Nonlinear Viscoelastic Response of Unidirectional Polymeric Laminated Composite Plates Under Bending Loads

Nonlinear bending analysis of polymeric laminated composite plate is examined considering material nonlinearity for viscoelastic matrix material through a Micro–macro approach. The micromechanical Simplified Unit Cell Method (SUCM) in three-dimensional closed-form solution is used for the overall behavior of the unidirectional composite in any combination of loading conditions. The elastic fibers are transversely isotropic where Schapery single integral equation in multiaxial stress state describes the matrix material by recursive-iterative formulation. The finite difference Dynamic Relaxation (DR) method is utilized to study the bending behavior of Mindlin annular sector plate including geometric nonlinearity under uniform lateral pressure with clamped and hinged edge constraints. The unsymmetrical laminated plate deflection is predicted for different thicknesses and also various pressures in different time steps and they are compared with elastic finite element results. As a main objective, the deflection results of viscoelastic laminated sector plate are obtained for various fiber volume fractions in the composite system.     

Postbuckling Analysis of Laminated Composite Plates Using a Higher-Order Zig-Zag Theory

This study examines the effects of incorporating zig-zag kinematics in the postbuckling analysis of laminated composite plates. A higher-order zig-zag plate element for nonlinear analysis was developed based on works of Averill and Yip. Their zig-zag element is especially suitable for a nonlinear structural laminate analysis due to its high accuracy and a low, constant number of degrees of freedom regardless of the number of layers. The article examines global postbuckling response as well as local displacement and stress fields of various laminated plates. The results derived from higher-order zig-zag theory are compared with predictions of first-order shear deformation theory (FSDT). Significant differences between these two theories are obtained for laminated plates with drastically different transverse stiffness properties with length-to-thickness aspect ratios L / t = 30 and 50. FSDT leads to good predictions of global and local behavior only for L / t = 50 and 100 with a typical layup in which the adjacent plies do not have very different transverse stiffness properties. Results presented in this article indicate that the zig-zag theory is required to predict accurately stresses and in-plane displacements through the thickness in moderately thick plates in the postbuckled state.     

Static Analysis of Laminated Composite Plates Using n-Order Shear Deformation Theory and a Meshless Global Collocation Method

In this article, an n-order shear deformation theory is used to analyze the static characteristic of laminated composite plates. The third-order theory of Reddy can be considered as a special case of present n-order theory (n = 3). Governing equations and boundary conditions expressed in terms of strong form based on the present n-order theory are discretized by a meshless global collocation method. Maximum deflection and stress of the simply-supported laminated plate under sinusoidal load are compared with available published results, which demonstrate the accuracy and efficiency of present n-order theory.     

Bending Analysis of Classical Symmetric Laminated Composite Plates by the Strip Element Method

A new formulation of strip element method based on classical laminated plate theory is derived for the bending analysis of laminated composite plates. In this method, an infinite-length plate is first considered and is discretized into a set of strip elements in the width direction. The principle of minimum potential energy is applied to obtain the ordinary differential equations, which are functions of only the coordinate in the length direction. These differential equations can then be solved analytically. The boundary conditions on the length coordinate direction are finally used to determine the deflection distribution in the plate. The strip element solutions are presented for a rectangular laminated composite plate with various boundary conditions and load cases. The solutions are compared with those of the Rayleigh-Ritz method, and very good agreement is obtained.     

采用分层理论计算层合板的固有频率和振型

采用有限元方法并结合分层理论对复合材料层合板的固有频率和振型进行理论计算,再用实验验证。通过分层有限元模型求解层合板的位移模式,对层合板固有频率进行计算。分析有限元网格数,铺设角度、铺设层数等对固有频率的影响,获得层合板自由振动的前九阶振型,采用实验进行了验证。结果表明,提出的方法可较精确计算层合板的固有频率和振型。     

Time-Dependent Compressive Strength of Unidirectional Viscoelastic Composite Materials

The strength of unidirectional composites is often lower in compressionthan in tension, making compressive strength an especially importantdesign criterion. Compressive strength in the fiber direction depends onthe stiffness of the matrix material, which softens over time due toviscoelastic effects, and thus lowers the strength of the composite.This reduction must be accounted for in assessing the long-termdurability of composite structures.The dependence of compressive strength on time and temperature hasbeen investigated for a unidirectional carbon/epoxy composite material.Experimental results for strength versus time are compared withanalytical predictions based on a one-dimensional fiber microbucklingmodel and numerical results from finite element analysis.     

基于灵敏度分析的复合材料层合板优化设计

工程结构中的复合材料层合板的几何参数往往具有随机性质.如何研究随机参数层合板的灵敏度,并对参数进行优化分析,这对正确估计结构设计的可靠性有着非常重要的意义.根据层合板的一阶剪切理论,采用样条有限元法,推导并建立了层合板的振动方程,刚度矩阵,质量矩阵,比例阻尼矩阵以及求解反对称层合板响应灵敏度的计算公式,在基于灵敏度分析的基础上,进行了复合材料层合板的基频分析和优化设计,并用网格法计算最佳铺层角.数值算例验证了算法的有效性.     

复合材料层合板故障诊断的一种新方法

本文计算了无损板在给定模态下各单元的能量,求得每个单元对该阶模态下全板能量的贡献,并通过模态实验得到损伤前后各阶固频的变化.分析发现两者之间存在着内在联系,从而得到一种分析小损伤位置和范围的新方法.     

Postbuckling Analysis of Shear-Deformable Composite Laminated Plates on Two-Parameter Elastic Foundations

Postbuckling analysis is presented for a simply supported, shear-deformable, composite laminated plate subjected to uniaxial compression and resting on a two-parameter (Pasternak-type) elastic foundation. The initial geometric imperfection of the plate is taken into account. Two cases of in-plane boundary conditions are considered. The formulations are based on Reddy’s higher-order shear-deformation plate theory, including plate–foundation interaction. The analysis uses a deflection-type perturbation technique to determine buckling loads and postbuckling equilibrium paths. Numerical examples are presented that relate to the performance of perfect and imperfect, antisymmetric angle-ply and symmetric cross-ply laminated plates resting on Pasternak-type elastic foundations from which results for Winkler elastic foundations are obtained as a limiting case. The effects played by foundation stiffness, transverse shear deformation, the character of the in-plane boundary conditions, plate aspect ratio, total number of plies, fiber orientation, and initial geometric imperfections are studied.     

考虑芯层横向变形的粘弹性复合材料夹层板结构的声振特性分析

夹层板结构具有很高的比强度和比刚度。若芯层采用粘弹性阻尼材料，夹层板结构还具有良好的隔振和隔声特性，因此在工程结构中得到广泛应用。以往的夹层板理论大多忽略了芯层的横向正应变和横向正应力，在分析芯层较厚的夹层板或者夹层结构的高频振动问题时由于不能体现芯层的横向压缩变形，往往显得不够合理。针对这一不足，构造了一个复合材料夹层板单元：夹层板的上下面板采用基于一阶剪切变形理论的Mindlin假定以及层合板理论进行分析；采用文献[6，7]中提出的Timoshenko层合厚梁理论构造了单元每边的转角和剪应变场，消除了Mindlin板单元当板厚变小时的剪切锁死问题；假定芯层的位移沿厚度方向线性变化，并用上下面板的自由度表示，最终形成以上下面板自由度表示的系统总的运动方程。该单元不仅考虑了芯层的横向剪切变形，还考虑了芯层的横向压缩变形。数值计算结果表明：无论对于静力问题、动力问题还是声辐射等问题，考虑芯层的横向压缩变形是合理的，也是有必要的。     

An Edge-Based Smoothed Discrete Shear Gap Method Using the C0-Type Higher-Order Shear Deformation Theory for Analysis of Laminated Composite Plates

The edge-based smoothing discrete shear gap method (ES-DSG3) using three-node triangular elements is combined with a C⁰-type higher-order shear deformation theory (HSDT) to give a new linear triangular plate element for static, free vibration, and buckling analyses of laminated composite plates. In the ES-DSG3, only the linear approximation is necessary, and the discrete shear gap method (DSG) for triangular plate elements is used to avoid the shear locking and spurious zero energy modes. In addition, the stiffness matrices are calculated relying on smoothing domains associated with the edges of the triangular elements through an edge-based strain smoothing technique. Using the C⁰-type HSDT, the shear correction factors in the original ES-DSG3 can be removed and replaced by two additional degrees of freedom at each node. The numerical examples demonstrated that the ES-DSG3 show remarkably excellent performance compared to several other published elements in the literature.     

Progressive Failure Analysis of Laminated Composite Plates With Two Serial Pinned Joints

This study presents experimental and numerical failure analyses for two serial pin loaded holes in unidirectional carbon fiber/epoxy resin composite laminates. The failure loads and failure modes of composite laminates are determined for different geometrical parameters and different stacking sequences. Three-dimensional ANSYS Parametric Design Language codes are developed in the ANSYS® finite element software. Hashin Failure Criteria and material degradation rules are used to determine failure loads and failure modes in the numerical analysis. Experimental and numerical results show that failure loads and failure modes were affected with geometrical parameters.     

Effects of Boundary Conditions in Laminated Composite Plates Using Higher Order Shear Deformation Theory

This paper extends the applicability of a modified higher order shear deformation theory to accurately determine the in-plane and transverse shear stress distributions in an orthotropic laminated composite plate subjected to different boundary conditions. A simpler, two-dimensional, shear deformable, plate theory accompanied with an appropriate set of through-thickness variations, is used to accurately predict transverse shear stresses. A finite element code was developed based on a higher order shear deformation theory to study the effects of boundary conditions on the behavior of thin-to-thick anisotropic laminated composite plates. The code was verified against three dimensional elasticity results. The study also compared the stresses and deformation results of higher order theory with those obtained using commercial software such as LUSAS, ANSYS and ALGOR. The commercial software are heavily used by designers to design various components/products made of composites. Various combinations of fixed, clamped and simply supported boundary conditions were used to verify a large class of anticipated applications. Results obtained from software are in good agreement for some cases and significantly differ for others. It was found that LUSAS and ANSYS yield better results for transverse deflection and in-plane stresses. But for transverse shear stresses, it is highly dependent on boundary conditions.     

复合材料层合板脱层诊断的实验研究

利用动态特性对复合材料层合板的脱层损伤进行无损检测,是一种方便、实用的方法.复合材料层合板发生脱层损伤时,其内部微观结构、应力分布以及材料性能参数都会发生变化,这些变化会引起材料的动态特性发生显著的变化.因此,分别研究层合板在健康状态下和损伤状态下的动态特性,就可以分析建立脱层损伤的诊断知识规则.     

Nonlinear Viscoelastic,Viscoplastic Characterization of Unidirectional GF/EP Composite

Viscoplastic strains of unidirectional continuous fiber composite (HEXCEL GF/EPprepreg system) are studied experimentally and theoretically. Creep and strainrecovery tests are used. Schapery's nonlinear viscoelastic viscoplasticconstitutive equations are used and generalized to describe inelastic behavior ofunidirectional composite under isothermal creep and strain recovery conditions. Themethodology to quantify the viscoplastic strains with respect to applied stress isproposed. Viscoplastic strains of composite are described by plastic shear strain inmaterial symmetry axis. Assumptions has been used and validated that the functiondescribing the stress and time dependence of viscoplastic strain can be presented asa product of two, time and correspondingly stress dependent, master curves.     

Optimum Design of Laminated Composite Plates Undergoing Large Amplitude Oscillations

The optimum design of composite laminated plates under going large amplitude free vibration is discussed. Von Karman's nonlinear strain displacement relations are considered to account for large amplitude. A higher order shear deformation theory with parabolic variation of transverse shear stresses through thickness is used in the finite element formulation. A nine-noded isoparametric element with 7 dof per node is adopted. Ritz formulation for nonlinear finite element analysis is implemented and the direct iteration method is used to solve the governing nonlinear equation. Optimization is carried out using genetic algorithm (GA) with tournament selection scheme.     

Triangular Differential Quadrature Method in Bending Analysis of Triangular Symmetric Laminated Plates

The main advantage of triangular differential quadrature method in numerical simulations of problems in triangular domain is that it needs very few grid points compared to those of low order methods. In the current work, the method is implemented to analyze the bending behavior of relatively thick triangular composite plates based on the concept of first-order shear deformation theory. A set of triangular symmetric laminated plates with various lay-ups, length to thickness ratios, and boundary conditions is considered. The results are discussed in detail and compared with those obtained from finite element method of analysis using ANSYS package.     

用加权残数法分析各向异性层合薄板的几何非线性问題

各向异性层合薄板的几何非线性问题,由于控制方程和边值问题求解的复杂性,历来解法繁杂,工作量大且存在较大局限性。本文利用加权残数法简捷,有效的特点,提出以具有良好拟合性和对边界条件灵活可适性的五次B—样条基函数的组合作为试函数基底,然后采用阻尼最小二乘法,应用于解决这类复杂问题。本文在计算时编制了较为通用的程序,若干具体算例表明,本方法收敛稳定,结果准确,且解法简捷,统一,便于程序标准化与推广应用。