A geometrically exact Cosserat shell-model including size effects, avoiding degeneracy in the thin shell limit. Part I: Formal dimensional reduction for elastic plates and existence of minimizers for positive Cosserat couple modulus
A geometrically exact Cosserat shell-model including size effects, avoiding degeneracy in the thin shell limit. Part I: Formal dimensional reduction for elastic plates and existence of minimizers for positive Cosserat couple modulus
- Continuum Mechanics and Thermodynamics, 16(6), p.577-628, 2004 .
A consistent dimensional reduction of a finite-strain three-dimensional Cosserat micropolar elasticity model to the two-dimensional situation of thin plates and shells was studied. It was observed that the three-dimensional transverse boundary conditions can be evaluated analytically in terms of the assumed kinematics. The model includes size effects, transverse shear resistance, drilling degrees of freedom and accounts implicitly for thickness extension, and asymmetric shift of the midsurface. It was shown that the dimensionally reduced Cosserat formulation is well-posed for positive Cosserat couple modulus µc>0 by means of the direct methods of variations.
ELLIPTIC SYSTEMS
MEMBRANES
NON-SIMPLE MATERIALS
PLATES
POLAR MATERIALS
SHELLS
SOLID MECHANICS
THIN FILMS
VARIATIONAL METHODS
A consistent dimensional reduction of a finite-strain three-dimensional Cosserat micropolar elasticity model to the two-dimensional situation of thin plates and shells was studied. It was observed that the three-dimensional transverse boundary conditions can be evaluated analytically in terms of the assumed kinematics. The model includes size effects, transverse shear resistance, drilling degrees of freedom and accounts implicitly for thickness extension, and asymmetric shift of the midsurface. It was shown that the dimensionally reduced Cosserat formulation is well-posed for positive Cosserat couple modulus µc>0 by means of the direct methods of variations.
ELLIPTIC SYSTEMS
MEMBRANES
NON-SIMPLE MATERIALS
PLATES
POLAR MATERIALS
SHELLS
SOLID MECHANICS
THIN FILMS
VARIATIONAL METHODS