scholarly journals Automated Adjoints of Coupled PDE-ODE Systems

2019 ◽  
Vol 41 (3) ◽  
pp. C219-C244
Author(s):  
P. E. Farrell ◽  
J. E. Hake ◽  
S. W. Funke ◽  
M. E. Rognes
Keyword(s):  
Ode Systems

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.

A Computational Tool for the Reduction of Nonlinear ODE Systems Possessing Multiple Scales

2005 ◽  
Vol 4 (3) ◽  
pp. 732-759 ◽  
Author(s):  
Robert Clewley ◽  
Horacio G. Rotstein ◽  
Nancy Kopell
Keyword(s):  
Multiple Scales ◽  
Computational Tool ◽  
Nonlinear Ode ◽  
Ode Systems

scholarly journals Taylor Series Based Solution of Nonlinear-Quadratic ODE Systems

2018 ◽  
Author(s):  
Vaclav Satek ◽  
Petr Veigend ◽  
Gabriela Necasova
Keyword(s):  
Taylor Series ◽  
Ode Systems
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