Comparison of Numerical Performance of a Modified MPS Method with a Least Squares Method Based on a Mixed Formulation for Elasticity Problems

High-precision stress analysis of structures under external loading represents a challenge in civil engineering. Although meshless numerical methods show great potential for solving such problems, their early versions often failed to provide acceptable accuracy. A conventional approach to addressing this is the use of a mixed formulation, which transforms second-order governing differential equations into a system of first-order equations. In this approach, both displacements and structural stresses are treated as unknowns. In contrast, in the original second-order formulation, only displacements are unknowns, and stresses are typically derived indirectly from displacement fields, often resulting in low accuracy. This research compares the numerical performance of an improved MPS gradient model by Shobeyri (۲۰۲۳), a well-known meshless method, for stress calculation via second-order equations with a mixed formulation coupled with a least-squares method. The comparison is conducted on two benchmark elasticity problems. The numerical findings reveal that the improved MPS method provides superior stress accuracy. These results suggest that solving the original second-order differential equations, followed by high-precision stress computation, offers a more effective alternative to the mixed formulation approach.

کلیدواژه ها:

Meshless methods ، Improved MPS gradient model ، Mixed formulation ، Least squares method ، Elasticity problems