TY  - BOOK
AU  - Saczuk,J.
TI  - A variational approach to the Cosserat-like continuum
KW  - INTEGRAL EQUATIONS
KW  - MATHEMATICAL TRANSFORMATIONS
KW  - NUMERICAL METHODS
KW  - STRESSES
KW  - VARIATIONAL TECHNIQUES
KW  - VECTORS
N2  - 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
UR  - https://drive.google.com/file/d/1p7AgE166sP2WHfR-mk4tjNJFbrbEw-np/view?usp=drivesdk
ER  -