基于Zig-Zag变形假定的复合材料夹层板的自由振动

针对复合材料夹层板的实际变形特征，基于Zig-Zag变形假定和Mindlin一阶剪切理论，建立了复合材料夹层板自由振动的有限元模型，在该模型中分别对上、下面板和芯体建立了三个独立坐标系，使三部分的转角独立，为具有厚夹芯和软夹芯的复合材料夹层板的动力分析提供了一种更为准确的有限元模型；在此基础上推导了相应的刚度阵和质量阵，并采用子空间迭代法求解。夹层板的固有频率。通过典型考题证明了本模型的有效性。文中最后还通过参数讨论，研究了具有不同长厚比的复合材料夹层板基频的变化规律。     

四边简支硬夹芯夹层板的弯曲问题研究

现有的夹层结构理论都是将夹芯视为软夹芯,忽略了其面内应力分量和弯曲刚度.该理论不能满足近年来出现的硬夹芯夹层结构.对此,考虑了以上被忽略的因素,修正了Reissner理论的软夹芯假设,提出了考虑夹芯面内应力分量和弯曲刚度的硬夹芯夹层板基本假设.根据最小势能原理得到了硬夹芯夹层板弯曲的基本方程和边界条件,给出了四边简支硬夹芯夹层板在横向载荷下弯曲的解析解.另外本文还研究了硬夹芯夹层板弯曲问题的有限元法,推导了四节点四边形等参单元的有限元列式,并用MATLAB编程求解了具体算例.     

复合材料夹层板的振动及阻尼分析

本文对复合材料夹层板的动态问题提出了一种新的位移修正模式，该位移模式包括了面板的横向剪切变形及夹芯的剪切变形，以此位移模式进行了有限元分析，给出了形成阻尼矩阵的方法。文中还分析了夹层板的阻尼比ψ与夹芯厚度ｈｃ，夹芯材料的阻尼损耗因子β以及夹芯剪切模量Ｇ之间的关系；算例与实验结果的对比表明：本文提出的计算方法可以给出满意的数值结果。     

轻质金属点阵夹层板热屈曲临界温度分析

本文针对均匀温度场下四边简支和四边固支金属点阵夹层板的临界热屈曲温度进行了求解和参数影响分析。将点阵夹芯等效为均匀连续体,并且将夹层板的剪切刚度近似为点阵夹芯的抗剪切刚度,忽略夹芯的抗弯刚度且认为夹层板主要由面板来提供抗弯刚度。对于无法获得解析解的四边固支条件,通过对未知变量进行双傅里叶展开的方法求解了Ressiner夹层板模型的临界屈曲温度,理论分析结果与有限元计算结果吻合良好。进一步分析了不同边界条件、点阵胞元构型、点阵材料相对密度、面板厚度等对临界屈曲温度的影响规律。     

基于Layerwise离散层理论的复合材料夹层板屈曲分析

复合材料夹层结构由于面板和芯层力学特性差异较大,屈曲分析时要分层考虑各层的剪切变形。基于Reddy的Layerwise离散层理论,假设每一层变形服从一阶剪切变形理论,在统一的位移场描述下,推导建立了一种用于复合材料夹层结构屈曲分析的四节点四边形板单元,并采用混合插值方法对单元的剪切锁定进行了修正。分别对三种典型的夹层板结构进行线性屈曲有限元分析,并将计算结果与文献中已有结果进行了对比。结果表明：本文的分析方法能离散考虑各层的力学特性,将结构离散为多层时,计算结果与三维弹性理论或高阶板理论吻合;将结构等效为单层时,计算结果与基于一阶剪切变形理论的文献结构吻合,验证了单元的有效性。     

考虑横向拉伸的FGM夹层双曲扁壳自由振动分析

在双曲正弦高阶剪切变形理论的基础上,针对横向位移增加厚度坐标的幂函数项,考虑了横向拉伸的影响,研究了简支条件下功能梯度夹层双曲扁壳的自由振动。基于Hamilton原理推导出了其动力学模型,利用Navier方法计算了表层是功能梯度材料,芯层是匀质材料的双曲扁壳的量纲为一的固有频率,并与已有结果进行了比较。分析了功能梯度材料性质梯度变化指数、芯层厚度、长厚比、曲率半径与厚度比对量纲为一的固有频率的影响。结果表明:与已有结果比较,基于考虑横向拉伸影响的正弦剪切变形理论,功能梯度夹层双曲扁壳对量纲为一的固有频率的计算结果是准确的;量纲为一的固有频率随着材料性质梯度变化指数的增加而单调减小,随着长厚比的增加而单调增加,随着芯层厚度的增加而单调增加。     

曲壁蜂窝夹层板的振动特性研究

曲壁蜂窝具有负刚度特性,可以在大变形过程中吸收能量、抗冲击,并且在冲击过后可以自我恢复而不像传统蜂窝被压溃。本文将曲梁构成的负刚度蜂窝作为芯层,建立夹层板的动力学模型;推导出了曲壁负刚度蜂窝胞元的等效弹性参数,将其周期性排列为蜂窝芯,应用Reddy高阶剪切变形理论、Von-Karman大变形关系和Hamilton原理推导了负刚度蜂窝夹层板的非线性动力学方程;应用Navier法计算了四边简支边界条件下的固有频率。并利用有限元软件ABAQUS建立模型,计算固有频率,与理论计算结果进行比较,结果显示二者的计算结果具有较好的一致性,验证了芯层等效弹性参数及模型的有效性。探讨了在蜂窝胞元具有较高吸能情形下,夹层板在不同芯层厚度、不同芯厚比以及不同胞元曲壁厚度时的固有频率的变化特性。     

蜂窝层芯夹层板结构振动与传声特性研究

蜂窝层芯夹层板应用于飞行器、高速列车等交通工具的主体及底板结构时需要考虑其振动及隔声特性. 针对声压激励下的四边简支蜂窝层芯夹层板结构,应用基于Reissner夹层板理论的结构振动方程建立了的声振耦合理论模型(声压以简支模态双级数的形式引入振动控制方程),结合流固耦合条件求解了声振耦合系统控制方程,应用有限元模拟对理论预测进行了验证. 基于理论模型的数值计算结果,系统研究了蜂窝层芯夹层板结构的振动特性和传声特性,刻画了层芯厚度、蜂窝壁厚、夹层板面内尺寸和声压入射角度等关键系统参数对夹层板振动和传声特性的影响,为此类结构的工程优化设计提供了必要的理论参考.     

考虑横向拉伸影响的FGM板的静态分析

在三阶剪切变形理论的基础上,添加关于厚度坐标z的幂函数项,并假设板结构的上下表面剪切力为0,提出了一种考虑横向拉伸影响的高阶剪切变形理论。并且研究了简支边界条件下受静态载荷作用的功能梯度材料矩形板的静态弯曲行为。基于虚功原理推导出了功能梯度矩形板的基本方程,利用Navier双三角级数法计算了功能梯度材料矩形板在静态载荷作用下沿厚度方向的位移及应力分布的数值结果。计算结果与三维精确解理论、其他高阶剪切变形理论得到的数值结果进行了比较。对比结果表明,改进的考虑横向拉伸影响的高阶剪切变形理论的正确性和优越性。     

双模量泡沫铝芯夹层梁的自由振动分析

对模量泡沫铝芯夹层梁的固有振动问题进行了研究。利用双模量的材料应力-应变方程,推导出了双模量材料剪切弹性模量计算公式,证明了双模量梁中性轴位置不受作用在梁上的横向载荷的影响。在考虑剪切变形的基础上,建立了双模量泡沫铝芯夹层梁的强迫振动控制方程,推导出了双模量泡沫铝芯夹层梁固有振动问题的振型函数及固有频率计算公式,并分析了剪切变形及泡沫铝芯夹层的拉压弹性模量对双模量泡沫铝芯夹层梁固有振动频率的影响。研究表明:泡沫铝芯夹层梁固有振动时,其固有振动波形是不连续的,奇数波型与偶数波型之间存在间断点;剪切变形及泡沫铝芯夹层的拉压弹性模量对双模量泡沫铝芯夹层梁固有振动的影响是不能忽略的。     

Vibration and buckling of laminated sandwich plates having interfacial imperfections

The vibration and buckling characteristics of sandwich plates having laminated stiff layers are studied for different degrees of imperfections at the layer interfaces using a refined plate theory. With this plate theory, the through thickness variation of transverse shear stresses is represented by piece-wise parabolic functions where the continuity of these stresses is satisfied at the layer interfaces by taking jumps in the transverse shear strains at the interfaces. The transverse shear stresses free condition at the plate top and bottom surfaces is also satisfied. The inter-laminar imperfections are represented by in-plane displacement jumps at the layer interfaces and characterized by a linear spring layer model. It is quite interesting to note that this plate model having all these refined features requires unknowns only at the reference plane. To have generality in the analysis, finite element technique is adopted and it is carried out with a new triangular element developed for this purpose, as any existing element cannot model this plate model. As there is no published result on imperfect sandwich plates, the problems of perfect sandwich plates and imperfect ordinary laminates are used for validation.     

Accurate transverse stress evaluation in composite/sandwich thick laminates using a C0 HSDT and a novel post-processing technique

An efficient method for accurate evaluation of through-the-thickness distribution of transverse stresses in thick composite and sandwich laminates, using a displacement-based C⁰ higher-order shear deformation theory (HSDT), is presented. The technique involves a least square of error (LSE) method applied to the 3D equilibrium equations at the post-processing phase, after a primary finite element analysis is performed using the HSDT. This is distinctly different from the conventional method of integrating the 3D equilibrium equations, for transverse stress recovery in composite laminates during post-processing. Competence of the technique is demonstrated in the numerical examples through comparison with results from first-order shear deformation theory (FSDT), another HSDT and those from analytical and 3D elasticity solutions available in literature.     

Enhanced first-order theory based on mixed formulation and transverse normal effect

An accurate prediction of displacements and stresses for laminated and sandwich plates is presented using an enhanced first-order plate theory based on the mixed variational theorem (EFSDTM) developed in this paper. In the mixed formulation, transverse shear stresses based on an efficient higher-order plate theory (EHOPT) developed by Cho and Parmerter [Cho, M., Parmerter, R.R., 1993. Efficient higher-order composite plate theory for general lamination configurations. AIAA Journal 31, 1299–1306] are utilized and modified to satisfy prescribed lateral conditions, and displacements are assumed to be those of a first-order shear deformation theory (FSDT). Relationships between the modified EHOPT and the FSDT are systematically derived via both the mixed variational theorem and the least-square approximation of difference between in-plane stresses including the transverse normal stress effect. It is shown that the transverse normal stress effect should be considered in predicting the in-plane stresses when the Poisson effect is dominant. The developed EFSDTM preserves the computational advantage of the classical FSDT while allowing for important local through-the-thickness variations of displacements and stresses through the recovery procedure. The accuracy and efficiency of the present theory are assessed by comparing its results with various plate models as well as the three-dimensional exact solutions for thick laminated and sandwich plates.     

Corotational nonlinear analyses of laminated shell structures using a 4-node quadrilateral flat shell element with drilling stiffness

A new 4-node quadrilateral flat shell element is developed for geometrically nonlinear analyses of thin and moderately thick laminated shell structures. The fiat shell element is constructed by combining a quadrilateral area co- ordinate method （QAC） based membrane element AGQ6- II, and a Timoshenko beam function （TBF） method based shear deformable plate bending element ARS-Q12. In order to model folded plates and connect with beam elements, the drilling stiffness is added to the element stiffness matrix based on the mixed variational principle. The transverse shear rigidity matrix, based on the first-order shear deformation theory （FSDT）, for the laminated composite plate is evaluated using the transverse equilibrium conditions, while the shear correction factors are not needed. The conventional TBF methods are also modified to efficiently calculate the element stiffness for laminate. The new shell element is extended to large deflection and post-buckling analyses of isotropic and laminated composite shells based on the element independent corotational formulation. Numerical re- sults show that the present shell element has an excellent numerical performance for the test examples, and is applicable to stiffened plates.     

Static analysis of functionally graded doubly-curved shells and panels of revolution

The Generalized Differential Quadrature (GDQ) Method is applied to study four parameter functionally graded and laminated composite shells and panels of revolution. The mechanical model is based on the so-called First-order Shear Deformation Theory (FSDT), in particular on the Toorani-Lakis Theory. The solution is given in terms of generalized displacement components of points lying on the middle surface of the shell. The generalized strains and stress resultants are evaluated by applying the Differential Quadrature rule to the generalized displacements. The transverse shear and normal stress profiles through the thickness are reconstructed a posteriori by using local three-dimensional elasticity equilibrium equations. In order to verify the accuracy of the present method, GDQ results are compared with the ones obtained with semi-analytical formulations and with 3D finite element method. A parametric study is performed to illustrate the influence of the parameters on the mechanical behavior of functionally graded shell structures made of a mixture of ceramics and metal.     

A double-superposition global–local theory for vibration and dynamic buckling analyses of viscoelastic composite/sandwich plates: a complex modulus approach

A higher-order global–local theory is proposed based on the double-superposition concept for free vibration and dynamic buckling analyses of viscoelastic composite/sandwich plates subjected to thermomechanical loads. In contrast to all theories proposed so far for analysis of the viscoelastic plates, the continuity conditions of the transverse shear and normal stresses at the layer interfaces and the nonzero traction conditions at the top and bottom surfaces of the sandwich plates are satisfied. Another novelty is that these conditions may be satisfied for viscoelastic plates with temperature-dependent material properties and nonlinear behaviors subjected to thermomechanical loads. Furthermore, transverse flexibility is also taken into account. Some dynamic buckling/wrinkling analyses of the viscoelastic plates are performed in the present paper, for the first time. Comparisons made between results of the paper and results reported by well-known references confirm the accuracy and the efficiency of the proposed theory and the relevant solution algorithm.     

A layerwise C0-type higher order shear deformation theory for laminated composite and sandwich plates

A novel layerwise C⁰-type higher order shear deformation theory (layerwise C⁰-type HSDT) for the analysis of laminated composite and sandwich plates is proposed. A C⁰-type HSDT is used in each lamina layer and the continuity of in-plane displacements and transverse shear stresses at inner-laminar layer is consolidated. The present layerwise theory retains only seven variables without increasing the number of variables when the number of lamina layers are intensified. The shear stresses through the plate thickness derived from the constitutive equation of the present theory have the same shape as those calculated from the equilibrium equation. In addition, the artificial constraints are added in the principle of virtual displacements (PVD) and are certainly fulfilled through a penalty approach. In this paper, two C⁰-continuity numerical methods, such as the Finite Element Method (FEM) and Bézier isogeometric element (BIEM) are utilized to solve a discrete system of equations derived from the PVD. Several numerical examples with various geometries, aspect ratios, stiffness ratios, and boundary conditions are investigated and compared with the 3D elasticity solution, the analytical, as well as, numerical solutions based on various plate theories.     

Free vibration of functionally graded sandwich plates using four-variable refined plate theory

This paper uses the four-variable refined plate theory (RPT) for the free vibration analysis of functionally graded material (FGM) sandwich rectangular plates. Unlike other theories, there are only four unknown functions involved, as compared to five in other shear deformation theories. The theory presented is variationally consistent and strongly similar to the classical plate theory in many aspects. It does not require the shear correction factor, and gives rise to the transverse shear stress variation so that the transverse shear stresses vary parabolically across the thickness to satisfy free surface conditions for the shear stress. Two common types of FGM sandwich plates are considered, namely, the sandwich with the FGM facesheet and the homogeneous core and the sandwich with the homogeneous facesheet and the FGM core. The equation of motion for the FGM sandwich plates is obtained based on Hamilton’s principle. The closed form solutions are obtained by using the Navier technique. The fundamental frequencies are found by solving the eigenvalue problems. The validity of the theory is shown by comparing the present results with those of the classical, the first-order, and the other higher-order theories. The proposed theory is accurate and simple in solving the free vibration behavior of the FGM sandwich plates.     

Free vibration of functionally graded sandwich plates using four-variable refined plate theory

This paper uses the four-variable refined plate theory (RPT) for the free vibration analysis of functionally graded material (FGM) sandwich rectangular plates.Unlike other theories, there are only four unknown functions involved, as compared to five in other shear deformation theories. The theory presented is variationally consistent and strongly similar to the classical plate theory in many aspects. It does not require the shear correction factor, and gives rise to the transverse shear stress variation so that the transverse shear stresses vary parabolically across the thickness to satisfy free surface conditions for the shear stress. Two common types of FGM sandwich plates are considered, namely, the sandwich with the FGM facesheet and the homogeneous core and the sandwich with the homogeneous facesheet and the FGM core. The equation of motion for the FGM sandwich plates is obtained based on Hamilton's principle. The closed form solutions are obtained by using the Navier technique. The fundamental frequencies are found by solving the eigenvalue problems. The validity of the theory is shown by comparing the present results with those of the classical, the first-order, and the other higher-ordex theories. The proposed theory is accurate and simple in solving the free vibration behavior of the FGM sandwich plates.     

An efficient and simple refined theory for nonlinear bending analysis of functionally graded sandwich plates

In this paper, an efficient and simple refined theory is presented for nonlinear bending analysis of functionally graded sandwich plates. The theory presented is variationally consistent, does not require the shear correction factor, and gives rise to transverse shear stress variations such that the transverse shear stresses vary parabolically across the plate thickness, satisfying shear-stress-free surface conditions. The energy concept along with the present theory and the first- and third-order shear deformation theories is used to predict the large deflection and the stress distribution across the thickness of functionally graded sandwich plates.