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

By David J Steigmann, Remi Vaillancourt, Ardeshir Guran

The contributions during this quantity are written by way of recognized experts within the fields of mechanics, fabrics modeling and research. They comprehensively tackle the center concerns and current the most recent advancements in those and similar components. particularly, the ebook demonstrates the breadth of present study task in continuum mechanics. various theoretical, computational, and experimental methods are pronounced, masking finite elasticity, vibration and balance, and mechanical modeling. The insurance displays the level and impression of the learn pursued through Professor Haseganu and her foreign colleagues.

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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. Another interesting problem is the analysis of two joint shells with slanted edges. Often this type of structure is used in pipelines. T h e problem becomes more complicated, but even in this case the asymptotic approach allows one to obtain approximate analytical solutions and develop algorithms to compute the optimal parameters (see [Filippov (1999)] 7 ).

This function increases for 0 < d < d*. 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.

Filippov 24 equations (18) corresponding to the freely supported or clamped shell edges x = 0 and x = I are represented in the forms (9) or (11). To determine the four boundary conditions for Eq. (20) from eight continuity conditions on the stiffened parallel x = Xj in the general case is a difficult problem. This problem was analyzed in [Filippov (1999)]7. We assume that the rings and the shell are made of the same material. The centers of gravity of the ring cross sections lie on the shell neutral surface and the characteristic size of the ring cross sections is a = Oie ).

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