Derivation and Validation of Element Geometric Strain Energy for Frame Structure

To obtain the element geometric strain energy,the element geometric stiffness matrix of spatial frame structure was derivated based on the element geometric stiffness matrix of planar frame structure.On the platform of MSC Patran software,the program was implemented to compute the element geometric stiffness matrix and the element geometric strain energy with PCL(Patran Command Language).Numerical examples show that summation of element geometric strain energy from the program is consistent with the results inferred from MSC Nastran,which indicates the validity of the element geometric stiffness matrix of spatial frame structure and establishes the foundation for the structure optimization considering buckling constraint.