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Thermal buckling and dynamic characteristics of composite plates under pressure load

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Abstract

The effect of geometrical nonlinearities due to pressure load on the thermal buckling and dynamic characteristics of composite plates are investigated in this paper, which is the main contribution of this research work. The mechanical behavior of the plate is described with the first-order shear deformation theory. The geometrical nonlinearity due to both thermal effect and pressure load is introduced in the finite element model of the plate via additional stiffness matrices. Thermal buckling and modal analysis of a four-sided simply supported rectangular composite plate under different pressure fields are conducted. Numerical results show that both the mode frequencies and critical buckling temperature of the plate rise with the increase of the pressure. The vibrational mode shapes change with the gradient pressure load field. The maximum buckled deflection point moves from the center to the place where is easier to reach compressive stress state under uniform thermal load. The pressure distribution has a significant effect on the buckling mode shapes of the plate.

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Abbreviations

a, b, h :

Dimension of the plate along x, y, z direction

u, v, w :

Deflections along x, y, z direction

φx, φy :

Rotational displacement of x-axis and y-axis

W :

Virtual work

N :

i-th shape function

B :

Strain-nodal displacement matrix

D :

Material property matrix

K0, Kσ :

Initial and additional stiffness matrix

K :

Structural stiffness matrix

K T0 :

Tangent stiffness matrix

P(x):

Pressure field along the x-direction

P 1 :

Maximum pressure

S :

Initial elemental stress matrix

α :

Thermal expansion coefficient

T :

Temperature environment

ΔT :

Temperature variation

T cr :

Critical buckling temperature

U :

Nodal displacement vector

ε :

Strain vector

σx, σy :

x-component and y-component of stress

ω :

Circular frequency

λ i :

i-th eigenvalue (buckling load factor)

Ψ i :

i-th eigenvector (buckling mode shape)

L, nL :

Linear and nonlinear

T:

Transpose

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Acknowledgments

The authors are very grateful to the supports of the National Natural Science Foundation of China (11572086, 11802059), the Natural Science Foundation of Jiangsu Province (BK20170022, BK20170656, BK20180062), and the Postgraduate Research & Practice Innovation Program of Jiangsu Province (KYCX18_0070).

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Authors and Affiliations

  1. Institute of Aerospace Machinery and Dynamics, Southeast University, Nanjing, 211189, China

    Xuan Yang, Qingguo Fei, Shaoqing Wu & Yanbin Li

  2. School of Mechanical Engineering, Southeast University, Nanjing, 211189, China

    Xuan Yang, Qingguo Fei & Yanbin Li

  3. Department of Engineering Mechanics, Southeast University, Nanjing, 211189, China

    Shaoqing Wu

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  1. Xuan Yang
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  2. Qingguo Fei
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  4. Yanbin Li
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Correspondence to Qingguo Fei.

Additional information

Recommended by Editor No-cheol Park

Qingguo Fei is a Professor of the Institute of Aerospace Machinery and Dynamics, Southeast University, Nanjing, China. His research interest includes structural dynamics, nonlinear analysis and modal analysis.

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Yang, X., Fei, Q., Wu, S. et al. Thermal buckling and dynamic characteristics of composite plates under pressure load. J Mech Sci Technol 34, 3117–3125 (2020). https://doi.org/10.1007/s12206-020-0702-6

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  • DOI: https://doi.org/10.1007/s12206-020-0702-6

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