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標題: 函數板逆運算問題之研究
On the inverse problem of functionally graded plates
作者: 謝俊杰
Hsieh, June-Jye
關鍵字: functionally graded material;inverse;perturbation;disturbed boundary;deflection;membrane stress;bending stress
出版社: 應用數學系

The inverse problem of functionally graded material (FGM) plates with large deflection and disturbed boundary under uniform load is studied in this thesis. The properties of functionally graded material are assumed to vary continuously through the thickness of the plate, and obey a simple power law expression based on the volume fraction of the constituents. Based on the classical nonlinear von Karman plate theory, the governing equations of a thin plate with large deflection were derived. In order to solve this non-classical problem, a perturbation technique was employed on displacement terms in conjunction with Taylor series expansion of the disturbed boundary conditions. The displacements of in-plane and transverse are obtained in a non-dimensional series expansion form with respect to center deflection of the plate. The approximate solutions of displacements are solved for the first three terms, and the corresponding internal stresses can also be obtained.
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