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论文类型：期刊论文

发表时间：2018-01-01

发表刊物：NUMERICAL HEAT TRANSFER PART B-FUNDAMENTALS

收录刊物：SCIE

卷号：73

期号：4

页面范围：206-224

ISSN号：1040-7790

摘要：In this article, two types of new quadrilateral and hexahedron quadratic isoparametric elements are proposed for the element differential method (EDM) for solving heat conduction problems. These elements, called as the Ultra elements, have the minimum numbers of nodes comparing with the existing elements and have the feature that a central node is included inside them, which is necessary for the EDM analysis. The EDM is a strong-form method, which does not require control volumes and any integration. In the previous EDM for solving heat conduction problems, the Lagrange elements were used, which had many elemental nodes. The proposed new types of elements can circumvent this deficiency, in which only a few nodes are required. The shape functions for these elements are constructed for the first time, and the first and the second order derivatives of the shape functions with respect to intrinsic and global coordinates are analytically derived. Several 2D and 3D numerical examples are given to demonstrate the effectiveness, the accuracy and the efficiency of the newly proposed elements for the EDM for solving heat conduction problems.