Automatic FEM Procedure Using on Object-Oriented Adaptive h Method for Solid Structures

针对三维曲面实体结构，研究了一种基于面向对象h型的自动有限元程序。给出了一种建立结构几何形状的简单方法。物理数据(如材料、载荷和边界条件)直接在几何图形上给出。描述了一种简单有效的六面体实体单元生成方法，该方法结合四面体和五面体单元，特别是在网格密度的瞬变区。在建立实体结构的几何模型并在几何上确定分析所需的物理数据后，只需给出要生成的单元总数即可进行结构分析，并给出了一种使用主应变方差的简单误差度量。通过给出有限元误差容许率，对网格进行自适应加密，并自动进行详细的结构分析，开发了基于面向对象的自适应h版本的自动有限元系统。数值算例表明了该方法的正确性和有效性。

An automatic FEM procedure based on an object-oriented h version has been studied for three dimensional solid structures with curved surfaces. A simple method to create the geometry of the structures is given. Physical data such as materials, loads, and boundary conditions are given directly on the geometry. A simple and efficient method to generate hexahedron solid elements accompanied with tetrahedron and pentahedron elements particularly in the transient region of the mesh density is described. After the geometry of a solid structure is created and physical data required for the analysis are befined on the geometry, the structural analysis is made simply by giving the total number of elements to generate.A simple error measure using the variance of principal strains is also given. Simply by giving an allowable ratio of finite element error, an adaptive mesh refinement is made and the detailed structural analysis is conducted automatically.An automatic finite element system has been developed based on the object-oriented adaptive h version. Numerical examples are given to show the validity and the effectiveness of the present method.