Title: Mathematical conditions for and physical meaning of a maximum of the determinant of K_T in the prebuckling regime
Language: English
Authors: Mang, Herbert A. 
Jia, Xin
Category: Research Article
Issue Date: 2013
Journal: Advances in Engineering Software
ISSN: 0965-9978
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.
Keywords: Buckling; Consistently linearized eigenproblem; Maximum of determinant; Percentage bending energy; Pressure vessel; Tangent stiffness matrix
DOI: 10.1016/j.advengsoft.2013.04.023
Library ID: AC15534600
URN: urn:nbn:at:at-ubtuw:3-8020
Organisation: E202 - Institut für Mechanik der Werkstoffe und Strukturen 
Publication Type: Article
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