Development of Curved Thermoplastic Composite Tubes Theory and Experiment

1. Development of Curved Thermoplastic Composite Tubes Theory and Experiment Prepared by: Hamidreza Yazdani Supervised by: Dr. Suong. V. Hoa and Dr. Mehdi Hojjati

2. Outline • Problem statement • Literature review • Toroidal Elasticity Theory • Conclusions • Future works

3. Problem Statement • Aluminum landing gears have some technical issues • Fabrication is difficult and expensive • Failure due to the corrosion and Fatigue • The objective of this research project is to investigate how a composite landing gear can be designed and manufactured using thermoplastic composite materials and automated fiber placement technology.

4. Literature Review • Finite element approach • (Redekop and Tan 1987) • Analytical approach • Shell bending theory (Boyle and Spence 1992) • Membrane theory (Bushnell 1981) • Toroidal Elasticity (TE) • Stress approach (Lang 1989) • Displacement approach (Redekop 1991, 1993)

5. Toroidal Elasticity for Orthotropic Materials • Displacement field for composite toroidal structures based on successive approximation method • The governing equations in three toroidal coordinate system • Method of successive approximation • The governing equations in different orders • Different order displacement components

6. Governing Equations • R is bend radius. • Angular coordinates are θ and φ, and radial coordinate is r.

7. Governing Equations • Kinematics relations • Constitutive equations • Governing Navier equations in toroidal coordinate

8. Method of Successive Approximation • The solution is a series in terms of a small parameter • ε=1/R.

9. Governing Equations for the Different Orders • The zeroth order: • The first order: • The second order: • The third order:

10. General Solution • Complementary solution • General form solution

11. Boundary Conditions • The boundary conditions on the curved surfaces are satisfied by each order

12. The Zeroth Order Solution

13. The First Order Solution • Governing equations • Displacement components

14. The Second Order Solution • Governing equations • Displacement components

15. The Third Order Solution • Governing equations • Displacement components

16. Conclusions • Toroidal elasticity is a developing three-dimensional theory which can be used for the elastostatic analysis of thick-walled curved tubes. • A displacement based toroidal elasticity has been used. • The governing equations in the toroidal coordinates are much more complicated than those used in Cartesian coordinates. • The successive approximation method has been employed to simplify the governing equations.

17. Previous and Future works • Literature review • Finding the appropriate theory • Obtain the displacement field for isotropic materials • Obtain the displacement field for a layer of orthotropic materials • Achieve the displacement field for a laminate of orthotropic materials • Analysis of the curved tube dynamically • Comparison of the theoretical result with the experimental one