Large Deflection Analysis of Membranes and Thin Plates

• Main Authors: Coe, Ya-Ren, 柯雅仁
• Other Authors: Chung Ming-Ping
• Format: Others
• Language: zh-TW
• Published: 1996
• Online Access: http://ndltd.ncl.edu.tw/handle/60280384385402297951

碩士 === 國立中央大學 === 機械工程學系 === 84 === This paper analyzes static deflection problems of thin plates and membranes which are homogeneous and isotropic by finite element method. 16-DOF conforming rectangular elements is used for the analysis of plates. 4-DOF non-conforming rectangular elements is used for the analysis of membranes. This paper first uses single complex function to solve the homogeneous solutions of biharmonic partial differential equation and the partial differential equation for deflection of membranes, and develops the closed-form shape functions. Because the homogeneous solutions have the closed property, the analysis is suitable for the problems of arbitrary boundary conditions. For the analyses of small deflection of thin plates and nonlinear membranes, the resultant which is got from the closed- form shape functions will be compared with the resultant which is got from polynomial shape functions and the analytic solution. Classic thin-plate theorem only solve small deflection problems, so this paper for large deflection problems is based on von Karman theorem and use Lagrangian strains to consider the stretching action of middle surface of plates. For the analyses of finite element method, this paper neglect the axial deplacements, so the tangent stiffness matrices is only composed of bending stiffness matrices and initial stress matrices (or is called geometrical stiffness matrices). Hence, the nonlinear solutions can be solved by direct iteratiev method. Every iterative step must update the initial stress matrices and iterations stop until solutions converge. Because this paper neglect the axial deplacements for large deflection problems, the method is suitable for the immovable edges and symmetric loading problems.