Legendre–Hadamard Inequalities for Cosserat Elastic Shells With a Single Deformable Director
Abstract
Abstract We consider the general nonlinear theory of Cosserat elastic shells with a single deformable director and apply the methods of variational calculus to obtain the relevant Legendre–Hadamard inequalities. These are pointwise necessary conditions for stable equilibrium states, which are obtained from the property that the second variation of the total potential energy is non-negative. Thus, we establish a stability criterion that must be satisfied by any stable solution of the equilibrium equations for shells.
Fields of Study & Subjects
Nonlocal and gradient elasticity in micro/nano structures
Advanced Mathematical Modeling in Engineering
Contact Mechanics and Variational Inequalities
Publication details
- Journal / source
- Journal of Applied Mechanics
- Publisher
- ASME International
- Volume
- 93
- Issue
- 9
- Publication date
- 27 April 2026
- Language
- EN