Meshfree local integration on line method (MLILM)‎ for linear elasticity

Abstract EN

The mesh free local integration on line method (MLILM) is presented for solving two-dimensional problems in linear elasticity.

For this purpose, local unsymmetrical weak forms (LUWF) are developed using weighted residual method locally from the equilibrium equations.

In this method, local domains are quadrangles and the test functions are pyramids centered on domain nodes.

Application of the LUWF based on these deliberately selected test functions results in eliminating the domain integrals for calculation of the system “stiffness” matrix.

A line-wise weighted least squares (LWLS) method is proposed to construct trial functions.

This method for construction of trial functions is found to be an accurate technique.

The formulation of the MLILM does not require calculating the derivatives of trial functions, leading to eliminating the process of differentiating the LWLS approximation for displacements.

Numerical studies show the MLILM leads to accurate results.