Nonlinear dynamic stability of composite laminated plates

Catastrophe theory was applied to the investigation of nonlinear dynamic stability of composite laminated plates. The influence of large deflection, initial imperfection,support conditions and ply-angle of the fibers were considered. The catastrophic models and the critical conditions of dynamic buckling of composite laminated plates are obtained.     

复合材料层合板壳的非线性热动态响应分析

本文基于高阶剪切变形理论，考虑同天应变和横向剪切应变的影响，对受热复合材料层合板壳的非线性热动态响应进行分析，计及了转动惯量的影响，给出了通用性较好的Ｃ＾０类有限元公式，文中数值算同现有文献和三维有限元计算结果进行了比较，证明了本文方法的精确、有效性，文中还就层合板的边界条件、纵厚比及铺设角度对非线性热动态响应的影响进行了分析。     

NONLINEAR THREE-DIMENSIONAL ANALYSIS OF COMPOSITELAMINATED PLATES

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Postbuckling analysis of laminated composite plates subjected to the combination of in-plane shear,compression and lateral loading

This study deals with postbuckling behavior of laminated composite plates under the combination of in-plane shear, compression and lateral loading using an Element-based Lagrangian formulation. Natural co-ordinate-based strains, stresses and constitutive equations are used in the present shell element. The Element-based Lagrangian formulation described in this paper, in comparison with the traditional approaches, is more attractive not only because it uses only single mapping but also it converges faster. In addition, the finite element (FE) formulation based on the assumed natural strain method for composite structures shows excellence from the standpoints of computational efficiency as well as its ability to avoid both membrane and shear locking behavior. The numerical results obtained are in good agreement with those reported by other investigators. In particular, new results reported in this paper show the influence of various types of loading, materials and number of layers on postbuckling behavior.     

组合荷载作用下层合板非线性弯曲的半解析摄动DQ法

研究不同边界约束层合薄板在面内与横向组合荷载作用下的非线性弯曲问题，给出了基于摄动技术，单向DQ格式和Galerkin法的半解析法，算例表明该方法是可靠有效的。     

Nonlinear vibration of viscoelastic laminated composite plates

The dynamic behavior of laminated composite plates undergoing moderately large deflection is investigated by considering the viscoelastic properties of the material. Based on von Karman's nonlinear deformation theory and Boltzmann's superposition principle, nonlinear and hereditary type governing equations are derived through Hamilton's principle. Finite element analysis and the method of multiple scales are applied to examine the effect of large amplitude on the dissipative nature as well as on the natural frequency of viscoelastic laminated plates. Numerical experiments are performed for the nonlinear elastic case and linear viscoelastic case to check the validity of the procedure presented in this paper. Limitations of the method are discussed also. It is shown that the geometric nonlinearity does not affect the dissipative characteristics in the cases that have nonlinearity of perturbed order.     

Optimum design of laminated composite foam-filled sandwich plates subjected to strength constraint

Optimum design of laminated composite sandwich plates with both continuous (core thickness) and discrete (layer group fiber angles and thicknesses) design variables subjected to strength constraint is studied via a two-level optimization technique. The strength of a sandwich plate is determined in a failure analysis using the Tsai–Wu failure criterion and the finite element method which is formulated on the basis of the layerwise linear displacement theory. In the first level optimization of the design process, the discrete design variables are temporarily treated as continuous variables and the corresponding minimum weight of the sandwich plate is evaluated subject to the strength constraint using a constrained multi-start global optimization method. In the second level optimization, the optimal solution obtained in the first level optimization is used in the branch and bound method for solving a discrete optimization problem to determine the optimal design parameters and the final weight of the plate. Failure test of laminated composite foam-filled sandwich plates with different lamination arrangements are performed to validate the proposed optimal design method. A number of examples of the design of laminated composite foam-filled sandwich plates are given to demonstrate the feasibility and applications of the proposed method.     

Parametric instability of a rotating truncated conical shell subjected to periodic axial loads

Parametric instability of a rotating truncated conical shell subjected to periodic axial loads is studied in the paper. Through deriving accurate expressions of inertial force and initial hoop tension, a rotating conical shell model is presented based upon the Love's thin shell theory. Considering the periodic axial loads, equations of motion of the system with periodic stiffness coefficients are obtained utilizing the generalized differential quadrature (GDQ) method. Hill's method is introduced for parametric instability analysis. Primary instability regions for various natural modes are computed. Effects of rotational speed, constant axial load, cone angle and other geometrical parameters on the location and width of various instability regions are examined.     

Non-linear free periodic vibrations of variable stiffness composite laminated plates

Steady-state free vibrations, with large amplitude displacements, of variable stiffness composite laminated plates (VSCL) are analysed. The intentions of this research are: (1)?to find out how the natural frequencies and (mode) shapes evolve with the displacement amplitude in this new type of laminated composite material; (2)?to describe modal interactions in VSCL due to energy interchanges under the coupling induced by non-linearity; (3)?to compare the VSCL with traditional, constant stiffness, laminated plates. The VSCL of interest here have curvilinear fibres and the numerical analysis carried out is based on a recently developed p-version finite element with hierarchic basis functions. The element follows first-order shear deformation theory and considers Von Kármán??s non-linear terms. The time domain equations of motion are first reduced using the linear modes of vibration and then transformed to the frequency domain via the harmonic balance method. These frequency domain equations are solved by an arc-length continuation method.     

Theory of nonlinear dynamic stability for composite laminated plates

In this paper,the general equations of dynamic stability for composite laminatedplates are derived by Hamilton principle.These general equations can be used to considerthose different factors that affect the dynamic stability of laminated plates.The factors aretransverse shear deformation,initial imperfections,longitudinal and rotational inertia,andply-angle of the fiber,etc.The solutions of the fundamental equations show that someimportant characteristics of the dynamic instability can only be got by the considerationand analysis of those factors     

Exact bending solutions of orthotropic rectangular cantilever thin plates subjected to arbitrary loads

Exact bending solutions of orthotropic rectangular cantilever thin plates subjected to arbitrary loads are derived by using a novel double finite integral transform method. Since only the basic elasticity equations for orthotropic thin plates are used, the method presented in this paper eliminates the need to predetermine the deformation function and is hence completely rational thus more accurate than conventional semi-inverse methods, which presents a breakthrough in solving plate bending problems as they have long been bottlenecks in the history of elasticity. Numerical results are presented to demonstrate the validity and accuracy of the approach as compared with those previously reported in the literature     

具损伤压电智能层合中厚板的非线性动力稳定性分析

基于各向异性损伤理论和压电理论，采用能量法和Lagrange方程，建立了具损伤压电智能层合中厚板在参数激励下的非线性运动控制方程，应用增量谐波平衡法，求解了具损伤压电智能层合中厚板的非线性动力稳定性问题。算例中，分析了损伤参数和压电效应对压电智能层合板非线性动力稳定性的影响，揭示了力电耦合效应的内在特征，并与有关文献的结果进行了比较。     

Thermally induced dynamic instability of laminated composite conical shells

Thermally induced dynamic instability of laminated composite conical shells is investigated by means of a perturbation method. The laminated composite conical shells are subjected to static and periodic thermal loads. The linear instability approach is adopted in the present study. A set of initial membrane stresses due to the elevated temperature field is assumed to exist just before the instability occurs. The formulation begins with three-dimensional equations of motion in terms of incremental stresses perturbed from the state of neutral equilibrium. After proper nondimensionalization, asymptotic expansion and successive integration, we obtain recursive sets of differential equations at various levels. The method of multiple scales is used to eliminate the secular terms and make an asymptotic expansion feasible. Using the method of differential quadrature and Bolotin's method, and imposing the orthonormality and solvability conditions on the present asymptotic formulation, we determine the boundary frequencies of dynamic instability regions for various orders in a consistent and hierarchical manner. The principal instability regions of cross-ply conical shells with simply supported–simply supported boundary conditions are studied to demonstrate the performance of the present asymptotic theory.     

Stability of tribotechnical laminated coatings subjected to tracing loads

The problems of surface stability of laminated coatings subjected to the combined effect of tracing surface loads and a stationary temperature field is considered. The material of the layer and the base are considered linearly elastic and trasversally isotropic. Fulfillment of conditions of absolutely rigid force and ideal contacts are assumed between the individual elements of the laminar medium. The subcritical stress state of the laminar medium under consideration is piecewise-homogeneous. Interbranch Engineering Center “Tribotekhnika”, Dnepropetrovsk, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 35, No. 6, pp 32–38, June, 1999.     

Computational simulation of damage progression of composite thin shells subjected to mechanical loads

Defect-free and defected composite thin shells with ply orientation (90/0/ ± 75) made of graphite/epoxy are simulated for damage progression and fracture due to internal pressure and axial loading. The thin shells have a cylindrical geometry with one end fixed and the other free. The applied load consists of an internal pressure in conjunction with an axial load at the free end, the cure temperature was 177°C (350°F) and the operational temperature was 21°C (70°F). The residual stresses due to the processing are taken into account. Shells with defect and without defects were examined by using CODSTRAN an integrated computer code that couples composite mechanics, finite element and account for all possible failure modes inherent in composites. CODSTRAN traces damage initiation, growth, accumulation, damage propagation and the final fracture of the structure. The results show that damage initiation started with matrix failure while damage/fracture progression occurred due to additional matrix failure and fiber fracture. The burst pressure of the (90/0/ ± 75) defected shell was 0.092% of that of the free defect. Finally the results of the damage progression of the (90/0/ ± 75), defective composite shell was compared with the (90/0/ ± θ), where θ = 45 and 60, layup configurations. It was shown that the examined laminate (90/0/ ± 75) has the least damage tolerant of the two compared defective shells with the (90/0/ ± θ), θ = 45 and 60 laminates.     

Non-linear analysis of functionally graded plates under transverse and in-plane loads

Large deflection and postbuckling responses of functionally graded rectangular plates under transverse and in-plane loads are investigated by using a semi-analytical approach. Material properties are assumed to be temperature-dependent, and graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. The plate is assumed to be clamped on two opposite edges and the remaining two edges may be simply supported or clamped or may have elastic rotational edge constraints. The formulations are based on the classical plate theory, accounting for the plate-foundation interaction effects by a two-parameter model (Pasternak-type), from which Winkler elastic foundation can be treated as a limiting case. A perturbation technique in conjunction with one-dimensional differential quadrature approximation and Galerkin procedure are employed in the present analysis. The numerical illustrations concern the large deflection and postbuckling behavior of functional graded plates with two pairs of constituent materials. Effects played by volume fraction, the character of boundary conditions, plate aspect ratio, foundation stiffness, initial compressive stress as well as initial transverse pressure are studied.     

Nonlinear dynamic response of piezoelastic laminated plates considering interfacial damage effects

This paper presents a nonlinear model for cross-ply piezoelastic laminated plates containing the damage effect of the intralayer materials and interlaminar interfaces. The model is based on the general six-degrees-of-freedom plate theory, the discontinuity of displacement, and electric potential on the interfaces are depicted by three shape functions, which are formulated according to solutions about three equilibrium equations and conservation of charge. By using the Hamilton variation principle, the three-dimensional nonlinear dynamic equations of piezoelastic laminated plates with damage are presented. Then using the finite difference method and the Newmark scheme, an analytical solution is presented. In numerical examples, the effects of different damage models, damage evolution, amplitude and frequency of electric loads on the nonlinear dynamic response of piezoelectric laminated plate with interfacial imperfections are investigated.     

Analysis of composite laminated plates

In the static and dynamic analysis of composite laminates, a theory for the laminated plates is presented in this paper. Because the deflection W_b which is caused by the classical bending deformation and the deflection W₅ which is caused by the shear deformation are divided from the total deflection W in the theory, this makes it easy to solve the governing equations. In addition, this theory is convenient for the discussion and analysis of the effects of transverse shear deformations on bendings, vibrations and stabilities of laminated plates.