An extension to classical lamination theory for buckling and vibration of functionally graded plates
An extension to classical lamination theory (CLT) is presented to analyse the natural fre- quencies and critical buckling loads of simply supported functionally graded plates. The variation of the through-thickness properties of the plate is governed by a power law which is subsequently represented by a polynomial series of su cient order and varies according to the law of mixtures or the Mori-Tanaka Homogenization method. The sti ness matrices are found, from which the position of the neutral plane is established which allows for the governing equations for the natural frequency and critical buckling load to be derived using the Rayleigh-Ritz method. The natural frequency and critical buckling loads are determ- ined for various volume indices, aspect and span ratios and the accuracy thereof is validated against 2D, 3D and quasi-3D solutions found in literature. A comparison with CLT found that the present study produces natural frequencies and critical bucking loads which are more accurate and which converge faster than CLT.
A research report submitted to the Faculty of Engineering and the Built Environment, University of the Witwatersrand, Johannesburg, in partial fulfilment of the requirements for the degree of Master of Science in Engineering, August 2019
Catanho, Roberto Vincent, (2019). An extension to classical lamination theory for buckling and vibration of functionally graded plates, University of the Witwatersrand, https://hdl.handle.net/10539/29151