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 siip 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.
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Abbreviations
- r, θ,z :
-
system of cylindrical coordinates
- a :
-
radius of plate boundary
- t :
-
thickness of the face
- h :
-
thickness of the core
- h 0 :
-
distance from middle of thickness of lower face to middle of thickness of upper face
- E :
-
Young's modulus of the face
- ν:
-
Poisson's ratio of the face
- G 2 :
-
shear modulus of the core
- D f :
-
flexural rigidity of the face
- D :
-
flexural rigidity of the plate
- C :
-
shear rigidity of the plate
- q :
-
uniform lateral load
- u i ,v i ,w i(i=1, 2, 3) :
-
radial, tangential and normal displacement of upper face, core and lower face, respectively
- u :
-
radial displacement of the middle plane of the plate
- w :
-
deflection of the middle plane of the plate
- ψ:
-
rotation of connecting line of corresponding points in middle planes of two faces
- ε 1i ,ε θi ,ε zi ,γ rεi ,γ εzi ,γ rzi (i=1,2,3) :
-
strains at a point of upper face, core and lower face
- σ ri , σ θi , σ zi , τ rθi , τ θzi , τ rzi(i=1,2,3) :
-
stresses at a point of upper face, core and lower face
- σ rθ , σ θ0 :
-
radial and tangential stress of the middle plane of the plate, respectively
- U i(i =1, 2, 3):
-
strain energy of upper face, core and lower face, respectively
- V :
-
work done by the external force
- U :
-
total potential energy of the plate
- M r :
-
radial moment of the plate
- Q r :
-
shearing force of the plate
- m :
-
radial moment of the face
- φ:
-
stress function
- ρ:
-
dimensionless radial coordinate
- k :
-
dimensionless characteristic parameter
- W :
-
dimensionless deflection
- W 0 :
-
dimensionless center deflection
- S r ,S 0 :
-
dimensionless radial and tangential stress, respectively
- S r (0),S 0 (0):
-
dimensionless radial and tangential stress at center, respectively
- S 0(1):
-
dimensionless tangential stress at edge
- P :
-
dimensionless uniform lateral load
- A 2,A 3,B 2,B 3,a 1,.....,a 2,λ 1,λ 2,l 1,1,...l 1 1,3,m 1,...,m 33,n 0,2,...n 22,6,R 1,,...R 33 :
-
auxiliary quantity
- L :
-
differential operator
References
Zaid, M., Symmetrical bending of circular sandwich plates,Proceedings of the Second United States National Congress of Applied Mechanics, ASME, New York, (1954) 413.
Bruun, E. R., Thermal deflection of a circular sandwich plate,AIAA J, 1, 5 (1963), 1213.
Huang, J. C. and Ebcioglu, I. K., Circular sandwich plate under radial compression and thermal gradient,AIAA J, 3, 6 (1965), 1146.
Amato, A. J., Axisymmetric buckling of annular sandwich panels,AIAA J, 10, 10 (1972), 1351.
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.
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.
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.
Liu Ren-huai, 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.
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.
Liu Ren-huai, The Characteristic relations of corrugated circular plates,Acta Mechanica Sinica, 1 (1798), 47.
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.
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.
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).
Chinese Research Institute of Mechanics, Bending,Stability and Vibration of Sandwich Plates and Shells, Science Press, Peijing (1977), 42.
Reissner, E., Finite deflection of sandwich plates,J. Aeron. Sci., 15, 7 (1948), 435; 17, 2 (1950) 125.
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Ren-huai, L. Nonlinear bending of circular sandwich plates. Appl Math Mech 2, 189–208 (1981). https://doi.org/10.1007/BF01876778
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DOI: https://doi.org/10.1007/BF01876778