A new efficient buckling investigation of functionally graded CNT/fiber/polymer/metal composite panels exposed to hydrostatic pressure considering simultaneous manufacturing-induced agglomeration and imperfection issues

Abstract

The ultimate buckling capacity of the composite cylinders exposed to external hydrostatic pressure is identified as a critical factor in design, manufacturing and in-service life stages of these structures. This study deals with study and analysis of a new class of polymeric composite panels, consisting of metallic and fibrous layers and reinforced with functionally graded carbon nanotubes (FG-CNTs). Manufacturing-induced geometrical imperfection and CNT-agglomeration issues are among the commonly-reported problems associated with FG-CNT-reinforced composite panels under external pressure. On this account, this study will thoroughly scrutinize the influence of various parameters such as the fiber orientation, metal type and volume fraction, CNT volume fraction and distribution pattern, while both agglomeration and imperfection flaws are taken into account. The Galerkin method together with micromechanics models is employed in the solution procedure, and after verifying the proposed approach, the results are discussed in detail. Finally, key conclusions are presented to achieve the highest practical buckling capacity in the presence of agglomeration and imperfection problems.

Appendix

$$ a_{11} = A_{11} \left( {1 - \frac{{\tilde{a}}}{h}} \right) + A_{33} n^{2} \left( {1 + \frac{{\tilde{a}}}{h}} \right) $$

$$ a_{12} = a_{21} = - \left[ {A_{12} (1 - \frac{{\tilde{a}}}{h}) + A_{33} (1 + \frac{{\tilde{a}}}{h}) - \frac{{\tilde{a}}}{2R}(A_{12}^{\prime } - 2A_{33}^{\prime } )} \right]n $$

$$ a_{13} = a_{31} = \frac{{A_{12} }}{R}(\frac{{\tilde{a}}}{h} - 1) + \frac{{\tilde{a}}}{2}\left[ {A^{\prime}_{11} + (A^{\prime}_{12} - 2A^{\prime}_{33} )n^{2} } \right] $$

$$ a_{22} = A_{22} \left( {1 - \frac{{\tilde{a}}}{h}} \right)n^{2} + A_{33} \left( {1 + \frac{{\tilde{a}}}{h}} \right) + \frac{1}{{R^{2} }}(D_{22} n^{2} + 2D_{33} ) - \frac{{\tilde{a}}}{2R}(2A_{22}^{\prime } n^{2} - 3A_{33}^{\prime } ) + \frac{{A_{22} n^{2} }}{{2R^{2} }}\left( {\tilde{a}^{2} - \frac{{3\tilde{a}^{3} }}{2h}} \right) + \frac{{A_{66} }}{{R^{2} }}\left( {\tilde{a}^{2} + \frac{{3\tilde{a}^{3} }}{2h}} \right) $$

$$ a_{23} = a_{32} = \frac{{A_{22} n}}{R}\left( {1 - \frac{{\tilde{a}}}{h}} \right) + \frac{{D_{22} n^{3} + (D_{12} + 2D_{66} )n}}{R} - \frac{{\tilde{a}}}{2}\left[ {A_{22}^{\prime } \left( {n^{3} + \frac{n}{{R^{2} }}} \right) + (A_{12}^{\prime } + 2A_{66}^{\prime } )n} \right] + \frac{{A_{22} n^{3} + A_{12} n}}{2R}\left( {a^{2} - \frac{{a^{3} }}{2h}} \right) + \frac{{A_{66} n}}{2R}\left( {\tilde{a}^{2} + \frac{{\tilde{a}^{3} }}{2h}} \right) $$

$$ a_{33} = \frac{{A_{22} }}{R}\left( {1 - \frac{{\tilde{a}}}{h}} \right) + D_{11} + D_{22} n^{4} + 2(D_{12} + 2D_{66} )n^{2} - \frac{{\tilde{a}}}{2}\left[ {\frac{2}{R}(A_{12}^{\prime } + A_{22}^{\prime } n^{2} )} \right] + \frac{{A_{11} + A_{22} n^{4} + 2A_{12} n^{2} }}{2}\left( {\tilde{a}^{2} - \frac{{\tilde{a}^{3} }}{2h}} \right) + \frac{{A_{33} n^{2} }}{2}\left( {\tilde{a}^{2} + \frac{{\tilde{a}^{3} }}{2h}} \right) $$

$$ b_{11} = b_{12} = b_{13} = b_{21} = b_{31} = 0 $$

$$ b_{22} = \frac{1}{R} $$

$$ b_{23} = b_{32} = n $$

$$ b_{33} = \left( {n^{2} + \frac{1}{2}} \right)R $$