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

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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.