Advanced Numerical Modeling for Plate/Shell Structures with Multicomponent and Composite Materials--Meshless Technique Approach

功能梯度材料(FGM)是一种多相材料，其相体积分数在空间上以预定的轮廓逐渐变化。这导致在(宏观)结构尺度上连续分级的热性能和机械性能。由于功能梯度材料具有连续的梯度结构和性能，与传统复合材料相比具有一定的优势。由于初边值问题的高度数学复杂性，功能梯度材料的分析方法仅限于简单的几何和边界条件。因此，功能梯度材料的分析需要准确、高效的数值方法。通过使用特殊的梯度单元，有限元方法可以成功地应用于材料性质任意变化的问题。然而，在商业计算机代码中，材料属性被认为在每个元素上是一致的。边界元方法(BEM)也是一种适合于此目的的数值工具。然而，对于一般的连续非均匀物体，许多控制方程的基本解是不可用的。近年来，无网格法越来越流行，它们已成功地应用于各向同性和各向异性功能梯度材料的二维和三维轴对称瞬态热传导分析以及弹性力学中。在过去的几十年里，复合材料层合板在工程结构中得到了广泛的应用。所有以前的边界元应用都是处理各向同性Reissner-Mindlin板。尽管有限元和边界元作为精确有效的数值工具在解决复杂形状区域的边界或初边值问题上取得了巨大的成功，但人们仍然对发展新的先进的数值方法产生了越来越大的兴趣。在过去的十年中，连续介质力学问题的无网格方法引起了人们的极大关注，特别是因为它们具有很强的适应性和为数值分析准备输入数据的低成本。许多无网格方法都是从全局域或局部子域上的弱形式推导而来的。在全局公式中，弱形式的积分需要背景单元。在基于局部弱形式公式的方法中，不需要单元，因此它们通常被称为真正的无网格法。基于移动最小二乘法(MLS)的广义位移在简单区域上的无网格化近似，使得区域积分的数值积分变得简洁而有效。对于拉普拉斯变换参数的不同取值，需要解决几个准静态边值问题。采用Stehfest反演法得到随时间变化的解。该方案的创新之处在于：(1)首次在各向异性功能梯度板壳中建立了无网格元。(2)考虑了非定常条件。(3)该方法对几何形状、材料级配、各向同性或各向异性性质和加载条件没有限制。(4)还可以考虑热力耦合作用。

Functionally graded materials (FGMs) are multi-phase materials with the phase volume fractions varying gradually in space, in a pre-determined profile. This results in continuously graded thermal and mechanical properties at the (macroscopic) structural scale. FGMs posses some advantages over conventional composites because of their continuously graded structures and properties. Due to the high mathematical complexity of the initial-boundary value problems, analytical approaches for the FGMs are restricted to simple geometry and boundary conditions. Thus, analyses in FGM demand accurate and efficient numerical methods. The finite element method can be successfully applied to problems with an arbitrary variation of material properties by using special graded elements. In commercial computer codes, however, material properties are considered to be uniform on each element. The boundary element method (BEM) is a suitable numerical tool for this purpose, too. However, for a general continuously nonhomogeneous body the fundamental solution for many governing equations are not available. Recently, meshless methods are becoming popular, and they have been successfully applied to 2-D and 3-D axisymmetric transient heat conduction analyses for isotropic and anisotropic FGMs and in elasticity. During the last several decades, laminated composite plates have been widely used in engineering structures. All previous BEM applications are dealing with isotropic Reissner-Mindlin plates. In spite of the great success of the FEM and the BEM as accurate and effective numerical tools for the solution of boundary or initial-boundary value problems in domains with complex shapes, there is still a growing interest in developing new advanced numerical methods. Meshless approaches for problems of continuum mechanics have attracted much attention during the past decade especially owing to their high adaptivity and low costs to prepare input data for numerical analyses. Many meshless methods are derived from a weak-form formulation on global domain or a set of local subdomains. In the global formulation background cells are required for the integration of the weak-form. In methods based on local weak-form formulation no cells are required and therefore they are often referred to as truly meshless methods. Meshless approximation of the generalized displacements on a simple domain, based on the Moving Least-Squares (MLS) method, allows for elegant and efficient numerical integration of the domain-integral. Several quasi-static boundary value problems have to be solved for various values of the Laplace-transform parameter. The Stehfest's inversion method is applied to obtain the time-dependent solution. The novelty of the proposed project can be stated as:(1) The proposed meshless LIE will be developed for the first time in FGM plates and shells with anisotropic properties.(2) Non-stationary conditions are considered.(3) The method has no limitations on the geometry, material gradation, isotropic or anisotropic properties and loading conditions. (4) Coupling of thermo-mechanical fields can be considered too.