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Shobeyri, Gholamreza. (1406). Comparison of Numerical Performance of a Modified MPS Method with a Least Squares Method Based on a Mixed Formulation for Elasticity Problems. پژوهشنامه مدیریت اجرایی, 3(2), 26-36. doi: 10.22080/ceas.2026.31619.1095
Gholamreza Shobeyri. "Comparison of Numerical Performance of a Modified MPS Method with a Least Squares Method Based on a Mixed Formulation for Elasticity Problems". پژوهشنامه مدیریت اجرایی, 3, 2, 1406, 26-36. doi: 10.22080/ceas.2026.31619.1095
Shobeyri, Gholamreza. (1406). 'Comparison of Numerical Performance of a Modified MPS Method with a Least Squares Method Based on a Mixed Formulation for Elasticity Problems', پژوهشنامه مدیریت اجرایی, 3(2), pp. 26-36. doi: 10.22080/ceas.2026.31619.1095
Shobeyri, Gholamreza. Comparison of Numerical Performance of a Modified MPS Method with a Least Squares Method Based on a Mixed Formulation for Elasticity Problems. پژوهشنامه مدیریت اجرایی, 1406; 3(2): 26-36. doi: 10.22080/ceas.2026.31619.1095

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

Civil Engineering and Applied Solutions
دوره 3، شماره 2، تیر 2027، صفحه 26-36    اصل مقاله (1.02 M)
نوع مقاله: Original Article
شناسه دیجیتال (DOI): 10.22080/ceas.2026.31619.1095
نویسنده
Gholamreza Shobeyri*
Faculty of Civil, Water & Environmental Engineering, Shahid Beheshti University, Tehran, Iran
تاریخ دریافت: 08 اردیبهشت 1405،  تاریخ بازنگری: 09 خرداد 1405،  تاریخ پذیرش: 26 خرداد 1405 
چکیده
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 (2023), 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.
کلیدواژه‌ها
Meshless methods؛ Improved MPS gradient model؛ Mixed formulation؛ Least squares method؛ Elasticity problems
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