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Structural Engineering and Mechanics Volume 85, Number 2, January25 2023 , pages 147-161 DOI: https://doi.org/10.12989/sem.2023.85.2.147 |
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Numerical nonlinear bending analysis of FG-GPLRC plates with arbitrary shape including cutout |
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Reza Ansari, Ramtin Hassani, Yousef Gholami and Hessam Rouhi
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| Abstract | ||
| Based on the ideas of variational differential quadrature (VDQ) and finite element method (FEM), a numerical approach named as VDQFEM is applied herein to study the large deformations of plate-type structures under static loading with arbitrary shape hole made of functionally graded graphene platelet-reinforced composite (FG-GPLRC) in the context of higherorder shear deformation theory (HSDT). The material properties of composite are approximated based upon the modified Halpin-Tsai model and rule of mixture. Furthermore, various FG distribution patterns are considered along the thickness direction of plate for GPLs. Using novel vector/matrix relations, the governing equations are derived through a variational approach. The matricized formulation can be efficiently employed in the coding process of numerical methods. In VDQFEM, the space domain of structure is first transformed into a number of finite elements. Then, the VDQ discretization technique is implemented within each element. As the last step, the assemblage procedure is performed to derive the set of governing equations which is solved via the pseudo arc-length continuation algorithm. Also, since HSDT is used herein, the mixed formulation approach is proposed to accommodate the continuity of first-order derivatives on the common boundaries of elements. Rectangular and circular plates under various boundary conditions with circular/rectangular/elliptical cutout are selected to generate the numerical results. In the numerical examples, the effects of geometrical properties and reinforcement with GPL on the nonlinear maximum deflection-transverse load amplitude curve are studied. | ||
| Key Words | ||
| cutout with arbitrary shape; finite element method; mixed formulation; nanocomposite plate | ||
| Address | ||
| Reza Ansari, Ramtin Hassani, Yousef Gholami: Faculty of Mechanical Engineering, University of Guilan, P.O. Box 3756, Rasht, Iran Hessam Rouhi: Department of Engineering Science, Faculty of Technology and Engineering, East of Guilan, University of Guilan, P.C. 44891-63157, Rudsar-Vajargah, Iran | ||