Key Problems Of Reduced-order Solution Of Geometric Nonlinear Vibration Response Of Plate&Shell

To solve dynamic response of a structure, reduced order method is an effectiveapproach with a sufficient accurate and a small computation consumption. Theoutstanding feature of reduced order method is the computation consumption ofreduced order method does not significantly increase, when the degrees of freedomof problem increase greatly. Although principle of the reduced order method issimple, a geometrically nonlinear problem can not be solved directly by this methoddue to inaccessibility of the nonlinear stiffness matrix.This thesis investigates the geometrically nonlinear vibration response of plateand shell structures by using the reduced order method based on platform ofMSC.NASTRAN. The main contents are as follows.(1) A method for determining the nonlinear stiffness coefficients for an arbitraryfinite element model is presented. Prescription of particular displacement fieldsrenders a series of inverse linear and nonlinear static problems, which are solved todetermine the unknown nonlinear stiffness coefficients. A reduced model isformulated with participation of nonlinear stiffness coefficients.(2) A flowchart of reduced order solution procedure for a dynamic system ispresented. A reduced order solution is implemented by using the FORTRAN, DMAPand PCL syntax based on the platform of MSC.NASTRAN.(3) Verification of nonlinear stiffness coefficients is performed. A series ofdifferent displacement fields are prescribed to determine the unknown nonlinearmodal stiffness coefficients on a simply supported rectangular plate. Verification ofthe nonlinear modal stiffness coefficients is performed by comparing displacementsobtained from the nonlinear static problem.(4) The accuracy of reduced order method by a number of modal vectorsparticipated in the solution is studied for a harmonic vibration problem. Reducedorder model can deal with nonlinear dynamics problems is verified by comparingdisplacements obtained by linear, nonlinear and reduced order methods. The impactof the participation number of the modal vectors is studied by comparison ofdisplacements obtained from different reduced order models.