Manifold Finite Element Method And its Application for Naval Structural Analysis.

有限覆盖法和流形法的特点是定义独立于物理场的近似数学场，其中要求满足偏微分方程。在数学领域中，通过一些分布覆盖构造了近似。由于数学场的定义与物理场的几何形状无关，任何复杂的结构都可以简单地用规则形状的数学覆盖。利用体素数据进行覆盖分布，采用方形或立方覆盖，从而继承体素分析的优点，提高实体结构分析的效率。讨论了有限覆盖法的线性无关性问题，给出了线性无关性的一些数学条件。针对三维实体分析中刚度矩阵的积分和边界条件的评估，提出了“形状体素”技术。数值算例表明，由于使用体素信息生成模型非常简单，因此整体分析更加有效。然后将有限覆盖法应用于大变形问题，由于覆盖分布简单，重网格负担明显减少。采用有限覆盖法开发了一个结构分析系统，该系统可以在输入CAD数据后自动处理。该方法克服了复杂三维实体分析中模型生成的困难。

The characteristic idea of the Finite Cover Method and Manifold Method is to define the mathematical field for approximation independent from the physical field, where the partial differential equation is required to be satisfied. The approximation is constructed ton the mathematical field by some distributed covers. Since the mathematical field is defined irrelevant with the geometrical shape of the physical field, any complex structure can be covered simply by mathematical covers with regular shapes. The voxel data is employed for cover distribution by using square or cubic covers so that the merit of voxel analysis can be inherited to improve the efficiency of solid structural analysis. The problem of linear independence is discussed for Finite Cover Method and some mathematical conditions for linear independence are proposed. The technique of "Shape Voxel" is proposed for integration of stiffness matrix and evaluation of boundary conditions in 3D solid analysis. Numeric examples show that since the model generation using voxel information is very simple, the total analysis becomes more effective. The Finite Cover Method is then applied for large deformation problem, and the re-mesh burden is reduced obviously due to the simple cover distribution. A structural analysis system is developed with the Finite Cover Method, which can process automatically after inputting CAD data. The proposed method can surmount difficulties of model generation in complex 3D solid analysis.