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An enhanced asymptotic homogenization method of the static and dynamics of elastic composite laminates

机译:弹性复合材料层合静动态的改进渐近均质化方法。

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The homogenization method has been used often in analyzing the composite materials but has had limited use with the laminated structures. This is due to a limitation of the homogenization theory, which assumes the unit cell should be periodically represented in any specific area. The main attraction of the homogenization method is its systematic capability to develop the homogenized macroscopic constitutive relation of composite materials and to compute the stresses in the microstructure of composites. In other words, both the macro- and micromechanics can be treated in the same context. In this paper, we will develop an enhanced asymptotic homogenization method (EHM); this method is developed from the partial asymptotic expansion and the condensed third-order shear deformation theory. This theory uses the reduced matrix method to consolidate all the stiffness matrices into four stiffness matrices (the extension; coupling; bending and transverse shear stiffness matrices) in the same manner as with the first-order shear deformation theory (FSDT). Two FORTRAN programs PRELAM and POSTLAM [Int. J. Comput. Struct. 76 (2000) 319; An enhanced asymptotic homogenization method of elastic composite laminates, Ph.D. Thesis, The University of Michigan, 1999] were also developed from the finite element implementation of the enhanced homogenization method. The pre-processor, PRELAM, reads the unit cell model and generates the homogeneous material stiffness matrix for a laminated structure. The post-processor, POSTLAM, calculates the local stress distribution based on the strains and curvatures obtained from the global structure analysis generated by the commercial finite element software, i.e., ABAQUS or MSC/NASTRAN. By the nature of homogenization method, these computational methods are capable of handling geometrically complicated microstructures and predicting the microscopic stress distributions. Since, the number of unknown variables for EHM and FSDT are the same, this implies that the results from EHM is easily utilized by ABAQUS in the global analysis. Therefore, one of the main benefits to EHM is that it is readily applied in commercial FEM packages, but not that it is as accurate as other methods. Numerical examples are also presented to validate these two programs.
机译:均质化方法通常用于分析复合材料,但对叠层结构的使用却受到限制。这是由于均质化理论的局限性所致,该理论假设应在任何特定区域中定期表示晶胞。均质化方法的主要吸引力在于它具有开发复合材料的均质宏观本构关系和计算复合材料微观结构应力的系统能力。换句话说,宏观和微观力学都可以在相同的背景下进行处理。在本文中,我们将开发一种增强的渐近均质化方法(EHM);该方法是基于局部渐近展开和压缩三阶剪切变形理论发展而来的。该理论使用简化矩阵方法,以与一阶剪切变形理论(FSDT)相同的方式,将所有刚度矩阵合并为四个刚度矩阵(扩展,耦合,弯曲和横向剪切刚度矩阵)。两个FORTRAN程序PRELAM和POSTLAM [Int。 J.计算机结构。 76(2000)319;弹性复合材料增强渐近均质化方法,博士学位。论文,密歇根大学,1999]也是从增强均质化方法的有限元实现中获得的。预处理器PRELAM读取晶胞模型并生成用于层压结构的均质材料刚度矩阵。后处理器POSTLAM根据应变和曲率计算局部应力分布,该应变和曲率是通过商业有限元软件(即ABAQUS或MSC / NASTRAN)生成的全局结构分析获得的。通过均质化方法的性质,这些计算方法能够处理几何复杂的微观结构并预测微观应力分布。由于EHM和FSDT的未知变量数量相同,这意味着ABAQUS可以轻松地将EHM的结果用于全局分析。因此,EHM的主要优点之一是它很容易在商业FEM封装中应用,但它不像其他方法一样准确。还提供了数值示例来验证这两个程序。

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