One of the tasks of the upper limit analysis of plate structures is to accurately evaluate the yield and failure mechanisms of materials, especially when the load and geometric conditions are complex. In this paper, the regional smooth radial point interpolation method (SRPIM) is used to improve the accuracy of the yield limit analysis. Using the regional smooth radial function, the displacement field of the plate is first constructed by point interpolation. Secondly, the limit analysis theory is proposed and combined with the optimization algorithm to solve the ultimate bearing capacity of the structure under different load conditions. Finally, numerical simulations are carried out to test the influence of different material parameters and geometric shapes on the ultimate bearing capacity. Using the SRPIM method, the simulated value of the ultimate bearing capacity is close to the actual value, with a difference of 101N under a load of 500N. SRPIM has been clearly verified to improve the prediction effect of the upper limit analysis of plate structures and has great application prospects in future applications.

Shucong Xiao. Regional Smooth Radial Point Interpolation Method for Upper Limit Analysis of Flat Plate Structures. International Journal of Frontiers in Engineering Technology (2025), Vol. 7, Issue 1: 42-48. https://doi.org/10.25236/IJFET.2025.070107.

[1] Dai Beibing, Yuan Xin, Zhou Xiwen, Liu Fengtao. Upper bound method of smooth finite element limit analysis considering discontinuous velocity field[J]. Rock and Soil Mechanics, 2024, 45(9): 2849-2858.

[2] Chen Xinxin, Wang Wei. Upper limit analysis of axisymmetric structures based on natural element method[J]. Chinese Journal of Computational Mechanics, 2020, 37(2): 159-164.

[3] Rao Pingping, Ni Xue, Shi Yunwei. Analysis of upper limit of slope stability under slope top overload[J]. Low Temperature Building Technology, 2020, 42(2): 84-87+121.

[4] Zhang Yongfa, Zhou Rongming, Xu Guozheng, Hu Jibo, Li Xiang. Analysis of upper limit of soil slope stability under earthquake action[J]. Building Structure, 2022, 52(S02): 2602-2608.

[5] Wu Zhaowen. Analysis on the upper limit of soil pressure between anti-slide piles[J]. Municipal Engineering, 2020, 38(2): 257-260+282.

[6] Kumar J, Rahaman O. Lower bound limit analysis using power cone programming for solving stability problems in rock mechanics for generalized Hoek–Brown criterion[J]. Rock Mechanics and Rock Engineering, 2020, 53(7): 3237-3252. 

[7] Keawsawasvong S, Shiau J, Yoonirundorn K. Bearing capacity of cylindrical caissons in cohesive-frictional soils using axisymmetric finite element limit analysis[J]. Geotechnical and Geological Engineering, 2022, 40(7): 3929-3941.

[8] Zhang R, Xiao Y. A nonlinear programming algorithm for finite element limit analysis using feasible arc searching technique[J]. International Journal for Numerical Methods in Engineering, 2023, 124(22): 5102-5119.

[9] Mortara G. Limit analysis solutions for the bearing capacity of strip foundations under seismic conditions[J]. Géotechnique, 2023, 73(4): 337-352.

[10] Sun B, Zhang P, Wu R, et al. Improvement of upper limit of mining under an aquifer of a super thick unconsolidated layer in Huainan based on multi-physics field monitoring[J]. Exploration Geophysics, 2021, 52(2): 150-169.

[11] Yan-peng Z H U, Xi-nan H O U, Xiang-xiang M A, et al. Limit analysis of slope stability supported by framed prestressed anchor rods[J]. Chinese Journal of Geotechnical Engineering, 2021, 43(S1): 7-12.

[12] Mertens F G, Mevius M, Koopmans L V E, et al. Improved upper limits on the 21 cm signal power spectrum of neutral hydrogen at z≈ 9.1 from LOFAR[J]. Monthly Notices of the Royal Astronomical Society, 2020, 493(2): 1662-1685.

[13] Andrade K E, Fuson J, Gad-Nasr S, et al. A stringent upper limit on dark matter self-interaction cross-section from cluster strong lensing[J]. Monthly Notices of the Royal Astronomical Society, 2022, 510(1): 54-81.

[14] Keller P M, Nikolic B, Thyagarajan N, et al. Search for the Epoch of Reionization with HERA: upper limits on the closure phase delay power spectrum[J]. Monthly Notices of the Royal Astronomical Society, 2023, 524(1): 583-598. 

[15] Farajidizaji B, Borrego E I, Athukorale S, et al. Triphenylene-Enchained Perfluorocyclobutyl Aryl Ether Polymers: A Modular Synthetic Route to Processable Thermoplastics Approaching Upper Limit T g and Photostability[J]. Macromolecules, 2021, 54(16): 7666-7672.