MATRIX FORMULATION OF CHEBYSHEV SOLUTION TO SHELL PROBLEMS | ||
| International Conference on Aerospace Sciences and Aviation Technology | ||
| Article 37, Volume 10, 10th International Conference On Aerospace Sciences & Aviation Technology, May 2003, Pages 571-587 PDF (2.35 M) | ||
| Document Type: Original Article | ||
| DOI: 10.21608/asat.2013.24469 | ||
| Authors | ||
| A. OKASHA EL-NADY1; HANI M. NEGM2 | ||
| 1Aerospace Research Center, A01. | ||
| 2Aerospace Eng. Dept., Cairo University. | ||
| Abstract | ||
| Any continuous function f(E) can be expanded in a Chebyshev series. The nth derivative of the function f(0 can be written in matrix form in terms of the expansion coefficients of the function. Also, the product of two functions f(E) and g(0 can be written in matrix form in terms of the expansion coefficients of the two functions. Therefore, any system of differential equations with variable coefficients can be written as a system of algebraic equations in terms of Chebyshev coefficients of the functions, which can be easily solved. The method is used to solve the problem of isotropic conical shell with different loads and boundary conditions. Results are computed and compared with the exact ones. Comparison proves onvergence, accuracy and reliability of the proposed method. | ||
| Keywords | ||
| Boundary-value problems. Differential equations. Chebyshev series. Shells. Conical shells | ||
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