Neumann's method to solve boundary problems of elastic thin shells

Abstract

This paper studies possibilities to use Neumann's method to solve boundary problems of elastic thin shells. Variational statement of statical problems for shells allows examining the problems within the space of distributions. Convergence of the Neumann's method is proved for the shells with holes when the boundary of the domain is not completely fixed. Numerical implementation of the Neumann's method normally takes a lot of time before some reliable results can be achieved. This paper suggests a way to improve convergence of the process and allows for parallel computing and checkout procedure during calculations.

Keywords

• boundary problems
• theory of thin elastic shells
• Neumann's method
• variational principles
• Korn's inequality
• distributions
• embedding theorems
• Green tensor