Development and Implementation of New Triangular Finite Element in ABAQUS for Linear, Nonlinear and Free Vibration Problems

Abstract

Purpose – A new triangular membrane finite element based on the strain approach is developed for the linear, nonlinear and free vibration analysis.

Design/methodology/approach – The current element has two degrees of freedom at each of the three corner nodes and the internal node (two translations) and satisfies the exact representation of the rigid body modes of displacements. 

Findings - The displacements field of the element has been developed by the use of the strain-based approach and it based on the assumed independent functions for the various components of strain satisfying the compatibility equations.

Originality/Value – The developed element is implemented in the ABAQUS code using the UEL subroutine (User Element subroutine of ABAQUS). For elastoplastic analysis, Von Mises and Mohr–Coulomb yield criteria are adopted. Several numerical tests were performed, including linear, nonlinear and free vibration problems. The results obtained were compared to the available analytical and numerical solutions. It turned out that the use of this element allows acquiring effective convergence and accurate results.