Applying Preloads with the Differential Stiffness ApproachDifferential Stiffness TheoryIn geometric nonlinear problems, displacements are large. Therefore, the equilibrium equations must be written with respect to the deformed geometry. This theory assumes that the geometric stiffness matrix can be added to the structural (or differential) stiffness matrix; therefore, the change in geometry of the structure is only reflected in the stiffness matrix. Differential Stiffness MatrixA matrix that is necessary to account for the change in potential energy associated with rotation of continuum elements under load. (stiffness effects that depend linearly on displacements) Fundamental AssumptionExternal loads do not change in magnitude or direction as the structure deflects. However, the loads do travel with the grid points. Properties of KDGG (Differential Stiffness Matrix)
Setting Up the NASTRAN Data DeckUsing the differential stiffness approach to applying preloads to a NASTRAN finite element model consists of two executions of the model. The first model is set up to obtain the differential stiffness matrix (KDGG) as a results of the preload. The second model is where the differential stiffness matrix is added to the geometric stiffness matrix and desired results are requested. The DMAPs shown are for use in MSC/NASTRAN Version 67. The First ModelExecutive Control Sol 5 Compile sol5, souin=mscsou Alter 313 Output4 KDGG//1//11 $(creates a fort.11 file of KDGG) Exit $ Case Control Title = 'title' Subtitle = SPC = 'boundary points' 'Output requests'  probably want to output elements in which the preload is being applied to verify the magnitude. Subcase 1 Deform = 'id' Subcase 2 Bulk Data Add the necessary number of 'DEFORM' bulk data cards. The 'DEFORM' card requests the deformation of a one dimensional element, i.e. BAR, ROD, TUBE. For a preload on a bar, the deformation is:
where P is the applied preload. You can verify that the correct preload has been applied to the element by reviewing the BAR, ROD, or TUBE, element forces. The Second ModelExecutive Control Sol 24 Compile sol24, souin=mscsou Alter 90 Inputt4 /KDGG,,,,/1/11/1 $ Add KGG, KDGG/K1X $ Equiv K1X,KGG/Always $ Endalter Case Control and Bulk Data decks should be set up as any other run would be. NOTE: The differential stiffness matrix can be very big. Therefore, you should be careful to ensure that the matrix is not sent across the network. This will slow the job execution substantially. If this is a problem, use the ASSIGN card to write the matrix to the scratch directories on the computer that is executing the NASTRAN job. Cherie Congedo 



HOME  FEMCI BOOK  PRESENTATIONS  REFERENCES  WORKSHOP  LINKS  ABOUT  MINUTES  PRIVACY