A Two-Step Perturbation Method in Nonlinear Analysis of Beams, Plates and Shells

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Nonlinear vibration of functionally graded graphene-reinforced composite laminated beams resting on elastic foundations in thermal environments (2017, methodology): “In such a case the motion equations may be rewritten as γ11 ∂4W ∂x4 − γ12 ∂ 3 x ∂x3 −π {∫ π 0 [ γ13 2 ( ∂W ∂x )2 + γ14 ∂ x ∂x − γ15 ∂ 2W ∂x2 ] dx } ( ∂2W ∂x2 + ∂ 2W ∗ ∂x2 ) −π {∫ π 0 [ γ13 2 ( 2 ∂W ∂x ∂W ∗ ∂x + ( ∂W ∗ ∂x )2) + γ14 ∂ ∗ x ∂x − γ15 ∂ 2W ∗ ∂x2 ] dx } ∂2W ∂x2 = λq − ( K1W − K2 ∂ 2W ∂x2 )”
Postbuckling of axially compressed nanotube-reinforced composite cylindrical panels resting on elastic foundations in thermal environments (2014, background): “All of the major steps of the solution methodology will be described below and more details may be found in [52].”
Nonlinear vibration of nanotube-reinforced composite cylindrical panels resting on elastic foundations in thermal environments (2014, background): “All of the major steps of the solution methodology will be described below and more details may be found in [35].”