Nonlinear Static/Dynamic Analysis Of The Non-Circular Cross-section Laminated Thick Column Shells

Non-circular cross-section laminated thick column shell structures have been widely used in so many engineering areas. It is interesting and challengeable to study the static and dynamic characteristics of the shells. Recent developments about nonlinear vibration, nonlinear dynamic stability and nonlinear dynamic response of non-circular cross-section laminated thick column shells are briefly summarized. Then introducing into the non-linear geometry relations, and considering the influence of deformation and the rotation inertia, and the analysis of the non-linear dynamics behavior of non- circular cross-section laminated thick column shells is investigated. Based on the Timoshenko-Mindlin hypothesis and the nonlinear theory of shells, The non-linear geometrical relations of thick shell and the constitutive relations are established. Then according to the Reisser variation principal, the nonlinear governing equations of motion for the non-circular cross-section laminated column thick shells are founded.On the basis of the above research works, the nonlinear governing equations of motion for the non-circular cross-section laminated thick column shells are solved by using the Galerkin procedure and the method of harmonic balance. In numerical calculations, the L-curve section laminated thick cylindrical shells with both ends simply supported are investigated, and the effects of sectional shape and the radium-to-thickness ratio on the nonlinear amplitude-frequency response curves of non-circular cross-section laminated column shells are discussed. The present results are compared with existing results.Using the Galerkin procedure, the Mathieu equation only with time variable is obtained, and this equation is solved by the method of increase harmonic balance. In numerical calculations, the L-curve section laminated thick cylindrical shells with both ends simply supported are investigated, and the effects of sectional shape, factors of nonlinear deflection and transverse shear on the nonlinear dynamic stability of laminated non-circular cylindrical shells are discussed. The present results are compared with available date.Based on the Hamilton principle, the nonlinear governing equations of motion for the non-circular cross-section laminated thick column shells considering the lateral shear deformation and the rotation inertia are established. The spatial variable of the governing equations can be separated by using the trigonometric series and the orthogonal point collocation method. The time variable of the governing equations can be separated by using the Newmark-βmethod, and the response time of the external load are equally divided into many small moments. Then the nonlinear dynamic response of laminated non-circular cross-section column shells is studied by iterative method. In numerical calculations, the L-curve section laminated thick cylindrical shells with both ends fixed supported are investigated, and the effects of sectional shape, the geometrical nonlinearity and transverse shear deformation on the nonlinear dynamic stability of non-circular laminated thick cylindrical shells are discussed. The present results are compared with the simulation results.