An Analysis of Folded Plate Based on Rayleigh-Ritz Method Using Buckling and Vibration Eigenmodes of Beams Moon Sung Lee
ABSTRACT Generally, it is very complex and time-consuming procedure to analyze the 3-dimensional structure. Therefore for simplicity and time-efficiency, we mostly assume that the structure is under plain strain condition and analyze it. However, the assumption of the plain strain condition is not true for the part near the longitudinal end points, and the error is a lot bigger as the structure is shorter in longitudinal direction. In this paper, a more effective method with less degree of freedom which applies the finite element method to the 2-dimensional section and Rayleigh-Ritz method to the 1-dimensional longitudinal direction is suggested. The 3-dimensional structure under consideration is modeled into plate structure and the soil which surrounds the structure. And the plate structure is modeled into bending deformation and inplane deformation, which are mutually independent. As eigenmode which represents the longitudinal behavior of the structure, buckling and vibration modes of beams is used. Such an analyzing procedure already exists. However, mostly it is applied to the structure of simply supported and fixed supported longitudinal boundary condition. Therefore it has been somewhat difficult to apply to the common structure of free boundary condition. In this paper, it is laid emphasis on to find the eigenmode which is applied to the structure of free boundary condition. And the suggested method becomes more practical by modeling soil which surrounds the structure. This method is applied to the tunnel structure in which inplane deformation is dominant and to the rectangular folded plate in which the bending deformation is dominant, so it shows its validity and effectivity. And the result is compared with that of 3-dimensional analysis by ABAQUS.
Key Word Eigenmode, Rayleigh-Ritz method, Finite element method, Bending deformation, Inplane deformation
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