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An original HSDT for free vibration analysis of functionally graded plates
Imene Ait Sidhoum,Djilali Boutchicha,Samir Benyoucef,Abdelouahed Tounsi 국제구조공학회 2017 Steel and Composite Structures, An International J Vol.25 No.6
This work presents a free vibration analysis of functionally graded plates by employing an original high order shear deformation theory (HSDT). This theory use only four unknowns, which is even less than the classical HSDT. The equations of motion for the dynamic analysis are determined via the Hamilton‟s principle. The original kinematic allows obtaining interesting equations of motion. These equations are solved analytically via Navier procedure. The accuracy of the proposed solution is checked by comparing it with other closed form solutions available in the literature.
Sidhoum, Imene Ait,Boutchicha, Djilali,Benyoucef, Samir,Tounsi, Abdelouahed Techno-Press 2018 Smart Structures and Systems, An International Jou Vol.22 No.3
An original quasi-3D hyperbolic shear deformation theory for simply supported functionally graded plates is proposed in this work. The theory considers both shear deformation and thickness-stretching influences by a hyperbolic distribution of all displacements within the thickness, and respects the stress-free boundary conditions on the upper and lower surfaces of the plate without using any shear correction coefficient. By expressing the shear parts of the in-plane displacements with the integral term, the number of unknowns and equations of motion of the proposed theory is reduced to four as against five in the first shear deformation theory (FSDT) and common quasi-3D theories. Equations of motion are obtained from the Hamilton principle. Analytical solutions for dynamic problems are determined for simply supported plates. Numerical results are presented to check the accuracy of the proposed theory.
Imene Ait Sidhoum,Djilali Boutchicha,Samir Benyoucef,Abdelouahed Tounsi 국제구조공학회 2018 Smart Structures and Systems, An International Jou Vol.22 No.3
An original quasi-3D hyperbolic shear deformation theory for simply supported functionally graded plates is proposed in this work. The theory considers both shear deformation and thickness-stretching influences by a hyperbolic distribution of all displacements within the thickness, and respects the stress-free boundary conditions on the upper and lower surfaces of the plate without using any shear correction coefficient. By expressing the shear parts of the in-plane displacements with the integral term, the number of unknowns and equations of motion of the proposed theory is reduced to four as against five in the first shear deformation theory (FSDT) and common quasi-3D theories. Equations of motion are obtained from the Hamilton principle. Analytical solutions for dynamic problems are determined for simply supported plates. Numerical results are presented to check the accuracy of the proposed theory.