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Buckling of bimodular composite plates

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Buckling and Postbuckling of Composite Plates

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Abstract

The linear theory of elasticity, based on the assumption of finite strain, assumes that materials obey Hooke’s generalized linear stress-strain relations. In general the elastic moduli relating the components of stress and strain only depend on the orientation of the coordinate system. Some materials exhibit elastic behaviour that differs under tension and compression. The stress-strain behaviour of these materials is not linear and hence a bilinear model is usually adopted as an approximate means of representing the moduli (Fig. 7.1). These materials are thus called bimodulus, bimodular, bilinear or different-modulus materials.

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Abbreviations

A y , B y , D y , E y , F y , G y , H y :

the laminate stiffnesses

a, b :

dimensions of the plate in x, y directions

C ijk , C ykl :

stiffness coefficients of stress-strain relations for isotropic and cross-ply plates

σ m :

in-plane bending stress

σ n :

in-plane normal stress

h :

plate thickness

z n :

neutral surface location for isotropic plate and Z n =z n/h

z nx , z ny :

neutral surface location for cross-ply plate and Z nx= Z nx/ h, Z ny= Z ny/ h

K :

non-dimensional buckling coefficient, Nxx b 2/ (π 2 D 22)

N y , M y , M y * , P y , P y * , R y , R y * :

initial stress resultants

Pl, ΔPl:

the applied surface traction and perturbing surface traction

S :

ratio of bending stress to normal stress, σ m / σ n

u l :

displacements of plate in x, y, z directions

u x , u y , w :

displacements of plate (z = 0) in x, y, z directions

φx, φy,φz:

rotations of plate in x, y, z directions

ξx, ξy, ξz,∅x,∅y:

higher-order shear deformation terms

E t , E c :

respective tensile and compressive Young’s moduli for isotropic plate

E t l , E c l :

respective tensile and compressive Young’s moduli in directions x, y, z and i = 1, 2, 3

G t , G c :

respective tensile and compressive shear moduli for isotropic plate

G ij t , G y c :

respective tensile and compressive shear moduli for orthotropic plate and i, j = 1, 2, 3

v t , v c :

respective tensile and compressive Poisson’s ratios for isotropic plate

v t y , v c y :

respective tensile and compressive Poisson’s ratios for orthotropic plate and i, j = 1, 2, 3

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Authors
  1. J. L. Doong
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  2. L. W. Chen
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Editor information

Editors and Affiliations

  1. Engineering Department, Lancaster University, UK

    G. J. Turvey

  2. Mechanical and Manufacturing Engineering Department, University of Paisley, UK

    I. H. Marshall

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© 1995 Springer Science+Business Media Dordrecht

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Doong, J.L., Chen, L.W. (1995). Buckling of bimodular composite plates. In: Turvey, G.J., Marshall, I.H. (eds) Buckling and Postbuckling of Composite Plates. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1228-4_7

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  • DOI: https://doi.org/10.1007/978-94-011-1228-4_7

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-4537-7

  • Online ISBN: 978-94-011-1228-4

  • eBook Packages: Springer Book Archive

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