Development Of New Generalized Finite Element Based On Framework

Finite element method is one of the most important methods in Computational Mechanics. Since the period of "The Twelfth Five Year Plan", China Academy of Engineering Physics has been implementing project High Performance Technology and Engineering Computing Strategy. It reconstructs and develops major equipment engineering mechanics h type finite element parallel analysis software platform PAND, basing on unstructured meshes framework JAUMIN (J Adaptive Unstructured Meshes applications Infrastructure). This article is supported by project High Performance Technology and Engineering Computing Strategy and it focus on PANDA’s demand for advanced computing functions. Thus this article will study on a new finite element development model based on framework. On the one hand it will develop and improve the Generalized Finite Element (GFE) to expand calculation function for PANDA platform, on the other hand it’s also a previous technology exploration about advanced computing function based on the shape function improved class for PANDA platform. The major progress has been made in the research work of this paper are as follows:a) Reconstructing and expanding element relating class to develop Generalized Finite Element on PANDA platform. This was based on Generalized Finite Element theory and framework finite element developing method. Numerical examples verified and tested the correctness and accuracy of Generalized Finite Element. It expanded PANDA’s analysis function and verified the feasibility of expanding advanced computing function based on the shape function improved class for PANDA platform.b) Developing New Generalized Finite Element (NGFE) for plane stress and plane strain problem. Combining with Generalized Finite Element and Rational Finite Element, new shape function was constructed fully considering the Poisson’s effect of elastic body, and the additional terms are constructed according to the control equations of elastic mechanics. Then element area coefficient was introduced to develop the plane New Generalized Isoparametric element. With the technique of developing finite element on framework, this work developed two kinds of new elements on PANDA platform. Numerical tests indicated that, both plane stress/strain New Generalized Finite Element can obtain more accuracy than traditional finite element and Generalized Finite Element in regular and irregular grid.c) Developing three-dimensional New Generalized Finite Element. The interpolation functions were assumed on fine calculation, and the coefficients in interpolation functions were determined by node displacement constraint. Then element volume coefficient was introduced to develop the three-dimensional New Generalized Isoparametric element. With the technique of developing finite element on framework, this work developed 3D NGFE on PANDA platform. Numerical tests indicated that 3D NGFE can obtain more accuracy.The research work of this thesis has certain academic significance in the development of finite element theory. At the same time this work has established a technical foundation of expanding high-precision p type and h-p type finite element, Extended Finite Element, Multi scale Finite Element and so on which are based on shape function improved class for the domestic independent intellectual property rights of software platform PANDA.