Novel Solutions of Toroidal Shells Under Axisymmetric Loading
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摘要: 指出了现有渐近解的不足之处.本文统一用广义Airy函数表示齐解和非齐特解的完全渐近展开,而现有的渐近解是用Besel或Airy函数表示齐解,用Lommer函数表示非齐特解的.本文所得到的新解是全域一致有效的,达到了薄壳的理论精度,且齐解和特解之间满足变动参数关系.事实上,本文给出了三个特解,其中之一正好与Tumarkin(1959)和Clark(1963)的解相同.Abstract: Several improvements are made for existing asymptotic expansions for the axisymmetric toroidal shells.The new expansions are numerically satisfaytory and satisfy the accuracy of the theory of thin shells.All of them are expressed in terms of generalized Airy functions,instead of Bessel or Airy function for the homogeneous and Lommel function for the particular solutions,respectively,as in the existing work.In fact,three particular solutions are given in the paper,one of which is just the solution obtained by Tumarkin(1959) and Clark(1963).
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Key words:
- toroidal shells /
- asymptotic /
- generalized Airy function
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[1] Clark R A.J Math Phys,1950,29:146～178. [2] Clark R A.Asymptotic solutions of a non-homogeneous differential equation with a turning Point[J].Arch Rational Mech Anal,1963,12:34～51. [3] Drazin P D,Reid W H.Hydrodynamic Stability[M].Cambridge:Cambridge University Press,1981. [4] Nayfeh A H.Perturbation Methods[M].Printed in the Uited States of America:John Wiley and Sons Inc,1973. [5] V.V.诺沃日洛夫,薄壳理论[M].北京:科技出版社,1963. [6] Olver F W J.Asymptotic and Special Functions[M].New York:Academic press,1974. [7] Tumarkin S A.Asymptotic solutions of a linear non-homogeneous second order differential equation with a transition point and its application to the computation of loroidal shells and propeller blades[J].J Appl Math Mech,1959,23:1549～1565. [8] Zhang W,Dissertation T H.Berlin published partly [J].Sci Rep Nat Tsinghua Universtiy,Ser,A,1949,5:289～349. [9] Zhang Ruojing.Toroidal shells under nonsymmetic loading[J].Int J Solids Structures,1994,31(19):2735～2750. -
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