Please use this identifier to cite or link to this item: http://hdl.handle.net/11455/18170
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
摘要: 
本論文旨在研究函數梯度板(另譯功能梯度板)受均勻載重下產生大變形與微擾動邊界之逆運算問題,函數梯度板之材料性質假設於厚度方向具有連續性變化,且其材料性質為一羃次式之函數。本文大變形薄板之控制方程式,乃以古典之非線性板殼理論為基礎,而推出非線性位移偏微分方程聯立方程式,為解決此複雜之非線性板位移問題,我們應用擾動法,將位移函數以級數形態表示,並將微擾動之邊界以泰勒級數展開,複雜之邊界條件得以簡化,再以函數梯度板受均勻載重時之中心變形量為參數,將此參數設為級數之羃次項。最後位移函數之近似解以級數前三項合為主,板之內應力亦因解出之位移函數而求得。

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.
URI: http://hdl.handle.net/11455/18170
Appears in Collections:應用數學系所

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