Calculation of Elastic Deflections of Thin Stiff Shells Based on the Finite Element Method out of the Kirchhoff’s Theory

Abstract

The computational method of determining thin stiff shells deflections formulated on the basis of the plane-spatial problem of the FEM without using Kirchhoff’s hypothesis is developed; in virtue of the geometric properties of the finite element stiffness matrix, a tensor of flexion stiffness is introduced. A linear and a nonlinear modification of the plane-spatial problem of the FEM for calculation of small elastic deflections of thin shells are formulated. An example of calculation of fragment of sloping conical shell is given in accordance with the common principles of two-dimensional domain discretization and some elements of fractal geometry.

Keywords

• finite element method
• antiplane shear
• plane-spatial problem
• kirchhoff’s hypothesis
• flexion stiffness
• tensor of flexion stiffness
• fractal geometry
• fragment of shell