Multiple Equilibrium State And Elastic "Snap Through"of Plates And Stiffened Plates

The stiffened plates are widely used in maritime engineering, aerospace engineering, bridge engineering, construction and other modern industrial structure. With the structures (especially aviation structure) improve requirement of weight loss, the stiffened plates more and more widely used in navigation structure and aerospace structures. The stiffened plates when subjected to compression or other effects, which buckling occurs first. In fact, the structure is not immediately destroyed after buckling; it still has great carrying capacity, which is called post-buckling strength. The post-buckling strength can be used to increase the carrying capacity of the structure so as to achieve the purpose of weight loss. The core issue of the modern stability theory is the study of post-buckling behavior. On the structural stability issues, starting with the mid-eighteenth century L. Euler carried out a study on the stability of struts. Stability theory developed from the linear buckling theory to the theory of nonlinear buckling. According to the theory of nonlinear buckling, stability and strength of the structural problems are mutually linked. In the modern theory of structural stability, regardless of the use of numerical methods, will face two difficult issues, one of which is how to establish and describe geometric nonlinearity with large deflection, nonlinear physics, the initial defect (geometrical defects, load defects) and structural stability theory and the various factors described in the form of linked problems; second is how to describe the entire structural instability solving nonlinear equations form. The former is a mathematical model of the problem, while the latter is a matter of calculation methods.In this paper, the finite element method is used to simulate the stability of plate and stiffened plates under axial compression load. The geometric nonlinearity of the structures is taking into account. In this paper, the pseudo-arc-length method is used to solve nonlinear equations. Pseudo-arc method can pass the critical point of solution curve, which can track a wide range of load-deflection curve.First, the post-buckling behavior of thin plates is researched. Consider the geometric imperfections of thin plates, the geometric models of square plates under different boundary conditions are established. Under the clamped supported boundary conditions, in the post-buckling process, there will be several snap-through. In the case of different thickness, the number of sudden jump from2to3times, the difference of load-deflection curve is very obvious. Different boundary conditions:simply supported and clamped supported, the buckling and post-buckling paths are also very different; it illustrates the effect of boundary conditions on the post-buckling behavior is very large.Second, the simply supported stiffened plates are simulated. According to the shape and the position of the rib is divided into several types. When the shape of the ribs are arranged symmetrically on both sides of the plate, the position of the rib in the intermediate plate, under the same area of cross-sections, the different paths of post-buckling of the ribs are compared. The position of the ribs is divided into1/2,1/3and1/6of the plate. Also we considered in the same cross-sectional area, the impact of the height of the ribs carrying capacity.