively control the dynamic response of an integrated structure through a closed control loop. The influence of the stacking sequence and position of sensors/actuators on the response of the laminated cylindrical shell is evaluated. Numerical results show that piezoelectric sensors/actuators can be used to control the shape and vibration of laminated composite cylindrical shell.     

Geometrically nonlinear bending analysis of laminated composite plate

In this work, a transverse bending of shear deformable laminated composite plates in Green–Lagrange sense accounting for the transverse shear and large rotations are presented. Governing equations are developed in the framework of higher order shear deformation theory. All higher order terms arising from nonlinear strain–displacement relations are included in the formulation. The present plate theory satisfies zero transverse shear strains conditions at the top and bottom surfaces of the plate in von-Karman sense. A C⁰ isoparametric finite element is developed for the present nonlinear model. Numerical results for the laminated composite plates of orthotropic materials with different system parameters and boundary conditions are found out. The results are also compared with those available in the literature. Some new results with different parameters are also presented.     

Quasi-three-dimensional theory for solution of dynamic thermoelastic problem of laminated composite plates

An uncoupled dynamic thermoelastic problem for laminated composite plates has been considered. The hypotheses used take into account the nonlinear distribution of temperature and displacements over the thickness of a laminated plate. On the basis of these hypotheses a quasi-three-dimensional (layerwise) theory is constructed that makes it possible to investigate the internal thermal and stress-strain states, as well as the edge effects of the boundary layer type for laminated plates. Systems of the heat conduction and motion equations are derived using the variational method. The order of the equations depends on the number of layers and terms in expansions of temperature and displacements of each layer. An analytical solution of the dynamic thermoelastic problem is presented for a cross-ply laminated rectangular plate with simply supported edges. The reliability of the results is confirmed by a comparison with the known exact solutions. The results based on the proposed theory can be used for verifying various two-dimensional plate theories when solving the dynamic thermoelastic problems for laminated composite plates.