Classic Plate Equation: Constitutive

Hooke's Law

The constitutive equation describes how the stresses and straines are related within the plate (Hooke's law).

In linear elasticity, the most generalized Hooke's law contains six (6) components of stresses that are linearly related to six (6) components of strains. Nevertheless, classical plate theory typically uses isotropic material in the Hooke's Equation.

The compliance (stress to strain) form is

The stiffness (strain to stress) form is

Note that the stresses and strains are functions of x, y, and z throughout the entire plate.

Constitutive Equation of Classical Plates Materials

Based on the kinematics of classical plates, the stress-strain relations can be simplified to

alternatively, they can be written as

and

which yields

 

 

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