MLS based local approximation in numerical manifold method. Issue 7 (1st October 2018)

• Record Type: Journal Article
• Authors: Chen, Yuanqiang; Zheng, H.; Li, Wei; Lin, Shan
• Is Part Of: Engineering computations. Volume 35:Issue 7(2018)
• Page Start: 2429
• Page End: 2458
• Publication Date: 2018-10-01
• Subjects: Continuous nodal stress -- Linear dependence problem -- Moving least square interpolation -- Numerical manifold method -- Trig3-MLScns; Computer-aided engineering -- Periodicals; Computer graphics -- Periodicals; 620.00285
• DOI: 10.1108/EC-12-2017-0485
• Languages: English
• ISSNs: 0264-4401

Abstract

Abstract : Purpose: The purpose of this paper is to propose a new three-node triangular element in the framework of the numerical manifold method (NMM), which is designated by Trig3-MLScns. Design/methodology/approach: The formulation uses the improved parametric shape functions of classical triangular elements (Trig3-0) to construct the partition of unity (PU) and the moving least square (MLS) interpolation method to construct the local approximation function. Findings: Compared with the classical three-node element (Trig3-0), the Trig3-MLScns element has a higher order of approximations, much better accuracy and continuous nodal stress. Moreover, the linear dependence problem associated with many PU-based methods with high-order approximations is eliminated in the present element. A number of numerical examples indicate the high accuracy and robustness of the Trig3-MLScns element. Originality/value: The proposed element inherits the individual merits of the NMM and the MLS.