Mang, H. A., & Jia, X. (2013). Mathematical conditions for and physical meaning of a maximum of the determinant of K_T in the prebuckling regime. Advances in Engineering Software. https://doi.org/10.1016/j.advengsoft.2013.04.023
E202 - Institut für Mechanik der Werkstoffe und Strukturen
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Journal:
Advances in Engineering Software
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ISSN:
0965-9978
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Date (published):
2013
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Publisher:
Elsevier Ltd.
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Peer reviewed:
Yes
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Keywords:
Buckling; Consistently linearized eigenproblem; Maximum of determinant; Percentage bending energy; Pressure vessel; Tangent stiffness matrix
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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.
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