ON SECOND ORDER ASYMPTOTIC SOLUTIONS OF AXIAL SYMMETRICAL PROBLEMS OF r>0 THIN UNIFORM CIRCULAR TOROIDAL SHELLS WITH A LARGE PARAMETER a 2/R0h

Abstract

Abstract: According to the classital shell theory based on the Love-Kirchhoff assumptions, the basic differential equations for the axial symmetrical problems of r>0 thin uniform circular toroidal shells in bending are derived, and the second order asymptotic solutions are given for r>0 thin uniform circular toroidal shells with a large parameter a²/R₀h.In the resent paper, the second order asymptotic solutions of the edge problems far from the apex of toroidal shells are given, too. Their errors are within the margins allowed in the classical theory based on the Love-Kirchhoff assumptions.

Key words: lip-shaped crack, strained reinforcement layer, concentrated load, remote load, eigenstrain, interfacial stress

Chen Guo-dong . ON SECOND ORDER ASYMPTOTIC SOLUTIONS OF AXIAL SYMMETRICAL PROBLEMS OF r>0 THIN UNIFORM CIRCULAR TOROIDAL SHELLS WITH A LARGE PARAMETER a2/R₀h. Applied Mathematics and Mechanics (English Edition), 1988, 9(4): 401-416.

TrendMD

References

[1] Chien, W.Z., Equations of symmetrical ring shells in complex quantities and their general solutions for slender ring shells, Journal of Qinghua University, 19, 1 (1979), 27-47.
[2] Tölke, F., Zur Integration der Differentialgeichungen der Rotationsschale, lngenieur Archiv, 9 (1938), 282-288.
[3] Clark, R.A., On the theory of thin elastic toroidal shells, J. Math. Phys., 29 (1950), 146-178.
[4] Novozhilov, V.V., the Theory of Thin Shells, Noordhoff, Groningen, The Netherlands (1959).
[5] Chien, W.Z., General solutions of axial symmetrical ring shells, Applied Mathematics and Mechanics, 1, 3 (1980).
[6] Chang, W., The state of stress in toroidal and similar shells with azimental rings under torsionally symmetrically stress, Science Report of National Tsinghua University, 5 (A) (1949), 289-349. (in Chinese).
[7] Zhao Hong-bin, Wu Zhen-hui and Shen Zhu-pei, The equations in complex variables under axial symmetric loads and their asymptotic solutions, Journal of Qinghua University,21, 2 (1981), 1-14. (in Chinese).
[8] Chien, W.Z., The Treatises of Applied Mathematics and Mechanics, Jiangsu Science and Technique Press, China (1980). (in Chinese).
[9] Desilva, C.N. and P.M. Naghdi, Asymptotic solutions of a class of elastic shells of revolution with variable thickness, Q. Appl. Math., 15, 2 (1957), 169-182.
[10] Clark, R.A., Asymptotic solutions of toroidal shell problems, Q. Appl. Math., 16,1 (1958), 47-60.
[11] Tumarkin, S.A., Asymptotic solution of a linear nonhomogeneous second order differential equatlon with a transition point and its application to the computations of toroidal shells and propeller blades, Prikl. Mate. i. Mekh., 29 (1959), 1549-1569.
[12] Chen Guo-dong, Exact solutions of toroidal shells in. pressure vessels and piping, Int. J. Pres. Ves. and Piping, 19, 2 (1985), 101-116.
[13] Chen Guo-dong, The uniformly valid asymptotic solutions for spherical thin shells with constant thickness under edge loads, Proceedings of the Fifth Engineering Mechanics Division Specialty Conference ASCE, Aug. (1984), 261-269.
[14] Chen Guo-dong, The uniformly valid asymptotic solution of ellipsoidal shell heads in pressure vessels, J. Pressure Vessel Technol., Trans. ASME, 107, 1 (1985), 92-97.

ON SECOND ORDER ASYMPTOTIC SOLUTIONS OF AXIAL SYMMETRICAL PROBLEMS OF r>0 THIN UNIFORM CIRCULAR TOROIDAL SHELLS WITH A LARGE PARAMETER a2/R₀h

PDF

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 10

Recommended Articles

Metrics

Comments

[1]	Jian WU, C. Q. RU, Liang ZHANG, Ling WAN. Geometrical shape of in-plane inclusion characterized by polynomial internal stress field under uniform eigenstrains [J]. Applied Mathematics and Mechanics (English Edition), 2016, 37(9): 1113-1130.
[2]	MA Hang;GUO Zhao;QIN Qiang-Hua. Two-dimensional polynomial eigenstrain formulation of boundary integral equation with numerical verification [J]. Applied Mathematics and Mechanics (English Edition), 2011, 32(5): 551-562.
[3]	LIU You-Wen;XIE Chao;JIANG Chun-Zhi;FANG Qi-Hong. Analytical solution for a strained reinforcement layer bonded to lip-shaped crack under remote mode III uniform load and concentrated load [J]. Applied Mathematics and Mechanics (English Edition), 2010, 31(09): 1125-1140.
[4]	MA Hang;XIA Li-wei;QIN Qing-hua. Computational model for short-fiber composites [J]. Applied Mathematics and Mechanics (English Edition), 2008, 29(6): 757-767 .
[5]	M. K. Ghosh;M. Kanoria. Displacements and stresses in composite multi-layered media due to varying temperature and concentrated load [J]. Applied Mathematics and Mechanics (English Edition), 2007, 28(6): 811-822 .
[6]	LIU Han-bing;LIU Wen-hui;ZHANG Yun-long. CALCULATION ANALYSIS OF SHEARING SLIP FOR STEELCONCRETE COMPOSITE BEAM UNDER CONCENTRATED LOAD [J]. Applied Mathematics and Mechanics (English Edition), 2005, 26(6): 735-740 .
[7]	HE Ling-hui;LIM Chee-wah;LIU Ren-huai . ANALYSIS OF ELASTIC LAYERS WITH DILATIVE EIGENSTRAINS VARYING THROUGH THE THICKNESS [J]. Applied Mathematics and Mechanics (English Edition), 2003, 24(9): 997-1008.
[8]	Bian Yuhong. BENDING OF RECTANGULAR PLATE WITH EACH EDGES ARBITRARY A POINT SUPPORTED UNDER A CONCENTRATED LOAD [J]. Applied Mathematics and Mechanics (English Edition), 2000, 21(5): 591-596.
[9]	Sheng Hongyu;Fan Jiarang. AXISYMMETRIC BENDING FOR THICK LAMINATED CIRCULAR PLATE UNDER A CONCENTRATED LOAD [J]. Applied Mathematics and Mechanics (English Edition), 2000, 21(1): 95-102.
[10]	Bian Yuhong. THE BENDING OF SET SQUARES WITH ONE FREE OBLIQUE EDGE UNDER A CONCENTRATED LOAD [J]. Applied Mathematics and Mechanics (English Edition), 1997, 18(7): 697-706.