Existence of minimizers in the geometrically non-linear 6-parameter resultant shell theory with drilling rotations

TL;DR

This paper proves the existence of global minimizers for a general class of geometrically non-linear 6-parameter elastic shell models with drilling rotations, applicable to various anisotropic shell types.

Contribution

It establishes the first existence theorem for minimizers in a comprehensive 6-parameter shell theory with drilling degrees of freedom, covering general anisotropic shells.

Findings

Existence of global minimizers for non-linear 6-parameter shell equations.

The proof relies on convexity of the energy in strain and curvature measures.

Results applicable to isotropic, orthotropic, and composite shells.

Abstract

The paper is concerned with the geometrically non-linear theory of 6-parametric elastic shells with drilling degrees of freedom. This theory establishes a general model for shells, which is characterized by two independent kinematic fields: the translation vector and the rotation tensor. Thus, the kinematical structure of 6-parameter shells is identical to that of Cosserat shells. We show the existence of global minimizers for the geometrically non-linear 2D equations of elastic shells. The proof of the existence theorem is based on the direct methods of the calculus of variations using essentially the convexity of the energy in the strain and curvature measures. Since our result is valid for general anisotropic shells, we analyze separately the particular cases of isotropic shells, orthotropic shells, and composite shells.