Error estimates in 2‐node shear‐flexible beam elements

Abstract

SUMMARYThe objective of the paper is to report the investigation of error estimates=or convergence characteristics of shear-exible beam elements. The order and magnitude of principal discretization error in the usage of various types beam elements such as: (a) 2-node standard isoparametric element, (b) 2-node ÿeld-consistent/reduced integration element and (c) 2-node coupled-displacement ÿeld element, is assessed herein. The method employs classical order of error analyses that is commonly used to evaluate the discretization error of ÿnite di erence methods. The ÿnite element equilibrium equations at any node are expressed in terms of di erential equations through the use of Taylor series. These di erential equations are compared with the governing equations and error terms are identiÿed. It is shown that the discretization error in coupled-ÿeld elements is the least compared to the ÿeld-consistent and standard ÿnite elements (based on exact integration).