Thermal postbuckling analysis of fiber–metal laminated plates including interfacial damage

Considering the effects of interfacial damage, geometric nonlinearity and transverse shear deformation, thermal postbuckling of fiber–metal laminated plates including interfacial damage is analyzed in detail. Firstly, the Heaviside step function and higher order shear deformation functions are introduced into displacement field so that the damage degree can be characterized. Then, the shape functions can be determined by using the stress continuity conditions between interfaces and the stress boundaries on surfaces. By using the generalized variational principle, the thermal postbuckling equilibrium equations of fiber–metal laminated plates including interfacial damage are established. Finally, the thermal postbuckling problem is solved by adopting finite difference method and iteration method. In numerical examples, the effects of interfacial damage, width-to-thickness ratio and thermal load on the thermal postbuckling of fiber–metal laminated plates including interfacial damage are investigated.     

Analysis of delamination fatigue growth for delaminated piezoelectric elasto-plastic laminated beams under hygrothermal conditions

A nonlinear analysis model of fatigue delamination growth for piezoelectric elasto-plastic laminated beams under hygrothermal conditions is presented. Based on the incremental elasto-plastic constitutive equations, the incremental nonlinear governing equations of the piezoelectric elasto-plastic laminated beams with delamination are derived when taking into account the hygrothermal environments, transverse shear deformation, geometrical nonlinearity and piezoelectric effect. According to the elasto-plastic fracture dynamics and J-integral theory, the energy-release-rate along the delamination is obtained. Then, applying the Paris law, the delamination growth rate is obtained and the delamination growth lengths along the delamination fronts under cyclic loads are finally determined by using the cyclic skip method. The equations are solved by the finite difference method and iterative method as a whole. Effects of voltages, variation of temperature and humidity, delamination length and depth on the energy-release-rate and delamination growth length for the piezoelectric elasto-plastic laminated beams are discussed in numerical examples.     

考虑损伤效应的粘弹性层合板的非线性动力响应分析

扩展了Ladeveze 的复合材料单层板的损伤模型, 使之可用于考虑剪切粘弹性的复合材料层合板的损伤分析, 基于Von Karman 方程, 建立了考虑损伤效应的粘弹性复合材料层合板的非线性动力学方程, 且应用有限差分法和迭代法进行求解。数值结果表明, 考虑结构的损伤和损伤演化时, 结构的非线性动力响应将发生显著的变化。     

Nonlinear static analysis of composite laminated plates with evolving damage

Considering geometric nonlinearity and damage evolution, the static response characteristics of laminated composite plates subjected to uniformly distributed loading are investigated using finite element approach based on the first-order shear deformation theory. The damage evolution is modeled employing generalized macroscopic continuum theory within the framework of irreversible thermodynamics. The governing nonlinear equations are solved using Newton–Raphson iterative technique. The resulting finite element-based continuum damage model enables to predict the progressive damage and failure load. A detailed parametric study is carried out to investigate the influences of damage evolution, boundary conditions, span-to-thickness ratio, and lamination scheme on the static response of laminated plates undergoing moderately large deformation. It is revealed that the in-plane stretching forces owing to geometric nonlinearity significantly influence the failure load, damage, and stress distribution for immovable thin laminates.     

Analysis of the nonlinear dynamic response of viscoelastic symmetric cross-ply laminated plates with transverse matrix crack

Based on the Schapery’s 3-D constitutive relationship and the Von Karman’s plate theory, the constitutive equations and the nonlinear dynamic governing equations for viscoelastic symmetric cross-ply laminated plates with transverse matrix cracks are derived. By using the finite difference method and Newmark-β scheme, the unknown functions are separated and these equations are iterated to seek solutions. Numerical calculating results show that the effect of damage on the nonlinear dynamic responses of structures is significant.     

An analytical method for 3-D analysis of circular laminated composite plates

Summary In this paper, an analytical method is presented for 3-D (three-dimensional) researches of laminated composite plates. Using this method, the linear and nonlinear analytical 3-D solutions of high accuracy are obtained for circular laminated composite plates with rigidly clamped edges and under uniform transverse loading. Galerkin's method and the perturbation technique are used to obtained the solutions which satisfy the basic differential equations of linear and nonlinear 3-D problems. The geometric nonlinearity from a moderately large deflection is considered. Many numerical results of displacements and stresses are shown in figures. In the analytical method, there are not any restrictions regrading the stacking sequence of laminated composite plates, so the method may be used to analyze the 3-D problems of unsymmetrical laminated plates.     

Nonlinear dynamic response of laminated plates resting on nonlinear elastic foundations by the discrete singular convolution-differential quadrature coupled approaches

In this paper, nonlinear dynamic response of rectangular laminated composite plate resting on nonlinear Pasternak type elastic foundations is investigated. First-order shear deformation theory (FSDT) is used for modeling of moderately thick plates. The plate formulation is based on the von Karman nonlinear equation. The resulting nonlinear governing equations for transient analysis of laminated plates on elastic foundation are integrated using the discrete singular convolution-differential quadrature coupled approaches. The nonlinear governing equations of motion of plate are discretized in space and time domains using the discrete singular convolution and the differential quadrature methods, respectively. The validity of the present method is demonstrated by comparing the present results with those available in the open literature. The effects of the foundation parameters, boundary conditions and geometric parameters of plates on nonlinear dynamic response of laminated thick plates are investigated.     

Large deformation analysis of moderately thick laminated plates on nonlinear elastic foundations by DQM

In this paper, the nonlinear behavior of symmetric and antisymmetric cross ply, thin to moderately thick, elastic rectangular laminated plates resting on nonlinear elastic foundations are studied using differential quadrature method (DQM). The first-order shear deformation theory (FSDT) in conjunction with the Green’s strain and von Karman hypothesis are assumed for modeling the nonlinear behavior. Elastic foundation is modeled as shear deformable with cubic nonlinearity. The differential quadrature (DQ) discretized form of the governing equations with the various types of boundary conditions are derived. The Newton–Raphson iterative scheme is employed to solve the resulting system of nonlinear algebraic equations. Comparisons are made and the convergence studies are performed to show the accuracy of the results even with a few number of grid points. The effects of thickness-to-length ratio, aspect ratio, number of plies, fiber orientation and staking sequence on the nonlinear behavior of cross ply laminated plates with different boundary conditions resting on elastic foundations are studied.     

含界面脱粘及表板基体开裂损伤的复合材料夹层板非线性稳定性的研究

本文作者基于"zig-zag"模型和Mindlin一阶剪切变形板理论,推导了复合材料夹层板屈曲分析的有限元列式,在该列式中考虑了面板的横向剪切变形和芯体的面内刚度对夹层板力学性能的影响。针对具有面板和芯体间界面脱粘和纤维增强树脂基体微裂纹损伤的夹层板损伤特征,分别提出了分层模型和多标量损伤模型,并推导了多标量形式的损伤本构关系。采用修正的 Newton-Raphson迭代格式求解含损复合材料夹层板的非线性稳定性性状。通过算例研究了脱粘面积、基体的损伤演化、表板的铺设方式及载荷形式对复合材料夹层板屈曲性态的影响。本文作者给出的有限元模型和结论,对复合材料夹层板结构设计的损伤容限的制定具有一定的参考价值。     

Continuum damage mechanics approach to composite laminated shallow cylindrical/conical panels under static loading

Static response characteristics and failure load of laminated composite shallow cylindrical and conical panels subjected to internal/external lateral pressure are investigated using continuum damage mechanics approach considering geometric nonlinearity and damage evolution. The damage model is based on a generalized macroscopic continuum theory within the framework of irreversible thermodynamics and enables to predict the progressive damage and failure load. Damage variables are introduced for the phenomenological treatment of the state of defects and its implications on the degradation of the stiffness properties. The analysis is carried out using finite element method based on the first order shear deformation theory. The nonlinear governing equations are solved using Newton–Raphson iterative technique coupled with the adaptive displacement control method to efficiently trace the equilibrium path. The detailed parametric study is carried out to investigate the influences of geometric nonlinearity, evolving damage, span-to-thickness ratio, lamination scheme and semi-cone angle on the static response and failure load of laminated cylindrical/conical panels. It is revealed that the membrane forces due to geometric nonlinearity significantly influence the damage distribution and failure load.     

Large deformation flexural behavior of laminated composite skew plates: An analytical approach

The paper presents the large deformation flexural response of composite laminated skew plates subjected to uniform transverse pressure. Third order shear deformation theory (TSDT) and von-Karman’s nonlinearity is used for the analysis. Skew domain is mapped into a square domain and finite degree double Chebyshev series is used to discretize the space domain. No grid generation is required in the present solution technique. The nonlinear equations are linearized using quadratic extrapolation technique and the behavior of moderately thick laminated composite skew plates is studied. The effects of geometric nonlinearity, transverse shear, boundary conditions, aspect ratio and modular ratio on the behavior of laminated composite skew plates are discussed in detail.     

Nonlinear vibration and dynamic response of shear deformable laminated plates in hygrothermal environments

This paper deals with hygrothermal effects on the nonlinear vibration and dynamic response of shear deformable laminated plates. The temperature field considered is assumed to be a uniform distribution over the plate surface and through the plate thickness. The material properties of the composite are affected by the variation of temperature and moisture, and based on a micro-mechanical model. The formulations are based on higher-order shear deformation plate theory and general von Kármán-type equation of motion, which includes hygrothermal effects. The equations of motion are solved by an improved perturbation technique to determine nonlinear frequencies and dynamic responses of shear deformable antisymmetric angle-ply and unsymmetric cross-ply laminated plates. The numerical illustrations concern the nonlinear vibration and dynamic response of the shear deformable laminated plates under different sets of hygrothermal environmental conditions. Effects of temperature rise, the degree of moisture concentration, and fiber volume fraction on natural frequencies, nonlinear to linear frequency ratios and dynamic responses are studied.     

粘弹性对称铺设层合板的非线性动力响应

基于Karman板理论和线粘弹性Boltzmann叠加原理,建立了粘弹性对称铺设层合板的非线性积分—偏微分动力学方程。针对材料具积分型本构关系以及松弛模量为Prony级数的形式,应用Galerkin技术、Newmark方法和Newton-Cotes方法,给出了求解粘弹性层合结构非线性动力学问题的一种有效的数值算法。具体地求解了若干算例,且与相关文献进行了比较。     

复合材料层板层间缺陷分析——剪切滑移

根据三维弹性平衡方程和层间剪切滑移条件,导出了一个复合材料层板层间剪切滑移模型。本文模型具有一般形式的二维板壳理论的位移场及其平衡方程,但因引入了能反映层板界面粘贴情况及板面条件的剪切变形函数,模型因而简单又精确。层板的弯曲问题和屈曲问题被考虑,层间弱粘贴的影响被讨论。数值结果与精确解比较,表明了本文模型的高精度。      

Nonlinear flexural analysis of laminated composite plates using RBF based meshless method

The paper presents the nonlinear flexural response of laminated composite plates. The mathematical formulation of the actual physical problem of the laminated composite plate subjected to mechanical loading is presented utilizing higher order shear deformation theory and von-Karman nonlinear kinematics. These nonlinear governing differential equations of equilibrium are linearized using quadratic extrapolation technique. A meshfree technique based on multiquadric RBFs is used for analysis of the problems. Isotropic, orthotropic and laminated composite plates with immovable simply supported and clamped edges are analyzed.     

Nonlinear free vibration analysis of thermally post-buckled composite spherical shell panel

In this article, nonlinear free vibration behaviour of thermally post-buckled laminated composite spherical shallow shell panel is analyzed. The nonlinearity in geometry of the shell panel is considered in Green–Lagrange sense and the mathematical model is developed based on higher order shear deformation theory (HSDT). System of governing differential equations are derived using Hamilton’s principle. A direct iterative method in conjunction with nonlinear finite element approach is used to solve the system of equations. Effects of various geometries and material properties on the nonlinear free vibration frequencies are examined in detail and discussed. Results are obtained using the present model and are compared with those available in literature. The difference between the results speaks the necessity and the requirement of the present model for the prediction of actual nonlinear characteristics of the laminated structures having severe nonlinearity in thermal environment.     

复合材料层合板力学性质分析及角铺设层优化设计

基于Kirchhoff经典理论,用样条有限元法以三次B样条函数构成的样条基对反对称多层角铺设层合板的三个独立位移进行插值,推导了复合材料层合板刚度阵,质量阵列式,阻尼阵列式,并由Lagrange方程导出了层合板的动力学方程,通过瑞利一李兹法建立了特征方程。分析了层合板的固有频率及不同层数和不同约束条件下的基频变化等力学特性,在Kirchhoff假设的基础上,对层合板的非线性弯曲的力学特性进行了探讨。基于样条有限元法和遗传算法进行复合材料层合板的角铺设层的优化设计,数值算列验证了算法的有效性。     

The primary resonance of laminated piezoelectric rectangular plates

Based on Hamilton's principle and the Rayleigh- Ritz method, a model of a nonlinear dynamic laminated piezoelectric rectangular plate was established, and the governing equations were derived and solved for both the thin-plate and thick-plate models. In the present investigation, the nonlinear constitutive relations of piezoelectric materials were considered and the effects of the nonlinearity on the response of the plate were discovered. The primary resonance of rectangular plate is investigated with the use of the method of multiple scales. The results obtained in the present paper agree very well with the experiment results.     

Hamilton体系下含弱粘接复合材料层合板的无网格求解方法

该文结合径向基点插值函数、弹簧层模型和弹性材料修正后的H-R（Hellinger-Reissner）变分原理,推导了含弱粘接复合材料层合板控制方程的无网格列式。利用典型径向基函数Multiquadric（MQ）,计算了含弱粘接复合材料层合板的应力与位移。通过与精确法的对比,证明了控制方程无网格列式的正确性,并研究了弱粘...     

含吸声层和阻尼层叠层板的动力学建模研究

基于基板和吸声层的一阶微分控制方程,考虑阻尼层的自重,并借助黏弹性理论和层间连续性条件将阻尼层的剪应力及偏心力矩写为基板和吸声层状态向量的形式,该研究建立了含吸声层和阻尼层叠层板的整合动力学控制方程。结合边界条件和齐次扩容精细积分方法提出了一种求解此类叠层板力学特性的半数值半解析方法。为了验证该方法的正确性,采用有限元软件对层合板的动力学特性进行了数值仿真,结果表明该研究的模型具有较高的精度,研究中还采用该方法分析了孔隙率等材料参数对叠层板动力学特性的影响。