@Article{icces.2023.09510,
AUTHOR = {Xiaowei Gao, Huayu Liu, Weilong Fan},
TITLE = {Zonal Finite Line Method and Its Applications in Thermal-Mechanical  Analysis of Composite Structures},
JOURNAL = {The International Conference on Computational \& Experimental Engineering and Sciences},
VOLUME = {27},
YEAR = {2023},
NUMBER = {1},
PAGES = {1--1},
URL = {http://www.techscience.com/icces/v27n1/54103},
ISSN = {1933-2815},
ABSTRACT = {In this paper, a novel numerical method, Zonal Free Element Method (ZFLM), is proposed and used to solve 
thermal-mechanical problems composed of multiple and functionally graded materials. ZFLM is a 
collocation method, in which two or three lines in 2D or 3D problems, called as line-set, are used at each 
node to establish the solution scheme solving engineering problems governed by partial differential 
equations. In ZFLM, the Lagrange polynomial is adopted to approximate physical variables varying over each 
line of the line-set. The first-order partial derivative is derived by using a directional derivative technique 
along arclength of a line, and a recursive procedure is used to evaluate the second and higher order partial 
derivatives. The derived various order derivatives can be directly substituted into the governing equations 
and relevant boundary conditions to form the discretized system of equations. To solve the problem 
involving composite structures, a zonal technique is proposed, in which the computational domain is divided 
into several structured zones according to material types and geometric characteristics. For nodes shared 
by two or more zones, the traction/flux equilibrium equations are used to constrain their variation across 
the zonal interfaces. For irregular geometries and nodes with jumping loads, multiple line-sets are used at 
the same node to improve the accuracy and stability. The proposed method is used to solve some challenging 
thermal and mechanical problems of 2D and 3D composite structures to demonstrate the robustness of the 
proposed method.},
DOI = {10.32604/icces.2023.09510}
}