Neumann's method for boundary problems of thin elastic shells

doi:10.1007/s10483-017-2190-6

Abstract

Abstract:

The possibility of using Neumann's method to solve the boundary problems for thin elastic shells is studied. The variational statement of the static problems for the shells allows for a problem examination within the distribution space. The convergence of Neumann's method is proven for the shells with holes when the boundary of the domain is not completely fixed. The numerical implementation of Neumann's method normally requires significant time before any reliable results can be achieved. This paper suggests a way to improve the convergence of the process, and allows for parallel computing and evaluation during the calculations.

Key words: thin elastic shell theory, nonlinear elliptic equation, fixed point, mixed boundary condition, growth condition, maximal regularity, homogenized equation, boundary problem, variational principle, Korn's inequality, embedding theorem, Neumann's method, distribution, Green tensor

2010 MSC Number:

Y. S. NEUSTADT. Neumann's method for boundary problems of thin elastic shells. Applied Mathematics and Mechanics (English Edition), 2017, 38(4): 543-556.

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