Assumed stress quasi-conforming formulation for static and free vibration analysis of symmetric laminated plates

• Published in: Engineering computations 2020-05, Vol.37 (6), p.2051-2083
• Main Authors: Wang, Changsheng, Han, Xiao, Yang, Caixia, Zhang, Xiangkui, Hou, Wenbin
• Format: Article
• Language: English
• Subjects: Accuracy; Approximation; Composite beams; Deformation; Equilibrium; Equilibrium equations; Exact solutions; Finite element analysis; Free vibration; Initial stresses; Laminar composites; Laminates; Locking; Parameters; Performance enhancement; Plates; Strain; Strings; Vibration analysis
• ISSN: 0264-4401; 1758-7077
• DOI: 10.1108/EC-04-2019-0179

Purpose Numerous finite elements are proposed based on analytical solutions. However, it is difficult to find the solutions for complicated governing equations. This paper aims to present a novel formulation in the framework of assumed stress quasi-conforming method for the static and free vibration analysis of anisotropic and symmetric laminated plates. Design/methodology/approach Firstly, an initial stress approximation ruled by 17 parameters, which satisfies the equilibrium equations is derived to improve the performance of the constructed element. Then the stress matrix is treated as the weighted function to weaken the strain-displacement equations. Finally, the Timoshenko’s laminated composite beam functions are adopted as boundary string-net functions for strain integration. Findings Several numerical examples are presented to show the performance of the new element, and the results obtained are compared with other available ones. Numerical results have proved that the new element is free from shear locking and possesses high accuracy for the analysis of anisotropic and symmetric laminated plates. Originality/value This paper proposes a new QC element for the static and free vibration analysis of anisotropic and symmetric laminated plates. In contrast with the complicated analytical solutions of the equilibrium equations, an initial stress approximation ruled by 17 parameters is adopted here. The Timoshenkos laminated composite beam functions are introduced as boundary string-net functions for strain integration. Numerical results demonstrate the new element is free from shear locking and possesses high accuracy for the analysis of anisotropic and symmetric laminated plates.