A direct fourier approach for the analysis of thin finite-dimensional cylindrical panels

Abstract

A hitherto unavailable Fourier series solution to the boundary-value problem of thin cylindrical panels of rectangular planform, subjected to transverse loads, is presented. Sanders' kinematic relations (for classical shell theory) are utilized in the formulation, which generates one fourth-order (in terms of the transverse displacement component) and two second-order (in terms of the surface-parallel displacement components) partial differential equations with constant coefficients. A boundary-discontinuous double Fourier series approach is used to solve the system of three partial differential equations with the SS2-type simply-supported boundary conditions prescribed at all four edges. The final algebraic equations are expressed in terms of the boundary Fourier coefficients, which substantially reduce the size of the matrix, that is inverted using a digital computer. The accuracy of the series solution is ascertained by studying the convergence characteristics, and also by comparison with finite element solutions. Other important numerical results presented include variation of displacement and moment with the radius-to-thickness, length-to-thickness and length-to-width ratios. Also presented are variations of displacement and moment along the center line of the cylindrical panels. These numerical results contribute to our understanding of the complex deformation behavior of finite cylindrically curved panels—especially the influence of the boundary discontinuities on the computed displacements and stresses.