Qualitative Theory in Structural Mechanics by Dajun Wang & Qishen Wang & Beichang (Bert) He

Author:Dajun Wang & Qishen Wang & Beichang (Bert) He
Language: eng
Format: epub
ISBN: 9789811313769
Publisher: Springer Singapore

(5.3.1)

Rewrite the above equation as

(5.3.2)

Thus, Property (2) is valid.

Finally, Property (3), which needs to be proved, is equivalent to

(5.3.3)

Taking into consideration of Property (2), we only need to show in order to prove Eq. (5.3.3).

When , which corresponds to the bar being fixed on the left side, , and the above inequality is apparently satisfied. As a result, we only need to consider the case of . Let us again follow the process of proof by contradiction by assuming . Then, we get from Property (1) as well as the boundary condition for at the right end,

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