Because solid models are easier to handle than surface models when using CAD systems, they are generally utilized for modeling thin objects such as automobile bodies, plastic injection mold components, and sheet metal parts. Shell finite elements are preferred to 3D solid finite elements for computational efficiency and accuracy in the analysis of thin structures. Given tetrahedral and hexahedral elements, hexahedral elements are generally preferred in the finite element analysis. However, hexahedral mesh generation is usually more difficult than a tetrahedral mesh generation. In order to model with plate or shell finite elements for thin objects, it is necessary to determine the medial surfaces from thin solid objects. Hexahedral elements can be created by offsetting shell elements or by sweeping the divided simple areas, if necessary.
This paper describes quadrilateral and hexahedral mesh generation for various shell structures. After generating one-layered tetrahedral mesh by an advancing front algorithm, the chordal surfaces are constructed by cutting of tetrahedral elements. The surfaces are classified into top, bottom and lateral by using the dihedral angles of the initial triangular elements. Tetrahedral elements are generated by using this information of the surfaces. In order for the cutting planes of the tetrahedral elements to become the medial surfaces of a given 3D object, minimum number of new nodes should be created inside the 3D object. In addition, four nodes of a tetrahedral element should not belong to the same surface to avoid the abnormal case. The cutting direction of a tetrahedron determines the shape of the sliced section, which is either triangular or quadrilateral. In order to determine the cutting directions, tetrahedral elements are classified into the basic, modified and inner nodes types proposed in this study. The numbers of faces and external edges of a tetrahedral element belonging to the top, bottom or lateral surfaces are used as the criteria for classification.
Since the choral surfaces are composed of tri/quad elements with poor quality, they are transformed into quadrilateral elements with good quality. A new quadrilateral mesh generation technique from an existing triangle mesh is proposed in this paper. The proposed method is based on the advancing front method and the zero thickness layer. Beginning with an initial triangular mesh, the boundary triangular elements are removed and quadrilateral elements with zero thickness are generated. The quality of the quadrilateral elements is improved during the mesh smoothing process. This procedure is repeated until all initial triangular elements are removed.
Hexahedral elements are then generated by offsetting these quadrilateral elements. The boundary nodes of hexahedral elements are generated on the outer surfaces of the original shell structures. Sample meshes were constructed to demonstrate the mesh generation capability of the proposed algorithm.
일반적으로 CAD 시스템에서 솔리드 모델링이 쉘 모델링보다 편리하여 자동차 바디, 사출성형 및 판금 제품 등과 같이 두께가 얇은 제품이더라도 솔리드로 모델링하게된다. 사각형 및 육면체 요소는 이러한 형상에 사면체 요소보다 더 정확한 해석 결과를 얻을 수 있다. 본 논문에서는 얇은 두께의 형상에 해당하는 삼각형 요소를 입력받아 사각형 및 육면체 요소를 생성시키는 방법을 제시하였다. 우선 입력받은 삼각형 요소를 이용해서 중립면 생성이 적합한 사면체 요소를 생성한 후, 이를 이용해서 중립면에 해당하는 삼각형, 사각형 요소를 추출한다. 사면체 요소는 내부에 가급적 절점이 존재하지 않아야 하고, 중립면 생성에 적합한 요소를 생성하기 위해서 초기에 입력받은 삼각형 요소를 상, 하위, 측면 곡면으로 분류한 정보를 이용하였다. 중립면 생성은 기존의 방법을 보완하고, 다양한 형상에 대해서 생성가능하도록 본 논문에서는 수정타입과 내부절점타입을 추가시켰다. 중립면에 생성된 요소의 품질은 매우떨어져 유한 요소 해석에 이용할 수 없다. 따라서 본 논문에서는 무두께 요소층과 전진경계 기법을 이용해서 이를 우수한 품질의 사각형 요소를 생성시키는 방법을 제시하였다. 육면체 요소는 중립면에 생성된 사각형 요소를 옵셋시켜 생성되며, 두께가 균일하지 않은 형상에도 적용가능하도록 하였다. 다양한 예제를 통하여 본 논문에서 제시한 방법을 검증하였다.
