Indexed by:Journal Papers

Date of Publication:2019-11-01

Journal:INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES

Included Journals:EI、SCIE

Volume:163

ISSN No.:0020-7403

Key Words:The Saint-Venant solution; Periodic heterogeneous beam structures; Finite element implementation

Abstract:This paper presents displacement solutions of the Saint-Venant problem for linear elastic heterogeneous beam structures with arbitrarily shaped periodic microstructures. The solutions are generated by introducing unknown axially periodic displacement functions in place of the axially invariant warping functions in Iesan's rational scheme, due to the periodic characteristics of the beam structure, while retaining the displacement fields integrated from rigid-body displacements, which represent basic kinematics in beam theories. The governing equations of the unknown functions, defined on a base cell, are then developed from equilibrium equations and boundary conditions of the periodic beam structure. Moreover, an improved FE formulation of the governing equations is presented and its efficient numerical implementation approach, which can be readily realized using FE software as a black box, is proposed with the aid of NIAH (Novel Numerical Implementation of Asymptotic homogenization) approach. To illustrate the validity of the Saint-Venant solution and the effectiveness of the numerical implementation approach, several numerical examples are presented and compared with detailed three-dimensional FE analysis for the heterogeneous beam structures in terms of stress components.