Using the Differential Quadrature Method to Analyze Post Buckling Of FGM Nanocomposite Symmetric Shell Reinforced By Graphene Plates

Seyed Ehsan Yousefi, Hamidreza Fahham, Mohammad Shojaee, Maziar Janghorban

Research output: Contribution to journalArticlepeer-review


The differential quadratic difference method or DQM for short is one of the numerical methods in which the governing differential equations are converted into groups of first-order algebraic equations using the weight coefficients. Thus, at each point, the derivative will be expressed as a linear sum of weight coefficients and function values at that point and other points of the domain and in the direction of the coordinate axes. In this research, the differential quadratic numerical method is used as a high-order numerical method with a small number of computational nodes, whose numerical results have good accuracy. In recent years, graphene sheets have been used as a reinforcing phase to improve the mechanical, thermal, and electrical properties of nanocomposites. The present study investigates the dynamic instability and postbuckling of the functionally graded porous incomplete cone reinforced with graphene sheets. The desired incomplete cone is surrounded by piezoelectric layers. Using Hamilton's principle and the assumption of the first-order displacement field and higher-order shear, the equations of motion were derived.

In order to investigate the instabilities and postbuckling, analysis of the governing partial equations of the problem was done using the differential quadratic method, and the Mathew matrix time equations were obtained, which were calculated using the dynamic unstable region bulletin method. All equations were written as calculation codes in MATLAB software. Influential parameters static and dynamic axial load range, boundary conditions, and size of graphene sheets (length, thickness, and width) reinforcing the dynamic unstable region And its aftermath has been checked.
Original languageEnglish
JournalJournal of New Researches in Mathematics
Early online date23 Nov 2022
Publication statusE-pub ahead of print - 23 Nov 2022
Externally publishedYes

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