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Mechanics in Engineering ›› 2018, Vol. 40 ›› Issue (1): 61-66.doi: 10.6052/1000-0879-17-213

• Applied Research • Previous Articles     Next Articles

NODAL DISPLACEMENT ACCURACY OF ONE-DIMENSIONAL FINITE ELEMENTS

XING Yufeng, HUANG Zhiwei   

  1. Institute of Solid Mechanics, Beihang University, Beijing 100083, China
  • Received:2017-08-19 Revised:2017-06-15 Online:2018-02-15 Published:2018-03-26

Abstract: One-dimensional (1D) components as rod, shaft and beam are widely used in engineering structures. This paper investigates the nodal displacement accuracy of 1D high-order rod element and beam elements subjected to arbitrary polynomial distributed loads. First, the exact solutions are derived for the uniform fixed-free rod and the Euler beam as well as the Timoshenko beam,then the free-end nodal displacements are obtained by using a second-order rod element, a fifth-order Euler beam element and a third-order Timoshenko beam element, respectively. By comparing the FEM results with the exact solutions, it is shown that accurate nodal displacements can be obtained by using linear or high-order rod elements, and cubic or high-order Euler and Timoshenko beam elements. Moreover, by taking the second-order rod element as an example, the present results and conclusions are validated by using the static condensation method.

Key words: finite element method|one-dimensional element|nodal displacement|accuracy|static condensation

CLC Number: 

  • O34