A Study On The Catastrophe And The Chaotic Motion Of Shallow Shells Under Pressure And Temperature And Transverse Periodic Load

The bifurcation and the elementary catastrophe theory and chaos theory have been employed to investigate some shells for the purpose of nonlinear analysis in this paper. The catastrophe analysis of shallow shells subjected to static pressure load and varying temperature is studied. The chaotic motion of shallow shells subjected to transverse periodic load and static load, varying temperature and initial defect of shells is investigated by Milnikov method and numerical analysis. We can introduce the beneficial study in this paper as follows: 1. The catastrophe analysis of Koiter general theoty of postbuckling problem has been completed in chapter2. 2. The postbuckling problem of shallow shells is studied in chapter3. This investigation is based on Donnel-Kàrmán eguations and a new nonlinear eguation is established, and the stress function and nonlinear dynamic system are carried out. In addition, the catastrophe analysis of shallow shells has been completed in chapter3. 3. The nonlinear dynamic system of double-curve shallow shells, plate, cylindrical shell and shallow spherical shell subjected to transverse periodic load and varying temperature are established in chapter4. The critical chaotic motion of cylindrical shell is given by Melnikov function, and the numerical analysis is carried out in chapter5, which contain rectangular plate, cylindrical shell and shallow spherical shell. The time-displacement history diagram and phase –plane diagram, chaos-bifurcation diagram and Poincare map are employed to determine the motion is chaotic or not. Using these theoretical and numerical methods, the chaotic motion of the nonlinear dynamic systems are investigated in this paper.