Fem Analysis of Progressive Failure for Composite Hypar Shells
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FEM ANALYSIS OF PROGRESSIVE FAILURE FOR COMPOSITE HYPAR SHELLS A. Ghosh1 and D. Chakravorty2
UDC 539.4
The finite element method is used to to study progressive failure aspects of laminar composite skewed hypar shells with straight edges employing the eight-node isoparametric element in linear and elastic ranges under uniformly distributed static loading. A stiffness decrease scheme is proposed in which the stiffness properties of the failed element are gradually reduced resulting in redistribution of eveloping stresses on the extent of damage it accumulates. Specific numerical problems of earlier investigators are solved to validate the present approach. Numerical experiments are further carried out for different parametric variations, including some complicated boundary conditions and stacking orders of practical importance to obtain the first ply and progressive failure loads. Well accepted failure criteria are used to evaluate the failure loads and its development. Progressive failure in hypar shells are examined to arrive at some conclusions useful to the practicing engineers regarding tailoring guidelines of laminar composites and planning of nondestructive test programs for their health monitoring. Keywords: composite, finite element method, skewed hypar shells, progressive failure, first ply failure. Notation a, b
– length and width of the shell
c
– rise of hypar shell
{d}
– global displacement vectors
E11 , E 22 , E 33 – elastic moduli G12 , G13 , G23 – shear moduli {Q}
– transverse shear force vectors
q
– transverse loading intensity
R xy
– twist radius of curvature of the hypar shell
R, S , T
– shear stress strengths of a lamina
u, v, w
– displacements along X, Y, and Z axes, respectively
W
– transverse displacement in cm
w
3 4 – non-dimensional transverse displacement of shell, w = WE 22 h ( qa )
XT , XC
– normal stress strengths of a lamina along the fiber direction in tension and compression, respectively
Civil Engineering Department, Jadavpur University, Kolkata, West Bengal, India (1arghyaghosh698@ gmail.com; [email protected]). Translated from Problemy Prochnosti, No. 4, pp. 16 – 30, July – August, 2020. Original article submitted December 14, 2018. 0039–2316/20/5204–0507 © 2020 Springer Science+Business Media, LLC
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– normal stress strengths of the matrix along the perpendicular to the fiber direction in tension and
YT , YC
compression, respectively X, Y, Z
– global coordinates of the laminate
Z k , Z k -1
– top and bottom distance of the kth ply from mid-plane of a laminate
a, b
– rotations about X and Y axes, respectively
g xy , g xz , g
yz
e x, e y 0
– in-plane and transverse shear strain components, respectively – in-plane strain components along x and y axis
{e }
– in-plane strain vectors at the mid-surface
e1, e 2
– in-plane normal strains along 1 and 2 axes of a lamina, respectively
e6
– in-plane shear strain in 1–2 plane of a lamina
k x , k y , k xy
– curvatures of the shell due to load
n ij
– Poisson’s ratio
s 1, s 2 , s 6
– in-pl
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