Subclasses of mechanical problems arising from the direct approach for homogeneous plates 

 -  In Recent Developments in the Theory of Shells. Springer, Cham., 43-63, 2019 .
<br/><br/> Pavel Andreevich Zhilin proposed a theory for deformable directed surfaces which builds a generalized framework in context of linear engineering theories of plates. We introduce this theory axiomatically, delineate the basic ideas and formalize the governing equations. In doing so we present a self-contained set of equations for time-invariant problems. Thereof, subclasses of mechanical problems can be deduced, whereby in present context the main existing theories are derived. These are in-plane and out-of-plane loaded plate problems. Next to the in-plane loaded plate problem, we also distinguish between transverse shear-deformable and transverse shear-rigid out-of-plane loaded plates. Typical representatives are the plate theories by Kirchhoff, Reissner, and Mindlin. 
<br/><br/><label>Subjects--Topical Terms: </label><br/>GENERALIZED PLATE THEORY<br/>IN-PLANE<br/>OUT-OF-PLANE<br/>TRANSVERSE SHEAR