Nonlinear Bending of Circular Sandwich Plates

摘要/Abstract

摘要： In this paper, fundamental equations and boundary conditions of nonlinear axisymmetrical bending theory for the circular sandwich plates with a soft core are derived by means of the method of calculus of variations. Especially in the case of very thin faces, the preceding fundamental epuations and boundary conditions simplity considerably. For example, a circular sandwich plate with edge clamped but free to slip under the action of uniform lateral load is considered. A more accurate solution of this problem has been obtained by means of the modified iteration method.

关键词: crack, line inclusion, the vertical contact point, singular stress, stress intensity factor

Abstract: In this paper, fundamental equations and boundary conditions of nonlinear axisymmetrical bending theory for the circular sandwich plates with a soft core are derived by means of the method of calculus of variations. Especially in the case of very thin faces, the preceding fundamental epuations and boundary conditions simplity considerably. For example, a circular sandwich plate with edge clamped but free to slip under the action of uniform lateral load is considered. A more accurate solution of this problem has been obtained by means of the modified iteration method.

Key words: crack, line inclusion, the vertical contact point, singular stress, stress intensity factor

刘人怀. Nonlinear Bending of Circular Sandwich Plates[J]. Applied Mathematics and Mechanics (English Edition), 1981, 2(2): 189-208.

Liu Ren-huai. Nonlinear Bending of Circular Sandwich Plates[J]. Applied Mathematics and Mechanics (English Edition), 1981, 2(2): 189-208.

参考文献

[1] Zaid,M.,Symmetrical bending of circular sandwich plates,Proceedings of the Second United States National Congress of Applied Mechanics,ASME,New York,(1954) 413.
[2] Bruun,E.R.,Thermal deflection of a circular sandwich plate,AIAA J,1,5(1963),1213.
[3] Huang,J.C.and Ebcioglu,I.K.,Clrcular sandwich plate under radial compression and thermal gradient,AIAA J,3,6(1965),1146.
[4] Amato,A,J.,Axisymmetric buckling of annular sandwich panels,AIAA J,10,10(1972),1351.
[5] Liu Ren-huai,Nonlinear axisymmetrical bending of circular sandwich plates under the action of uniform edge moment,Journal of the China University of Science and Technology,10,2(1980),56.
[6] Yeh Kai-yuan,Liu Ren-huai,ping Qing-yuan and Li Si-lai,Nonlinear stability of thin circular shallow spherical shell under actions of axisymmetric uniform distributed line loads,The Journal of Lanzhou University,2(1965),10;Bulletin of Sciences,2(1965).142.
[7] Yeh Kai-yuan,Liu Ren-huai,Zhang Chuan-zhe and Xu Yi-fan,Nonlinear stability of thin circular shallow spherical shell under the action of uniform edge moment,Bulletin of Sciences,2(1965),145.
[8] Liu Ren-hual,Nonlinear stability of circular shallow spherical shell with a hole in the center under the action of uniform moment at the inner edge,Bulletin of Sciences,3(1965),253.
[9] Liu Ren-huai,Axisymmetrical buckling of thin circular shallow spherical shell with a circular hole at the center by shearing forces uniformly distributed along the inner edge,Mechanics,3(1977),206.
[10] Liu Ren-huai,The Characteristic relations of corrugated circular plates,Acta Mechanica Sinica,1(1798),47.
[11] Liu Ren-huai,The characteristic relations of corrugated circular plates with plane center regiog,Journal of the China University of Science and Technology,9,2(1979),75.
[12] Yeh kai-yuan,Liu Ren-huai,Zhang Chuan-zhi and Xu Yi-fan,Nonlinear stability of thin elastic circular shallow spherical shell under the action of uniform edge moment,Applied Mathematics and Mechanics,1,1(1980),71.
[13] Liu Ren-huai,The thermal stability of bimetallic truncated shallow conical shells,Proceedings of the First Chinese National Congress of Elasticity and Plasticity,Chinese Institute of Mechanics,Beijing(1980).
[14] Chinese Research Institute of Mechanics,Bending,Stability and Vibration of Sandwich Plates and Shells,Science Press,Beijing(1977),42.
[15] Reissner,E.,Finite deflection of sandwich plates,J.Aeron.Sci.,15,7(1948),435;17,2(1950)125.