The intrinsic theory of thin shells and plates. II. Application to thin plates

Abstract

The general equations for a thin plate. We shall now investigate the equations of equilibrium and compatibility for a thin plate, not necessarily of constant thickness. First, we shall introduce the condition that the system is a plate, i.e., its middle surface in the unstrained state is plane. We have therefore bafi = 0, Raf) " = 0. (7.1) Furthermore, in order to simplify the problem, we assume in the following sections that the body force forms a parallel vector field, and therefore (3.38), (3.39) are satisfied; this is true for most practical problems. Substituting (7.1) and the conditions on body force into (6.34) and (6.35), we have three equations of equilibrium for a thin plate -2+ WJ)X(q*h')]py + A"^qTaquqpyh^ + Pa