Paper number 1362


G.L.Narasimham1 and R.Ramesh Kumar2

1Composites Group, Vattiyoorkavu, Vikram Sarabhai Space Center,Trivandrum 695013,India
2Structural Engg Group, VRC, Vikram Sarabhai Space Center,Trivandrum 695022,India

Summary A structural synthesis is made for FRP shell structure that does not buckle under axial load, and is stable up to compressive failure. A multi layer shell construction with defined non-geodesic filament orientation and shell wall thickness is determined. From equilibrium and stability requirements the shell surface turns out to be warped or to possess negative Gauss curvature K. They have zero normal curvature for the directions in which reinforcements run. The definition of isometric deformation is seen as shell bending. Hyperbolic geodesics introduced in this paper are in accordance with Gauss Egregium Theorem and are seen essential to the structural stability of thin walled shells. It is viewed as a stability criterion. Generalized Mohr's circles are drawn to depict changes in curvature during isometric bending. Initially finite element analysis of reticulated pseudospherical shell is carried out. A multi-layered FRP shell made of high modulus graphite composite has high resistance to buckling ,with stress at buckling highest so far obtained. The design of pseudosphere derived from static equilibrium and stability defined here is independant of length to maximum diameter ratio This size independance is theoretically built into synthesis and as well verified by analysis.
Keywords bending, iometric invariance, theorema egregium, hyperbolic geodesics, negative Gauss curvature, asymptotic directions, pseudosphere, non-Euclidean hyperbolic geometry ,generalized Mohr's circle for isometric bending, Tchebycheff net,inverse isometry.

Theme : Composite Structures ; Simulation

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