TY - JOUR
T1 - Numerical computation of effective stiffness for spatially graded beam-like structures based on asymptotic homogenization
AU - Xu, Liang
AU - Zhang, Yuchi
AU - Zhang, Degang
AU - Liu, Dianzi
AU - Qian, Zhenghua
N1 - Funding information: This work is supported by National Natural Science Foundation of China (No. 12002159), Natural Science Foundation of Jiangsu Province (No. BK20200411), the State Key Laboratory of Structural Analysis for Industrial Equipment (No. GZ20101), and a Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD).
PY - 2024/7
Y1 - 2024/7
N2 - This work investigates asymptotic homogenization method (AHM) for axially graded beams that are mapped from periodic ones. The unit cell problems, the homogenized constitutive and governing equations are first established theoretically. Then a novel FE formulation of unit cell problems and effective stiffness, distinct from that of the periodic beams, is derived and resolved for solid elements. Besides, to improve analysis efficiency, an updated concise formulation is acquired for shell elements with proper handle of in-plane rotational DOFs, and a MATLAB code is presented to show implementation details. At last, four numerical examples show the correctness of the proposed method.
AB - This work investigates asymptotic homogenization method (AHM) for axially graded beams that are mapped from periodic ones. The unit cell problems, the homogenized constitutive and governing equations are first established theoretically. Then a novel FE formulation of unit cell problems and effective stiffness, distinct from that of the periodic beams, is derived and resolved for solid elements. Besides, to improve analysis efficiency, an updated concise formulation is acquired for shell elements with proper handle of in-plane rotational DOFs, and a MATLAB code is presented to show implementation details. At last, four numerical examples show the correctness of the proposed method.
U2 - 10.1080/15376494.2023.2190738
DO - 10.1080/15376494.2023.2190738
M3 - Article
VL - 31
SP - 4051
EP - 4068
JO - Mechanics of Advanced Materials and Structures
JF - Mechanics of Advanced Materials and Structures
SN - 1537-6494
IS - 17
ER -