Mathematical conditions for and physical meaning of a maximum of the determinant of (K)over-tilde(T) in the prebuckling regime
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. (C) 2013 Elsevier Ltd. All rights reserved.
tangent stiffness matrix consistently linearized eigenproblem percentage bending energy buckling maximum of determinant pressure vessel