Article

# A DIFFERENTIAL QUADRATURE FINITE ELEMENT METHOD

International Journal of Applied Mechanics (Impact Factor: 1.29). 04/2012; 02(01). DOI: 10.1142/S1758825110000470

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**ABSTRACT:**This paper presents correct results for a paper by Liu and Xing (2011) [1] that had errors, greatly simplifies its formulations, overcomes its numerical stability problem, and provides some new results. In their early paper, Liu and Xing obtained exact closed-form solutions for free vibrations of orthotropic rectangular Mindlin plates by using the separation of variables method. The equations presented therein are correct, but the numerical values of the frequencies listed have some errors because the shear rigidities of the three-ply laminates were not correctly computed. In addition, the exact characteristic equations of the early paper can also be greatly simplified and the compact equations are presented herein. The characteristic equations in the early paper may have computational stability problem when plates become very thin. This paper overcome such computational difficulty. Some new exact frequency parameters are also included in this work.Composite Structures 12/2014; 118:316–321. · 3.12 Impact Factor -
##### Article: Exact solutions for free vibration of circular cylindrical shells with classical boundary conditions

International Journal of Mechanical Sciences 10/2013; 75:178-188. · 2.06 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**This paper deals with the static and dynamic analysis of multi-layered plates with discontinuities. The two-dimensional First-order Shear Deformation Theory (FSDT) is used to derive the fundamental system of equations in terms of generalized displacements. The fundamental set, with its boundary conditions, is solved in its strong form. A new method termed Strong Formulation Finite Element Method (SFEM) is considered in the present paper to solve this kind of plates. This numerical methodology is the cohesion of derivative evaluation of partial differential systems of equations and a domain sub-division. The numerical results in terms of natural frequencies and maximum deflections are compared to literature and to the same results obtained with a finite element code. The stability, accuracy and reliability of the present methodology is shown through several numerical applications.Meccanica 10/2014; · 1.82 Impact Factor

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