Mathematics

We analyze the problem of the stability and buckling phenomena of a plate under compression along its edges. To do this we introduce the Von Karman equations, a system of two fourth-order, nonlinear and parametric equations. From the mathematical point of view the nonlinearity can be seen as a problem in bifurcation theory and can be showed that the bifurcation point is related with the y axis-crossing of the eigenvalues of the linearized problem. Because of the high computational cost we study this problem in the framework of Reduced Order Methods, specifically with Reduced Basis Method. We will show  numerically the possible configurations that the plate could assume and their link with the eigenvalues. Finally we will characterize the possible existence of multiple bifurcation.