A variational approach to the Cosserat-like continuum
A variational approach to the Cosserat-like continuum
- International Journal of Engineering Science, 31(11), p.1475-1483, 1993 .
The exposition given here is intended to show an equivalent variational approach to formulation of the virtual work principle for the Cosserat-like continuum. Stationarity conditions of an action integral lead to the Euler-Lagrange equations identified with the balance equations for stresses and couple-stresses within micropolar and micromorphic continua. Vector fields as independent variables are taken so as to satisfy the known Stokes' decomposition. Based on the standard variational arguments, for a given Lagrangian function and an assumed 1-parameter family of transformations of both the independent and dependent variables, the fundamental variational formula identified with the virtual work principle of the Cosserat-like continuum is obtained. To determine the immediate relations between the geometric variation of the boundary and the variation of the field variables the transversality conditions are used. A notion of an independent integral is used to define invariance conditions of the integral in question which is invariant under an action of an r-parameter Lie group.
INTEGRAL EQUATIONS
MATHEMATICAL TRANSFORMATIONS
NUMERICAL METHODS
STRESSES
VARIATIONAL TECHNIQUES
VECTORS
The exposition given here is intended to show an equivalent variational approach to formulation of the virtual work principle for the Cosserat-like continuum. Stationarity conditions of an action integral lead to the Euler-Lagrange equations identified with the balance equations for stresses and couple-stresses within micropolar and micromorphic continua. Vector fields as independent variables are taken so as to satisfy the known Stokes' decomposition. Based on the standard variational arguments, for a given Lagrangian function and an assumed 1-parameter family of transformations of both the independent and dependent variables, the fundamental variational formula identified with the virtual work principle of the Cosserat-like continuum is obtained. To determine the immediate relations between the geometric variation of the boundary and the variation of the field variables the transversality conditions are used. A notion of an independent integral is used to define invariance conditions of the integral in question which is invariant under an action of an r-parameter Lie group.
INTEGRAL EQUATIONS
MATHEMATICAL TRANSFORMATIONS
NUMERICAL METHODS
STRESSES
VARIATIONAL TECHNIQUES
VECTORS