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Appl. Sci. 2018, 8(6), 975; https://doi.org/10.3390/app8060975

A Simple High-Order Shear Deformation Triangular Plate Element with Incompatible Polynomial Approximation

College of Civil Engineering, Tongji University, Shanghai 200092, China
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Received: 11 May 2018 / Revised: 9 June 2018 / Accepted: 12 June 2018 / Published: 14 June 2018
(This article belongs to the Special Issue Computational Methods for Fracture)

Abstract

The High-order Shear Deformation Theories (HSDTs) which can avoid the use of a shear correction factor and better predict the shear behavior of plates have gained extensive recognition and made quite great progress in recent years, but the general requirement of C1 continuity in approximation fields in HSDTs brings difficulties for the numerical implementation of the standard finite element method which is similar to that of the classic Kirchhoff-Love plate theory. As a strong complement to HSDTs, in this work, a series of simple High-order Shear Deformation Triangular Plate Elements (HSDTPEs) using incompatible polynomial approximation are developed for the analysis of isotropic thick-thin plates, cracked plates, and through-thickness functionally graded plates. The elements employ incompatible polynomials to define the element approximation functions u/v/w, and a fictitious thin layer to enforce the displacement continuity among the adjacent plate elements. The HSDTPEs are free from shear-locking, avoid the use of a shear correction factor, and provide stable solutions for thick and thin plates. A variety of numerical examples are solved to demonstrate the convergence, accuracy, and robustness of the present HSDTPEs. View Full-Text
Keywords: plate; FSDT; HSDT; Mindlin; incompatible approximation; fracture plate; FSDT; HSDT; Mindlin; incompatible approximation; fracture
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Gou, Y.; Cai, Y.; Zhu, H. A Simple High-Order Shear Deformation Triangular Plate Element with Incompatible Polynomial Approximation. Appl. Sci. 2018, 8, 975.

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