MLS based local approximation in numerical manifold method

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.

Citation

Chen, Y., Zheng, H., Li, W. and Lin, S. (2018), "MLS based local approximation in numerical manifold method", Engineering Computations, Vol. 35 No. 7, pp. 2429-2458. https://doi.org/10.1108/EC-12-2017-0485