ORALS

ABSTRACT: In this study, a completely new numerical method, Finite Line Method (FLM), is proposed for solving general thermal and mechanical problems. In this method, the computational domain is discretized into a number of collocation nodes as in the free element method [1], and at each node a set of straight or curved lines crossing the node is formed, which is called the cross-line element [2] and represented by a few nodes distributed over each line. The shape functions for each cross-line element are constructed using the Lagrange interpolation formulation and their first and high order partial derivatives with respect to the global coordinates are derived through an ingenious technique. The derived spatial partial derivatives are directly substituted into the governing differential equations and related boundary conditions of thermal and mechanical problems to form the final system of equations. FLM is a type of collocation method, not needing any integration to establish the solution scheme. Therefore, it is very convenient to be used to solve multi-physics coupled problems. Besides, since the Lagrange interpolation formulation is used to construct the shape functions, high order lines can be easily formulated. A number of numerical examples for heat conduction, elasticity, and thermal stress analysis of composite structures will be given to demonstrate the efficiency and stability of the proposed method. KEY WORDS: Cross line method, Finite line method, Free element method, Thermal mechanical problem, Composite structure

References:
REFERENCES:
[1] X.W. Gao, L.F. Gao, Y. Zhang, M. Cui, J. Lv, J., Computers and Structures 215 (2019) 10–26.
[2] X.W. Gao, Y. Liang, B.B. Xu, Engineering Analysis with Boundary Elements 108 (2019) 422-437.