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An alternative method for computing the splitting factor of noncompatible generalized mixed elements with distortion

Zhenyu Wang, Guanghui Qing and Jintao Zhou

Vol. 20 (2025), No. 2, 173–191
Abstract

A novel method for computing the splitting factor of the four-node noncompatible generalized mixed element in 2D linear elastic problems is proposed, based on the fact that the distorted elements alter the stiffness and compliance of generalized mixed models. Specifically, a quantity describing the distortion degree of the distorted element is defined by the sum of the deviations of the stiffness and compliance matrices between the distorted element and the rectangular or square element. Based on the distortion degree of distorted elements, a formulation for computing the splitting factor was constructed. Several representative examples with varying geometrical parameters, boundary and loading conditions are used to validate the effectiveness of proposed method. In comparison with the method using the splitting factor of 0.75 for all elements, the proposed method has the numerical results of higher accuracy and excellent convergence.

Keywords
noncompatible generalized mixed element, splitting factor, distorted mesh, distorted element, stiffness matrix, compliance matrix
Milestones
Received: 23 October 2024
Revised: 24 March 2025
Accepted: 6 April 2025
Published: 5 August 2025
Authors
Zhenyu Wang
School of Aeronautical Engineering
Civil Aviation University of China
Tianjin, 300300
China
Guanghui Qing
School of Aeronautical Engineering
Civil Aviation University of China
Tianjin, 300300
China
Jintao Zhou
School of Aeronautical Engineering
Civil Aviation University of China
Tianjin, 300300
China