Derivation of the Classical Theoretical Elasticity Plate Equation by Systematic Thickness Parameter Expansion . Herleitung der Plattengleichung der Klassischen Elastizitaetstheorie durch Systematische Entwicklung Nach Einem Dickenparameter

摘要

Elastic plate bending differential equations for top and bottom random loading are derived using two approximation methods. Firstly, a direct method is demonstrated, in which the boundary conditions on the top and bottom are developed using the parameter h, the half plate thickness divided by a characteristic length. Secondly, calculus of variations is used for approximation. For both methods the linear infinitesimal elasticity theory is employed and the result contains the known plate equations as the lowest approximation.