title: Mathematical conditions for and physical meaning of a maximum of the determinant of [Formula: see text] in the prebuckling regime.
abstract: It is shown that the determinant of the tangent stiffness matrix has a maximum in the prebuckling regime if and only if the determinant of a specific linear combination of the first and the third derivative of this matrix with respect to a dimensionless load factor vanishes. The mathematical tool for this proof is the so-called consistently linearized eigenproblem in the frame of the Finite Element Method. The physical meaning of the mentioned maximum is the one of a minimum of the percentage bending energy of the total strain energy. The paper provides mathematical and physical background knowledge on numerical results that were obtained 35 years ago.
authors.affiliation: Institute for Mechanics of Materials and Structures, Vienna University of Technology, Karlsplatz 13/202, 1040 Vienna, Austria.|Tongji University, Siping Road 1239, Shanghai, China.
authors.forename: H A
authors.initials: HA
authors.lastname: Mang
authors.affiliation: Institute for Mechanics of Materials and Structures, Vienna University of Technology, Karlsplatz 13/202, 1040 Vienna, Austria.
authors.forename: X
authors.initials: X
authors.lastname: Jia
keywords: Buckling; Consistently linearized eigenproblem; Maximum of determinant; Percentage bending energy; Pressure vessel; Tangent stiffness matrix