Determination of nonlinear stiffness with application to random vibration of geometrically nonlinear structures

A novel method for determining the nonlinear modal stiffness coefficients for an arbitrary finite element model is presented. The method is applicable to a wide class of problems exhibiting bending-membrane coupling and is suitable for use with commercial finite element codes having a geometrically nonlinear static capability. The equations of motion are written in modal coordinates with the nonlinear stiffness force components written as the product of second and third order modal displacements multiplied by unknown coefficients. Prescription of particular displacement fields renders a series of inverse linear and nonlinear static problems, which are solved to determine the unknown coefficients. Verification of stiffness coefficients found using this method and their use in equivalent linearization random vibration analysis are presented.