Finite element analysis of stiffened laminated plates under transverse loading

A finite element model is developed to study the behavior of stiffened laminated plates under transverse loadings. Transverse shear flexibility is incorporated in both beam and plate displacement fields. A laminated plate element with 45 degrees of freedom is used in conjunction with a laminated beam element having 12 degrees of freedom for the bending analysis of eccentrically-stiffened laminated plates. The validity of the formulation is demonstrated by comparing with the available solutions in the literature. The numerical results are presented for eccentrically-stiffened layered plates having various boundary conditions and with stiffeners varying in number.     

复合材料大变形任意加筋板单元

本文构造了用于复合材料偏心加筋板状结构大变形分析的任意加筋板单元。在此模型中,肋骨可放置在板单元内任意位置和任意方向,因而在网格划分时,可不必顾及肋骨的具体位置。在板和肋骨的基本方程中,引用Von-Karman大变形理论计及大变形的影响,按照 Mindlin-Reissoner一阶剪切变形理论考虑横向剪切变形。任意加筋板单元具有和常规板单元相同的自由度。数值计算表明本文的有限元模型具有很高的精度。     

复合材料加筋板的动力分析

本文构造了九自由度三角形拟协调罚函数复合材料板单元与六自由度复合材料梁单元,考虑了剪切变形与转动惯量的影响。用这两种单元对复合材料加筋板的自由振动、阻尼特性和瞬态响应问题进行了研究,给出一些有益结果。      

Analysis for buckling and vibrations of composite stiffened shells and plates

This paper deals with development of triangular finite element for buckling and vibration analysis of laminated composite stiffened shells. For the laminated shell, an equivalent layer shell theory is employed. The first-order shear deformation theory including extension of the normal line is used. In order to take into account a non-homogeneous distribution of the transverse shear stresses a correction of transverse shear stiffness is employed. Based on the equivalent layer theory with six degrees of freedom (three displacements and three rotations), a finite element that ensures C⁰ continuity of the displacement and rotation fields across inter-element boundaries has been developed. Numerical examples are presented to show the accuracy and convergence characteristics of the element. Results of vibration and buckling analysis of stiffened plates and shells are discussed.     

Boundary element analysis of shear deformable stiffened plates

In this paper a boundary element formulation for analysis of shear deformable stiffened plates is presented. The formulation is derived by coupling boundary element formulation of shear deformable plate and two-dimensional plane stress elasticity. Both concentric and eccentric stiffeners have been considered. The interaction forces between stiffeners and the plate are treated as either line distribution or area distribution of body forces along the attachment. A rectangular stiffened plate and a circular stiffened plate under uniform load are analysed by the proposed method. Good agreement has been achieved compared with other published results.     

复合材料加筋板热变形和热应力分析

复合材料及其结构的热响应是近年来复合材料力学研究的热点课题之一。本文用有限元法研究了复合材料加筋板的热变形和热应力。基于Mindlin假定导出了一阶剪切变形层合板梁理论。这两种理论也适用于中厚板和深梁。考虑的热载可以是瞬态的也可以是稳志的,实际工程应用表明,根据本丈模型研制的计算机程序具有较高的计算精度和效率。      

Stiffened cracked plates analysis by dual boundary element method

In this paper a boundary element formulation for analysis of shear deformable stiffened cracked plates is presented. By coupling boundary element formulation of shear deformable plate and two dimensional plane stress elasticity, dual boundary integral equations are presented. The interaction forces between stiffeners and the plate are treated as line distributed body forces along the attachment. Both concentric and eccentric stiffeners have been considered. Rectangular stiffened plate containing a single crack and double cracks subjected to uniform distributed moment on the crack surface and uniform shear load on the plate are analysed by the proposed method. Good agreement has been achieved compared with analytical solutions.     

Buckling response of laminated composite stiffened plates subjected to partial in-plane edge loading

This article presents the buckling analysis of laminated composite stiffened plates subjected to partial in-plane edge loading. The finite element method is used to carry out the analysis. The eight-noded isoparametric degenerated shell element with C⁰ continuity and first-order shear deformation and a compatible three-noded curved beam element are used to model the plate skin and the stiffeners, respectively. The eigen value analysis is carried out to track the buckling load. The convergence study is performed for some specific problems and the results are compared with the available results in the literature. It is observed that the convergence of results is very fast for this finite element model. Effect of different parameters like orientation of fibers, number of layers, and loading types are considered in the present investigation. It is also observed that all these parameters have significant effect on the buckling response of the composite stiffened plate.     

具有分层损伤复合材料加筋与无加筋层合板热-机械力屈曲性态

基于复合材料一维剪切理论——Mindlin 理论, 给出了材料性质与温度有关的含分层损伤复合材料加筋和无加筋层合板的线性和非线性热-机械力耦合情况下的屈曲问题有限元分析方法, 并研究了含分层损伤的加筋和无加筋层合板的两种不同类型的热- 机械力屈曲问题。通过典型算例分析, 讨论了热-机械力耦合效应和分层大小对含分层损伤结构的屈曲性态的影响关系。     

Stiffened plate bending analysis in terms of refined triangular laminated plate element

Based on the higher-order global–local theories, a finite element model is proposed to study the bending behavior of stiffened laminated plates. The proposed model treats the embedded stiffeners as the part of laminated plate, so that the compatibility of displacements and stresses between the plate and the stiffeners can be automatically satisfied. Distributions of the displacements and stresses through the thickness of laminates were also given for the first time, which can serve as references for future investigations as such information is lacking in the published literature. In addition, the impact of the stiffeners on the bending response of the stiffened laminated plates is also studied in terms of the quantity, the collocation and the geometry of stiffeners. Numerical results showed that the higher-order global–local theories are more suitable for predicting the bending response of thick and moderately thick stiffened laminated plates compared to the first order theory commonly used in engineering. By varying the quantity, the collocation and the geometry of stiffeners, the stiffness and the strength of stiffened laminated plates can be remarkably improved.     

Finite element analysis of laminated composite stiffened plates using FSDT and HSDT: A comparative perspective

Significance of using higher-order shear deformation theory (HSDT) over the first-order shear deformation theory (FSDT) for analyzing laminated composite stiffened plates is brought out using the finite element method (FEM). For this purpose, a C⁰ HSDT, is extended for application to stiffened configurations, for linearly elastic static and natural vibration analysis. The spatial displacement fields of both the plate and the stiffener are derived as functions of reference plane variables using Taylor series expansion. The developed computational tool is employed for analyzing systems having varying configurations using the FSDT and two different HSDTs, and their comparative effects are systematically studied, demonstrating the need for using HSDT instead of FSDT, for obtaining accurate structural response of such stiffened configurations.     

含分层损伤复合材料加筋层合板的动承载能力

采用有限元方法研究了含穿透分层损伤复合材料加筋层合板的动力响应和承载能力。根据复合材料层合板一阶剪切理论, 推导了复合材料层合板单元的刚度阵和质量阵列式;同时采用Adams 应变能法与Rayleigh阻尼模型相结合的方法, 构造了相应的阻尼阵列式;为了防止在低阶模态中分层处出现的上、下子板不合理的嵌入现象, 建立了含分层损伤复合材料加筋层合板动力分析中分层分析模型和虚拟界面联接模型。并采用Tsai提出的刚度退化准则和动力响应分析的精细积分法, 对在动荷载作用下含分层损伤复合材料加筋层合板结构进行了破坏和承载能力分析。通过典型算例分析, 分别讨论了外载频率、分层深度、筋的位置以及破坏过程中刚度退化对含损伤复合材料加筋层合板动力响应特征和承载能力的影响, 得到了一些具有理论和工程价值的结论。     

Finite element analysis of laminated composite plates using zeroth-order shear deformation theory

In this paper a generalized finite element model is developed for static and dynamic analyses of laminated composite plates using zeroth-order shear deformation theory (ZSDT). The theory ensures the parabolic distribution of transverse shear stresses across the plate thickness. A four-noded plate element is considered in this model and the generalized nodal variables are expressed using Lagrangian linear interpolation functions and Hermitian cubic interpolation functions. The solutions of the finite element model have been compared with the existing solutions for symmetric and antisymmetric laminated composite plates. The comparison confirms that the ZSDT can be efficiently used for finite element analysis of both thin and thick plates with high accuracy.     

联肢加劲钢板剪力墙滞回性能试验研究与数值分析

完成了3个1/3比例的3层联肢钢板剪力墙试件的低周反复加载试验。3个试件的钢板剪力墙分别采用非加劲、槽钢竖向加劲和井字加劲的形式,钢板剪力墙的竖向边缘构件采用方钢管混凝土。得到了联肢钢板剪力墙试件的荷载-位移滞回曲线和破坏形态,对试件的骨架曲线、应力发展、延性及耗能能力等进行了分析。采用有限元软件ABAQUS对试件进行了数值模拟。结果表明:非加劲和槽钢竖向加劲墙板先屈曲后屈服,井字加劲墙板先屈服后屈曲,墙板屈服后连梁与钢板剪力墙边框梁相继屈服。方钢管混凝土柱脚屈服较早,屈服后仍具有良好的承载力和弹塑性变形能力。采用非加劲墙板的试件承载力最低,滞回环捏缩效应最严重,其次是采用槽钢竖向加劲墙板的试件。采用井字加劲墙板的试件滞回环较饱满。井字加劲和槽钢竖向加劲试件的峰值荷载分别比非加劲试件的峰值荷载提高了11.7%和6.9%,井字加劲和槽钢竖向加劲试件的等效黏滞阻尼系数分别比非加劲试件的等效黏滞阻尼系数提高了65.9%和19.9%。各试件的延性系数均大于4.5,表明不同加劲形式的联肢钢板剪力墙均具有良好的延性。数值分析与试验结果吻合较好,可充分地反映试件的滞回性能和破坏过程。加劲肋对连梁和边缘构件的内力影响较小,但可显著提高剪力墙板的抗剪承载力。相较于两片单肢钢板剪力墙,联肢钢板剪力墙的承载力和耗能能力均有大于20%的提高。     

Behavior of laminated sandwich plates having interfacial imperfections by a new refined element

The static response of laminated sandwich plates having imperfections at the layer interfaces is investigated by a refined plate theory. The plate theory represents parabolic through thickness variation of transverse shear stresses, which are continuous at the layer interfaces and become zero at the plate top and bottom surfaces. In this plate model the interfacial imperfection is represented by a linear spring-layer. Moreover, with all these features of an accurate modeling, it involves unknowns only at the reference plane of the plate. To have generality in the analysis, finite element method is adopted. But any existing plate element cannot be used, as the plate theory demands certain inter-elemental continuity. Thus an attempt has also been made to develop a new triangular element. As there is no published result on imperfect sandwich plates, the problems of perfect sandwich plates and ordinary laminated plate with inter-laminar imperfection are used for validation.     

Free Vibration Analysis of Folded Plate Structures by the FSDT Mesh-free Method

Based on the first-order shear deformation theory, a mesh-free Galerkin method for free vibration analysis of stiffened and un-stiffened folded plates and plate structures is presented in this paper. The folded plate or plate structure is modelled as a composite structure that consists of flat plates. The stiffness and mass matrices of the flat plates are derived based on the mesh-free formulation. To avoid the failure of direct superposition, a treatment is introduced to modify the stiffness and mass matrices. The global stiffness and mass matrices of the entire folded plate or plate structure are then obtained by superposing the modified stiffness and mass matrices of the flat plates. The analysis of the stiffened folded plates or plate structures proceeds in a similar fashion, as they are regarded as composite structures of stiffened and un-stiffened flat plates. The stiffness and mass matrices of the stiffened flat plates are also given by the mesh-free method. As no meshes are used in deriving the stiffness and mass matrices, the proposed method is more flexible in studying problems for which remeshing is inevitable with the finite element methods. Several numerical examples are computed with the proposed method to demonstrate its accuracy and convergence. The results show good agreement with the solutions that have been given by other researchers and ANSYS.     

Analysis of laminated composite plates using a higher-order shear deformation theory

A higher-order shear deformation theory is used to analyse laminated anisotropic composite plates for deflections, stresses, natural frequencies and buckling loads. The theory accounts for parabolic distribution of the transverse shear stresses, and requires no shear correction coefficients. A displacement finite element model of the theory is developed, and applications of the element to bending, Vibration and stability of laminated plates are discussed. The present solutions are compared with those obtained using the classical plate theory and the three-dimensional elasticity theory.     

复合材料加筋板的大变形有限元分析

本文将考虑横向剪切变形的Mindlin's理论应用于复合材料加筋板的大变形分析,在Total-Lagrange坐标系下推导了八结点等参弯曲板单元和三结点等参梁单元的增量平衡方程和切线刚度矩阵,非线性问题采用增量法和Newton-Raphson迭代法相结合的方法求解.本文通过一些算例,证明了所采用单元具有良好的收敛性和足够的精度,并讨论了边界条件、纤维铺设角和加筋疏密等因素对复合材加料筋板非线性解的影响.     

复合材料层板的拟协调罚单元*

本文在文献提出的多变量拟协调元和罚函数相结合的方法基础上构造了考慮耦合和剪切效应的十五自由度三角形层合板单元。此单元适用于薄和中厚层合板的强度分析,具有收敛和应用范围广的优点。文中以各向同性和复合材料层合板多组数例证明了该单元的有效性,同时还讨论了跨厚比L/h和弹性模量比E₁/E₂与剪切效应的关系,得出了一些有意义的结论。     

An adhesively laminated plate element for PZT smart plates

An adhesively laminated element taking into consideration peel stress is developed for a piezoelectric smart plate. In this novel finite element analysis formulation, a four node piezoelectric element is firstly derived, and an adhesive element of finite thickness with both shear and peel stiffness is sandwiched between two collocated four node plate elements to form an adhesively laminated element for a piezoelectric smart plate. In this framework of finite element analysis, because the displacement filed in this adhesively laminated element is continuous and a plate element is derived based on the Reissner–Mindlin plate theory, and thus it can be accurately applied to a thin or moderately thick host plate with bonded or debonded piezoelectric actuators and sensors. The formulation is performed for an isotropic host plate and a fiber reinforced laminate plate. Numerical results are presented to compare with those of the exact solutions for smart beams, and validate with the experimental results of the isotropic and composite host plates available in the literature. Using the present finite element analysis formulation, energy transfer stresses in the adhesive and equivalent forces induced in the host plate are investigated. The present formulation is demonstrated to allow debondings of piezoelectric patches and the debonding detection.The authors are grateful to the support of the Australian Research Council via a Discovery Projects grant (grant No: DP0346419).