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

多组分复合材料板/壳结构的先进数值模拟--无网格技术方法

• 批准号: EP/E050573/1
• 负责人: Pihua Wen
• 金额: $ 6.24万
• 依托单位: Queen Mary University of London
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2007
• 资助国家: 英国
• 起止时间: 2007 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FE050573%2F1
• 关键词: Advanced; Numerical; Modeling; Plate; Shell

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.

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和机械性能。功能梯度材料具有连续梯度的结构和性能，与传统复合材料相比具有许多优点。由于初边值问题的数学复杂性，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精确有效的数值方法。通过使用特殊的梯度单元，有限元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，材料特性被认为在每个元素上是均匀的。边界元法（BEM）也是一种合适的数值工具。然而，对于一般的连续非均匀体，许多控制方程的基本解是不可得的。近年来，无网格方法逐渐成为一种流行的方法，并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处理各向同性Reissner-Mindlin板。尽管有限元法和边界元法作为求解复杂形状区域的边界或初边值问题的精确而有效的数值工具取得了巨大的成功，但人们对开发新的先进数值方法的兴趣仍在不断增长。连续介质力学问题的无网格方法在过去的十年中引起了人们的广泛关注，特别是由于其高适应性和低成本的准备输入数据的数值分析。许多无网格方法都是从整体域或局部子域上的弱形式公式推导出来的。在全局公式化中，需要背景单元用于弱形式的积分。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方法。基于移动最小二乘（MLS）方法的简单域上的广义位移的无网格近似，允许优雅和有效的数值积分的域积分。几个准静态边值问题必须解决的拉普拉斯变换参数的各种值。Stehfest的反演方法被施加到获得的时间依赖的解决方案。本课题的新奇在于：（1）首次在具有各向异性的功能梯度材料板壳中建立了无网格LIE。(2)考虑了非平稳条件。(3)该方法不受几何形状、材料级配、各向同性或各向异性性质以及荷载条件的限制。(4)也可以考虑热-机械场的耦合。