Get Advances in mechanics of solids: in memory of Prof. E.M. PDF

By David J Steigmann, Remi Vaillancourt, Ardeshir Guran

ISBN-10: 9812568670

ISBN-13: 9789812568670

The contributions during this quantity are written by way of famous experts within the fields of mechanics, fabrics modeling and research. They comprehensively handle the middle matters and current the newest advancements in those and comparable parts. particularly, the ebook demonstrates the breadth of present learn task in continuum mechanics. numerous theoretical, computational, and experimental ways are stated, overlaying finite elasticity, vibration and balance, and mechanical modeling. The assurance displays the level and influence of the learn pursued by way of Professor Haseganu and her overseas colleagues.

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Additional info for Advances in mechanics of solids: in memory of Prof. E.M. Haseganu

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Therefore, it attains its maximum for d £ [cZ*, 1]. For these values of d the function y(d) and its derivatives have the form y = d2+[3(d~2 y' = 2d + (3 - P/d2, + l/d), y" = 2 + 2/3/d3 > 0. The first derivative y'(d) increases for d £ [d*, 1] since y"(d) > 0. Consequently, the function y{d) has no local maximum in the interval [d*, 1]. This is also valid for the function fv = ^fy. e. / * = m a x [ / u ( d * ) , / „ ( l ) ] = max (r n V /d*, 1). The inequality rn^/d^ > 1 is valid if and only if g(r~2) inequality holds if < 0.

13. Conclusion T h e asymptotic technique presented in this paper can be used for various stiffened thin-walled structures. T h e buckling and vibrations of a ringstiffened cylindrical shell with a slanted edge have been considered in [Filippov (1997)] 6 . For such shells, the vibrations and buckling modes are localized near the longest generatrix of the cylindrical shell. T h e evaluation procedure of the critical external pressure, the fundamental vibration frequency and the optimal parameters is similar to the procedure used for a shell with a straight edge.

These equations have nontrivial solutions if the characteristic determinant G(a) is equal to zero: G{a) = 0. (24) In the general case one can find the roots an of Eq. (24) by means of numerical methods and then calculate the eigenvalue A by formula (8). Unfortunately, in the case of a stiffened shell it is impossible to obtain a simple formula for the lowest eigenvalue Ai similar to formula (17), since c and, consequently, an depend on m. n The eigenvalue Ai is proportional to the fundamental vibration frequency in the case of vibrations and to the critical pressure in the case of buckling and, therefore, the first (lowest) eigenvalue is of interest in the industrial applications.

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Advances in mechanics of solids: in memory of Prof. E.M. Haseganu by David J Steigmann, Remi Vaillancourt, Ardeshir Guran

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