The Mindlin plate theory, which accounts for shear deformation effects, is employed to ensure accurate modeling of moderately thick plates. This paper investigates the efficiency of various dynamic relaxation methods for the elastic analysis of Mindlin plates. The main objective is to evaluate the advantages of twelve different relaxation schemes. The distinctions among these approaches lie in the determination of artificial parameters such as damping and mass, which are essential for the convergence of dynamic relaxation. The study focuses on assessing these methods based on numerical stability, convergence rate, and computational efficiency. Several Mindlin plate examples with diverse geometries and boundary conditions are solved to compare the performance of different dynamic relaxation techniques. Given the variety of the analyzed cases, the obtained results can serve as benchmark problems for Mindlin plate analysis. Key criteria, including the number of iterations required for convergence and the total computational time, are recorded for each method. The results reveal significant variations in efficiency among the twelve algorithms, with some exhibiting rapid convergence while others require considerably more iterations. A comprehensive ranking based on these computational metrics is established to identify the most efficient and robust techniques for practical applications. Furthermore, the study demonstrates the sensitivity of dynamic relaxation convergence to the selection of artificial parameters. Numerical results indicate that the Underwood method is efficient in terms of analysis time, while the minimum residual energy scheme achieves the fewest iterations for Mindlin plate analysis.
Several benchmark cases of Mindlin plates with diverse geometries and boundary conditions are solved to compare the performance of the proposed DR schemes. Given the variety of solved examples, the results can serve as benchmark problems for Mindlin plate analyses. Key metrics, including the number of iterations required for convergence and total computational time, are recorded for each method. The results reveal significant variations in efficiency among the twelve algorithms: some exhibit rapid convergence, while others demand substantially more iterations. A comprehensive ranking system is established based on these computational criteria, identifying the most efficient and robust techniques for practical applications.
Furthermore, this study highlights the sensitivity of dynamic relaxation convergence to the selection of fictitious parameters. Numerical results demonstrate the effectiveness of the Underwood method in computational time and the minimum residual energy technique in iteration count for analyzing Mindlin plates.
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Estiri,H and Adineh,M . (2026). Analysis of Mindlin Plates by Dynamic Relaxation Method. Science and Technology in Mechanical Engineering, 4(2), 153-174. doi: 10.22034/stme.2025.531701.1137
MLA
Estiri,H , and Adineh,M . "Analysis of Mindlin Plates by Dynamic Relaxation Method", Science and Technology in Mechanical Engineering, 4, 2, 2026, 153-174. doi: 10.22034/stme.2025.531701.1137
HARVARD
Estiri H, Adineh M. (2026). 'Analysis of Mindlin Plates by Dynamic Relaxation Method', Science and Technology in Mechanical Engineering, 4(2), pp. 153-174. doi: 10.22034/stme.2025.531701.1137
CHICAGO
H Estiri and M Adineh, "Analysis of Mindlin Plates by Dynamic Relaxation Method," Science and Technology in Mechanical Engineering, 4 2 (2026): 153-174, doi: 10.22034/stme.2025.531701.1137
VANCOUVER
Estiri H, Adineh M. Analysis of Mindlin Plates by Dynamic Relaxation Method. STME. 2026;4(2):153-174 (In Persian). doi: 10.22034/stme.2025.531701.1137
Science and Technology in Mechanical Engineering