Saczuk, J. text xx 9999 monographic und

electronic

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 https://drive.google.com/file/d/1p7AgE166sP2WHfR-mk4tjNJFbrbEw-np/view?usp=drivesdk https://drive.google.com/file/d/1p7AgE166sP2WHfR-mk4tjNJFbrbEw-np/view?usp=drivesdk 250602 20260521091552.0