An extension to classical lamination theory for use with functionally graded plates

2011 ◽  
Vol 93 (2) ◽  
pp. 639-648 ◽  
Author(s):  
R.G. Reid ◽  
R. Paskaramoorthy
Keyword(s):  
Functionally Graded ◽  
Functionally Graded Plates ◽  
Classical Lamination Theory ◽  
Lamination Theory

Post-buckling analysis of non-uniformly heated functionally graded cylindrical shells enhanced by shape memory alloys using classical lamination theory

2019 ◽  
Vol 30 (16) ◽  
pp. 2421-2435
Author(s):  
Babak Mirzavand ◽  
Hamid Pourmohammad
Keyword(s):  
Shape Memory Alloys ◽  
Shape Memory ◽  
Material Properties ◽  
Cylindrical Shells ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Classical Lamination Theory ◽  
Nonlinear Equilibrium ◽  
Post Buckling ◽  
Lamination Theory

Thermal post-buckling analysis of functionally graded cylindrical shells enhanced by shape memory alloys under uniform and non-uniform heating is presented in this article. Nonlinear equilibrium equations are derived based on the classical lamination theory and von-Karman nonlinear kinematic relations and post-buckling field is investigated using Galerkin method. For temperature dependency of material properties, a numerical solution is applied to solve the nonlinear equilibrium equation using finite difference method to solve the nonlinear heat conduction equation and layered model to evaluate the thermal stress of hybrid cylindrical shells. A closed-form solution is also presented for temperature independency of material properties. Brinson model is adopted to describe the thermo-mechanical behavior of shape memory alloys. Numerical results are presented for evaluating the effects of shape memory alloy layer and functionally graded material cylindrical shells properties on suppressing of the post-buckling path of hybrid cylindrical shells.

Static Analysis of Moderately Thick Functionally Graded Plates With Various Boundary Conditions

2010 ◽  
Author(s):  
Nastaran Shahmansouri ◽  
Mohammad Mohammadi Aghdam ◽  
Kasra Bigdeli
Keyword(s):  
Boundary Conditions ◽  
Volume Fraction ◽  
Closed Form Solution ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Rectangular Plates ◽  
Functionally Graded Plates ◽  
Various Boundary Conditions ◽  
Fg Plates ◽  
Ode Systems

The present study investigates static analyses of moderately thick FG plates. Using the First Order Shear Deformation Theory (FSDT), functionally graded plates subjected to transversely distributed loading with various boundary conditions are studied. Effective mechanical properties which vary from one surface of the plate to the other assumed to be defined by a power law form of distribution. Different ceramic-metal sets of materials are studied. Solution of the governing equations, including five equilibrium and eight constitutive equations, is obtained by the Extended Kantorovich Method (EKM). The system of thirteen Partial Differential Equations (PDEs) in terms of displacements, rotations, force and moment resultants are considered as multiplications of separable function of independent variables x and y. Then by successful utilization of the EKM these equations are converted to a double set of ODE systems in terms of x and y. The obtained ODE systems are then solved iteratively until final convergence is achieved. Closed form solution is presented for these ODE sets. It is shown that the method is very stable and provides fast convergence and highly accurate predictions for both thin and moderately thick plates. Comparison of the normal stresses at various points of rectangular plates and deflection of mid-point of the plate are presented and compared with available data in the literature. The effects of the volume fraction exponent n on the behavior of the normalized deflection, moment resultants and stresses of FG plates are also studied. To validate data for analysis fully clamped FG plates, another analysis was carried out using finite element code ANSYS. Close agreement is observed between predictions of the EKM and ANSYS.

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