Refined Meshless Local Strong Form solution of Cauchy-Navier equation on an irregular domain
For researchers in computational mechanics, this provides a flexible meshless approach for linear elasticity on irregular domains, though it is an incremental application of existing methods.
The paper solves the Cauchy-Navier equation on irregular domains using a meshless local strong form method with weighted least squares approximation, demonstrating flexibility in nodal positioning and achieving accurate results with simple refinement algorithms.
This paper considers a numerical solution of a linear elasticity problem, namely the Cauchy-Navier equation, using a strong form method based on a local Weighted Least Squares (WLS) approximation. The main advantage of the employed numerical approach, also referred to as a Meshless Local Strong Form method, is its generality in terms of approximation setup and positions of computational nodes. In this paper, flexibility regarding the nodal position is demonstrated through two numerical examples, i.e. a drilled cantilever beam, where an irregular domain is treated with a relatively simple nodal positioning algorithm, and a Hertzian contact problem, where again, a relatively simple h-refinement algorithm is used to extensively refine discretization under the contact area. The results are presented in terms of accuracy and convergence rates, using different approximations and refinement setups, namely Gaussian and monomial based approximations, and a comparison of execution time for each block of the solution procedure.