A study of large displacement of 2-D curved beams with variable curvatures

• Main Authors: Chiu-Wen Lin, 林秋文
• Other Authors: Kuan-Chung Lin
• Format: Others
• Language: en_US
• Published: 2012
• Online Access: http://ndltd.ncl.edu.tw/handle/73558239273608702954

博士 === 國立中興大學 === 應用數學系所 === 100 === In this study, both Lagrangian and Eulerian description are used to derive for elasticity material and laminated composite material of large displacement analysis. The general solutions are expressed by fundamental geometric quantities. By choosing the deformed radius of curvature and deformed angle of tangent slope as parameters, the governing equations of curved beam under static loading are transformed into a set of equations in terms of angle of tangent slope. All the quantities of axial force, shear force, radial and tangential displacements of curved beam are expressed as functions of angle of tangent slope. The analytical solutions of curved beams of circular and spiral are presented. The analytical solutions of circular beam under a pair of forces are presented as well. The results are also compared with the results by using ANSYS large deformation static analysis. In pure bending cases, it shows good consistency. In circular curved beam under a pair of horizontal forces, when η2>0.36, the difference of tip displacement in force direction are less than 5％. The difference induced by neglected the shear deformation effect.