Large deflection and post-buckling analysis of non-linearly elastic rods by wavelet method |
| |
Institution: | 1. Laboratoire d’Ingénierie et Matériaux (LIMAT), Faculté des Sciences Ben M’sik, Hassan II University of Casablanca, Avenue Idris Al Harthy, Sidi Othman B.P 7955, Casablanca, Morocco;2. Laboratoire de Mécanique, Faculté des Sciences Ain Chock, Hassan II University of Casablanca, Morocco;3. Institut Supérieur des Etudes Maritimes (ISEM), Km 7 Route d’El Jadida, Casablanca, Morocco;4. Université de Lorraine, CNRS, Arts et Métiers ParisTech, LEM3, Metz 57000, France;5. DAMAS, Laboratory of Excellence on Design of Alloy Metals for low-mAss Structures, Université de Lorraine, Metz 57000, France |
| |
Abstract: | We propose a wavelet method in the present study to analyze the large deflection bending and post-buckling problems of rods composed of non-linearly elastic materials, which are governed by a class of strong non-linear differential equations. This wavelet method is established based on a modified wavelet approximation of an interval bounded L2-function, which provides a new method for the large deflection bending and post-buckling problems of engineering structures. As an example, in this study, we considered the rod structures of non-linear materials that obey the Ludwick and the modified Ludwick constitutive laws. The numerical results for both large deflection bending and post-buckling problems are presented, illustrating the convergence and accuracy of the wavelet method. For the former, the wavelet solutions are more accurate than the finite element method and the shooting method embedded with the Euler method. For the latter, both bifurcation and limit loads can be easily and directly obtained by solving the extended systems. On the other hand, for the shooting method embedded with Runge–Kutta method, to obtain these values usually needs to choose a good starting value and repeat trial solutions many times, which can be a tough task. |
| |
Keywords: | Wavelet Galerkin method Large deflection Post-buckling analysis Non-linearly elastic rod Ludwick constitutive law |
本文献已被 ScienceDirect 等数据库收录! |
|