Bending Sector Graphene Sheet Based on the Elastic Winkler-Pstrnak with the Help of Nonlocal Elasticity Theory Using Developed Kantorovich Method

Document Type : Persian


1 MSc Student, Department of Mechanical Engineering, Mashhad Branch, Islamic Azad University, Mashhad, Iran.

2 Assistant Prof., Department of Mechanical Engineering, Mashhad Branch, Islamic Azad University, Mashhad, Iran


In this study, the elastic bending of sector graphene sheet has been studied based on elasticity using Eringen Nonlocal Elasticity Theory. In order to do this, the balance equations governing the sector graphene sheet have been solved in terms of displacements with regard to nonlocal relationship of stress, shear theory of the first order, and obtained linear strains using developed Kantorovich method. In this method, the obtained partial differential equations are converted into two categories that can be solved using analytical and numerical methods. Developed Kantorovich method is a method with a high rate of convergence, in which the expected convergence is achieved with just three to four repetitions. With regard to the fact that no research has yet been conducted in this regard, the results, considering the nonlocal coefficient equal to zero, have been compared with other articles in order to check the validity. In the end, the effect of nonlocal coefficient variations on the results in terms of thickness, boundary conditions, hardness of elastic base and difference between nonlocal and local elasticity analysis has been studied.


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