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Postbuckling behavior of 3D braided rectangular plates subjected to uniaxial compression and transverse loads in thermal environments

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Abstract

Postbuckling behavior of the 3D braided rectangular plates subjected to uniaxial compression combined with transverse loads in thermal environments is presented. Based on a micro-macro-mechanical model, a 3D braided composite may be treated as a cell system and the geometry of each cell is deeply dependent on its position in the cross-section of the plate. The material properties of the epoxy are expressed as a linear function of temperature. Uniform, linear and nonlinear temperature distributions through the thickness are involved. The lateral pressure (three types of transverse loads, i.e. transverse uniform load; transverse patch load over a central area; and transverse sinusoidal load) is first converted into an initial deflection and the initial geometric imperfection of the plate is taken into account. The governing equations are based on Reddy’s higher-order shear deformation plate theory with a von Kármán-type of kinematic nonlinearity. Two cases of the in-plane boundary conditions are also taken into account. A perturbation technique is employed to determine buckling loads and postbuckling equilibrium paths of simply supported 3D braided rectangular plates. The results reveal that the temperature rise, geometric parameter, fiber volume fraction, braiding angle, the character of the in-plane boundary conditions and different types of initial transverse loads have a significant effect on the buckling and postbuckling behavior of the braided composite plates.

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Abbreviations

A ij , B ij , D ij :

Extensional, bending-extension coupling and bending stiffness

E f1, E f2, G f12 :

Young’s modulus, shear modulus of fiber

v f12, v f23 :

Poisson’s ratio of fiber

E m , G m :

Young’s modulus, shear modulus of matrix

v m :

Poisson’s ratio of matrix

E ij , F ij , H ij :

Higher-order stiffness

\(\bar F\), F :

Stress function and its dimensionless form

a :

Length of a rectangular plate

b :

Width of a rectangular plate

d :

Short axis of cross-section of the yarn

h :

Thickness of a rectangular plate

l k , m k , n k :

Direction cosines of a yarn in the coordinate system

M, N :

The numbers of thickness columns and wide rows of the braiding carriers

\(\bar N_i ,\bar M_i ,\bar P_i\) :

In-plane stress resultants, stress couples and higher-order stress couples, \(= \sum\limits_{k = 1}^m {\int_{t_k }^{t_{k + 1} } {\sigma _i \left( {1,Z,Z^2 } \right)dZ} }\)

\(\bar Q_{ij}\) :

The transformed elastic constants

H :

Pitch length

V f :

Fiber volume fractions

V m :

Matrix volume fractions

\(\bar U,\bar V\) :

Displacement components in the X and Y directions

\(\bar W\), W :

Deflection of plate and its dimensionless form

β :

Inclination angle between the projection of yarn axis on the Y′O′Z′ plane and the Y′-axis

γ :

Braiding angle between the yarn axis and the X′-axis

θ :

Surface braiding angle

φ i :

Solid cross-sectional orient angle of the yarn

\(\bar \Psi _X ,\bar \Psi _Y\) :

Rotations of the normals about the X and Y axes

Ψ x , Ψ y :

Dimensionless forms of \(\bar \Psi _X\) and \(\bar \Psi _Y\)

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Authors and Affiliations

  1. Shanghai Key Lab of Digital Manufacture for Thin-Walled Structures, School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China

    GuoPing Chu & ZhiMin Li

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  1. GuoPing Chu
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  2. ZhiMin Li
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Correspondence to ZhiMin Li.

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Chu, G., Li, Z. Postbuckling behavior of 3D braided rectangular plates subjected to uniaxial compression and transverse loads in thermal environments. Sci. China Technol. Sci. 57, 1439–1453 (2014). https://doi.org/10.1007/s11431-014-5568-3

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