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<div class="csl-entry">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. <i>Advances in Engineering Software</i>. https://doi.org/10.1016/j.advengsoft.2013.04.023</div>
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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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dc.description.sponsorship
Austrian Science Fund (FWF)
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dc.language
English
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dc.language.iso
en
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dc.publisher
Elsevier Ltd.
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dc.relation.ispartof
Advances in Engineering Software
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dc.rights.uri
http://creativecommons.org/licenses/by-nc-nd/3.0/
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dc.subject
Buckling
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dc.subject
Consistently linearized eigenproblem
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dc.subject
Maximum of determinant
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dc.subject
Percentage bending energy
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dc.subject
Pressure vessel
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dc.subject
Tangent stiffness matrix
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dc.title
Mathematical conditions for and physical meaning of a maximum of the determinant of K_T in the prebuckling regime