复合材料多层厚板的精化高阶理论及其有限元法

本文提出了一种经过改进的复合材料多层厚板的精化高阶剪切变形理论,采用Legendre多项式来逼近位移场沿厚度方向的分布,较好地模拟了横向剪切变形和层间拉、压变形,利用层板上,下自由表面横向剪应力为零的边界条件,对所假定的位移场作了化简,在此基础上构造了相应的有限元.文中通过一些典型算例,与Pagano的弹性力学精确解[9]以及其他高阶理论的解作了比较,说明本文的精化高阶剪切变形理论及其相应的有限元具有精度高和收敛快的优点.     

复合材料多层厚板的精化高阶理论及其有限元法

本文提出了一种经过改进的复合材料多层厚板的精化高阶剪切变形理论,采用Legendre多项式来逼近位移场沿厚度方向的分布,较好地模拟了横向剪切变形和层间拉、压变形,利用层板上,下自由表面横向剪应力为零的边界条件,对所假定的位移场作了化简,在此基础上构造了相应的有限元.文中通过一些典型算例,与Pagano的弹性力学精确解[9]以及其他高阶理论的解作了比较,说明本文的精化高阶剪切变形理论及其相应的有限元具有精度高和收敛快的优点.      

基于高阶剪切变形理论的复合材料层合板精化单元法

基于高阶剪切变形层合板理论(该理论满足层间位移、应力连续条件)建立了一种精化方法,由此建立了三角形精化板单元.该单元满足单元间C1类弱连续条件,其收敛性得到保证,且具有列式简单、计算效率和精度高的优点.      

从Levinson高阶梁理论的一致变分到高次翘曲梁理论

将矩形截面梁的截面翘曲位移设定为3次Legendre多项式的形式,利用弹性力学平面应力问题分项的不完全的广义变分原理,导出高次翘曲梁理论,得到形式简单易求解的方程。由于引入轴向拉伸的情况,使梁的平面内变形问题得以统一;计及了梁表面剪切荷载的作用,并严格满足表面剪应力边界条件;通过引入轴向位移约束参考点间距离的概念对梁端翘曲约束作更精致地描述,且使得该理论包含了变分一致或者不一致的高阶剪切梁理论。该理论的推导还表明,Levinson梁理论的变分不一致仅仅局限于有转角约束的梁端。通过算例,将高次翘曲梁理论与弹性力学平面应力问题以及Timoshenko梁理论、Levinson梁理论进行比较,初步显示出该理论的优越性。     

基于高阶剪切理论的脱层压电梁谐响应分析

基于Timoshenko梁理论,对位移函数进行了高阶剪切变形模式假设,考虑剪切变形和力电耦合效应,并对压电弹性层合脱层梁进行了分区处理,可方便地描述脱层长度和脱层位置,建立了弯曲波在梁中传播的基本方程式;通过长波情况下的电势分布简化,考虑无外加电压时,对该类悬臂梁进行了求解分析。给出了梁的频散关系,得到了各位移分量和电势的解析解,分析了脱层参数对位移和电势的影响规律。     

基于整体-局部位移假设的高阶理论及其三角形板单元

本文推导一种基于整体-局部位移假设的高阶理论, 该理论满足层间位移、应力连续条件, 满足上、下自由表面条件。建立基于此高阶理论的三节点三角形层合板单元。数值计算结果表明此高阶理论能很好地描述剪切变形效应, 该位移单元不仅能很好地计算整体位移参数, 而且能很好地计算横向剪切应力。      

Levinson 矩形微板谐振器热弹性阻尼解析解

基于 Levinson 高阶剪切板理论,给出了四边简支微板谐振器热弹性耦合自由振动的复频率以及板内变温场的精确解析解;由复频率法给出了表征微板热弹性阻尼的逆品质因子;通过数值结果分析了 Levinson 微板的热弹性阻尼随几何尺寸和振动模态变化的规律,并与一阶剪切变形理论和经典板理论的预测结果进行了比较,分析了剪切变形对热弹性阻尼的影响程度。数值结果表明,对于中厚板和厚板谐振器,经典板理论预测的热弹性阻尼值明显大于剪切变形板理论的预测值。这是由于经典板理论忽略了横向剪切变形,从而过高地估计了微板的抗弯刚度。另外,在四边简支条件下,还给出了 Mindlin 微板和 Levinson 微板热弹性阻尼预测值之间的比较。结果表明,Levinson高阶剪切变形理论能够更好地预测厚板谐振器的热弹性阻尼。这是因为 Levinson 理论下的位移场能够精确满足上下表面应力为零的条件,温度场包含了厚度方向坐标的高阶项。     

复合材料椭圆板的固有频率

本文用Ｒｉｔｚ能量法求解层叠复合材料椭圆板的固有频率。基于Ｒｅｄｄｙ的高阶剪切变形理论导出了板的能量泛函,然后用一个完备的二元多项式级数与一个满足边界条件的基本函数的乘积作为振型函数,由能量最小原理导出了求解固有频率的特征方程。文中给出了详细的数学公式,研究了方法的收敛性和计算精度,并与已有结果作了比较。     

薄壁箱梁剪滞效应的能量变分法

考虑了三个不同的剪滞纵向位移差函数以反映薄壁箱梁不同宽度翼板的剪滞变化幅度,提出了一种能对工程中常用的变高度梯形截面箱梁剪力滞及剪切变形效应进行分析的方法。应用能量变分原理,导出了箱梁受横向荷载作用下的剪滞控制微分方程和边界条件,获得相应的闭合解,并探讨了不同纵向位移差函数对剪力滞的影响。最后通过高阶有限条法计算验证了本文方法的正确性。所得的公式比以往剪滞理论有了发展,因此更具有一般性。     

基础激励下带金属外层的多黏弹性层纤维增强层合板的动力学模型

以包含三层黏弹性材料、二层纤维增强材料和金属外层的多黏弹性层纤维增强(MVFLM)层合板为例,建立其在基础激励作用下的动力学模型。将坐标系设置在层合板结构的中心层,使用高阶剪切变形理论(考虑多个黏弹性层的剪切应变影响)和经典层合板理论分别对纤维层和金属层进行建模,进而获得MVFLM层合板的位移场函数;将基础激励等效成均布惯性力载荷,基于能量法获得系统的动能、势能和外力功,并利用正交多项式法表示边界条件对应的振型函数,成功求解具有多个黏弹性层的MVFLM层合板的固有频率、模态振型和振动响应;分别通过与已有计算结果进行对比以及实例测试,验证了所建立的动力学模型的有效性。     

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.     

Static and dynamic analysis of laminated composite and sandwich plates and shells by using a new higher-order shear deformation theory

A new higher order shear deformation theory for elastic composite/sandwich plates and shells is developed. The new displacement field depends on a parameter “m”, whose value is determined so as to give results closest to the 3D elasticity bending solutions. The present theory accounts for an approximately parabolic distribution of the transverse shear strains through the shell thickness and tangential stress-free boundary conditions on the shell boundary surface. The governing equations and boundary conditions are derived by employing the principle of virtual work. These equations are solved using Navier-type, closed form solutions. Static and dynamic results are presented for cylindrical and spherical shells and plates for simply supported boundary conditions. Shells and plates are subjected to bi-sinusoidal, distributed and point loads. Results are provided for thick to thin as well as shallow and deep shells. The accuracy of the present code is verified by comparing it with various available results in the literature.     

Adding transverse normal stresses to layered shell finite elements for the analysis of composite structures

This work presents a formulation developed to add capabilities for representing the through thickness distribution of the transverse normal stresses, σ_z, in first and higher order shear deformable shell elements within a finite element (FE) scheme. The formulation is developed within a displacement based shear deformation shell theory. Using the differential equilibrium equations for two-dimensional elasticity and the interlayer stress and strain continuity requirements, special treatment is developed for the transverse normal stresses, which are thus represented by a continuous piecewise cubic function. The implementation of this formulation requires only C⁰ continuity of the displacement functions regardless of whether it is added to a first or a higher order shell element. This makes the transverse normal stress treatment applicable to the most popular bilinear isoparametric 4-noded quadrilateral shell elements.

To assess the performance of the present approach it is included in the formulation of a recently developed third order shear deformable shell finite element. The element is added to the element library of the general nonlinear explicit dynamic FE code DYNA3D. Some illustrative problems are solved and results are presented and compared to other theoretical and numerical results.     

Static and dynamic analysis of laminated composite and sandwich plates and shells by using a new higher-order shear deformation theory

A new higher order shear deformation theory for elastic composite/sandwich plates and shells is developed. The new displacement field depends on a parameter “m”, whose value is determined so as to give results closest to the 3D elasticity bending solutions. The present theory accounts for an approximately parabolic distribution of the transverse shear strains through the shell thickness and tangential stress-free boundary conditions on the shell boundary surface. The governing equations and boundary conditions are derived by employing the principle of virtual work. These equations are solved using Navier-type, closed form solutions. Static and dynamic results are presented for cylindrical and spherical shells and plates for simply supported boundary conditions. Shells and plates are subjected to bi-sinusoidal, distributed and point loads. Results are provided for thick to thin as well as shallow and deep shells. The accuracy of the present code is verified by comparing it with various available results in the literature.     

Bending and free vibration analysis of isotropic and multilayered plates and shells by using a new accurate higher-order shear deformation theory

Bending and free vibration analysis of multilayered plates and shells by using a new accurate higher order shear deformation theory (HSDT) is presented. It is one of the most accurate HSDT available in the literature, mainly because new non-polynomial shear strain shape functions (combination of exponential and trigonometric) used in the present theory are richer than polynomial functions, and free surface boundary conditions can be guaranteed a priori. The present HSDT is able to reproduce Touratier’s HSDT as special case. The governing equations and boundary conditions are derived by employing the principle of virtual work. These equations are then solved via Navier-type, closed form solutions. Bending and dynamic results are presented for cylindrical and spherical shells and plates for simply supported boundary conditions. Panels are subjected to sinusoidal, distributed and point loads. Results are provided for thick to thin as well as shallow and deep shells. The present results are compared with the exact three-dimensional elasticity theory and with several other well-known HSDT theories. The present HSDT is found to be more precise than other several existing ones for analyzing the bending and free vibration of isotropic and multilayered composite shell and plate structures.     

Bending and free vibration analysis of isotropic and multilayered plates and shells by using a new accurate higher-order shear deformation theory

Bending and free vibration analysis of multilayered plates and shells by using a new accurate higher order shear deformation theory (HSDT) is presented. It is one of the most accurate HSDT available in the literature, mainly because new non-polynomial shear strain shape functions (combination of exponential and trigonometric) used in the present theory are richer than polynomial functions, and free surface boundary conditions can be guaranteed a priori. The present HSDT is able to reproduce Touratier’s HSDT as special case. The governing equations and boundary conditions are derived by employing the principle of virtual work. These equations are then solved via Navier-type, closed form solutions. Bending and dynamic results are presented for cylindrical and spherical shells and plates for simply supported boundary conditions. Panels are subjected to sinusoidal, distributed and point loads. Results are provided for thick to thin as well as shallow and deep shells. The present results are compared with the exact three-dimensional elasticity theory and with several other well-known HSDT theories. The present HSDT is found to be more precise than other several existing ones for analyzing the bending and free vibration of isotropic and multilayered composite shell and plate structures.     

Analysis of a thick transversely isotropic circular cylindrical shell subjected to asymmetric load

Summary Solution for a thick transversely isotropic simply supported circular cylindrical shell subjected to asymmetric patch load has been obtained using a set of three displacement functions and elasticity approach. Numerical results have been carried out for patch loads with different material properties, thickness to mean radius. The results obtained from this analysis have been compared with elassical shell theory, shear deformation theory of Vinson and Chou and higher order shear deformation theory of Bhimaraddi and Stevens.     

Bending-stretching analysis of thick functionally graded micro-plates using higher-order shear and normal deformable plate theory

In the present article, higher-order shear and normal deformable plate theory together with modified couple stress theory are developed to study the bending analysis of thick functionally graded rectangular micro-plates. One material length scale parameter is used for capturing the size effects. Utilizing the variational approach and also a principle of virtual displacement, a new form of equilibrium equations and the corresponding boundary conditions are derived. It is assumed that material properties vary through the thickness according to the power law function. Finally, an analytical solution for the bending problem of a simply supported FG rectangular micro-plate is presented.     

Development of geometrically exact new shell elements based on general curvilinear co‐ordinates

In the present study first‐order shear deformable shell finite elements based on general curvilinear co‐ordinates are proposed. For the development of the present shell elements, a partial mixed variational functional with independently assumed strains is provided in order to avoid the severe locking troubles known as transverse shear and membrane lockings. Bubble functions are included in the shape function of displacement to improve the performance of the developed element. The proposed assumed strain four‐ and nine‐node elements based on the general tensor shell theory provide an efficient linkage framework for shell surface modelling and finite element analysis. In the several benchmark problems, the present shell elements with exact geometric representations demonstrate their performance compared to previously reported results. Copyright © 2002 John Wiley & Sons, Ltd.     

Triangular finite element for analysis of thick laminated shells

The development of a general curved triangular element based on an assumed displacement potential energy approach is presented for the analysis of arbitrarily laminated thick shells. The associated laminated shell theory assumes transverse inextensibility and layerwise constant shear angle. The present element is a quadratic triangle of C⁰-type in the curvilinear co-ordinate plane, which is then mapped onto a curved surface. Convergence of transverse displacement, moments, stresses and the effect of two Gauss quadrature schemes also form a part of the investigation. Examples of two laminated shell problems demonstrate the accuracy and efficiency of the present element. Comparison of the present LCST (layerwise constant shear-angle theory) based solutions, with those based on the CST (constant shear-angle theory) clearly demonstrates the superiority of the former over the latter, especially in the prediction of the distribution of the surface-parallel displacements and stresses through the laminate thickness.