A finite element / modal technique for nonlinear plate and stiffened panel response prediction

Abstract

A method is proposed for the modelling of the multiple mode response of geometrically nonlinear plates and panels to random acoustic excitation. Significant savings in computational time can be achieved compared with the direct integration nonlinear finite element method (FEM). The proposed technique identifies the nonlinear stiffness terms in a reduced basis modal dynamic model by performing a regression analysis upon a number of static nonlinear finite element test cases. Regression analysis is also used to identify an empirical relationship between modal displacements and point stresses, allowing the technique to encompass stress / strain analysis. Time domain numerical integration is then used to stimulate the kinematic, and stress response to band limited random acoustic excitation. Comparison with time domain finite element numerical simulations of nonlinear plates and stiffened panels shows that stress and displacement responses are predicted accurately in all cases.