Finite Element Analysis of 2-D Structures by New Strain Based Triangular Element

Abstract

In this investigation, a new simple triangular strain based membrane element with drilling rotation for 2-D structures analysis is proposed. This new numerical model can be used for linear and dynamic analysis. The triangular element is named SBTE and it has three nodes with three degrees of freedom at each node. The displacements field of this element is based on the assumed functions for the various strains satisfying the compatibility equations. This developed element passed both patch and benchmark tests in the case of bending and shear problems. For the dynamic analysis, lumped mass with implicit/explicit time integration are employed. The obtained numerical results using the developed element converge toward the analytical and numerical solutions in both analyses.

Free vibration analysis employing strain gradient notation four-node plane elements and considering the effects of parasitic shear

“…Further, other procedures are also employed for vibration analysis of plane structures such as the h-hierarchical adaptive scaled boundary finite element method (Yang, Zhang, Liu, & Ooi, 2011), finite element method based on the consecutive-interpolation procedure (CIP) (Bui, Nguyen, Zhang, Hirose, & Batra, 2016), generalized finite element method with trigonometric enrichment (Shang, Machado, & Abdalla Filho, 2019), time-discontinuous finite element method (TD-FEM) based on complex Fourier shape functions (Izadpanah, Shojaee, & Hamzehei-Javaran, 2018) and generalized / eXtended finite element method (Cittadin, Corrêa, Arndt, & Machado, 2022). Regarding the applications of in-plane vibrations, we find relevant studies on the seismic behavior of shear walls (El-Kashif, Adly, & Abdalla Filho, 2019;Sepehrnia, Rahami, Mirhosseini, & Zeighami, 2020) and the use of plane elements with drilling rotation in vibration analysis (Rebiai & Belounar, 2013;Rebiai, 2018;Fortas et al, 2019).…”

Techniques for element formulation and quadtree-based triangular mesh generation for strain-based finite elements

“…So far, strain-based finite elements have been developed to solve problems in solid mechanics. For example, strain-based elements have been used in the analysis of plates (subjected to static and free vibrations as well as bending) [2] , [3] , [4] , shell structures [5] , [6] , [7] , cylindrical panels [8] , circular structures [9] , and plane elasticity (static/linear and dynamic analyses including vibrations) [10] , [11] , [12] , [13] , [14] , [15] , [16] .…”

“…(2) and ( (3) and solved, zero values are not obtained, signifying that the equilibrium conditions are not met. Formulations that do not satisfy both conditions are prevalent in the literature [1] , [2] , [3] , [4] , [5] , [6] , [7] , [8] , [9] , [10] , [11] , [12] , [13] , [14] , [15] , [16] , 18] . Therefore, the application of these formulations is restricted [19] , [20] , [21] .…”