A new type of high-order elements based on the mesh-free interpolations

Hu, Dean, Wang, Yigang, Zhan, Haifei, & Long, Shuyao (2016) A new type of high-order elements based on the mesh-free interpolations. Engineering Analysis with Boundary Elements, 65, pp. 63-71.

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We propose a new type of high-order elements that incorporates the mesh-free Galerkin formulations into the framework of finite element method. Traditional polynomial interpolation is replaced by mesh-free interpolations in the present high-order elements, and the strain smoothing technique is used for integration of the governing equations based on smoothing cells. The properties of high-order elements, which are influenced by the basis function of mesh-free interpolations and boundary nodes, are discussed through numerical examples. It can be found that the basis function has significant influence on the computational accuracy and upper-lower bounds of energy norm, when the strain smoothing technique retains the softening phenomenon. This new type of high-order elements shows good performance when quadratic basis functions are used in the mesh-free interpolations and present elements prove advantageous in adaptive mesh and nodes refinement schemes. Furthermore, it shows less sensitive to the quality of element because it uses the mesh-free interpolations and obeys the Weakened Weak (W2) formulation as introduced in [3, 5].

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ID Code: 93064
Item Type: Journal Article
Refereed: Yes
Keywords: finite element method, meshfree Galerkin formulation, high-order element, strain smoothing technique, upper-lower bounds
DOI: 10.1016/j.enganabound.2016.01.001
ISSN: 0955-7997
Subjects: Australian and New Zealand Standard Research Classification > ENGINEERING (090000) > MECHANICAL ENGINEERING (091300)
Divisions: Current > Schools > School of Chemistry, Physics & Mechanical Engineering
Current > QUT Faculties and Divisions > Science & Engineering Faculty
Copyright Owner: Copyright 2016 Elsevier
Copyright Statement: Licensed under the Creative Commons Attribution; Non-Commercial; No-Derivatives 4.0 International. DOI: 10.1016/j.enganabound.2016.01.001
Deposited On: 19 Feb 2016 01:49
Last Modified: 25 Feb 2016 10:29

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