Abstract
In the present paper, two different numerical methods, generalized differential quadrature (GDQ) and dynamic relaxation method (DR) are employed to analyze elastic-plastic plates. These methods are initially evaluated for elastic beams and then they are utilized for elastic-plastic plates analysis. A new method, GDDR (Generalized Differential Dynamic Relaxation), is developed by the combination of two mentioned methods. The proposed method is validated by theoretical analysis for elastic problems, Abaqus simulation and experimental study for elastic-plastic plates. Reduction in the number of required discretizing nodes, lower computational time and decrease in the number of iterations (about 80%) are the advantages of introduced method compared with the conventional ones. Moreover, this method improves the accuracy of solutions, especially in terms of stresses, by increasing the differentiation accuracy of nodes for elastic-plastic analysis. Comparing the errors of proposed GDDR method with conventional DR method shows about 70% reduction in mean squared error. Moreover, this new method is able to solve problems by using only 3 nodes in each direction, while other methods need at least 8.
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