A dimensional splitting method for the linearly elastic shell
Kaitai Li, Xiaoqin Shen · International Journal of Computer Mathematics · 2007
In this paper, we split the 3-D linearly elastic shell problem into a 2-D problem by using the approach of formal asymptotic expansion. The approximate solution U KT (x, ξ) for the 3-D linearly elastic shell consists of , where u 0, u 1, u 2 are independent of ξ. The leading term u 0 satisfies a 2-D elliptic boundary value problem, and other terms u 1, u 2 will be derived using the algebraic expression for u 0 without solving PDEs. We prove that the solution u 0(x) exists and is unique, and give the error estimation for an elliptic membrane, which is smaller than the error with other models.