MindlinTimoshenkoTheorie

The Mindlin-Timoshenko theory, also known as the Timoshenko-Mindlin theory, is a model used in the analysis of thick plates and shells. It extends the classical Kirchhoff-Love theory by incorporating the effects of shear deformation. Classical plate theory assumes that plane sections remain normal to the neutral surface after deformation, which is a valid assumption for thin plates. However, for thicker plates, shear deformation becomes significant and cannot be neglected.

The Mindlin-Timoshenko theory accounts for this by allowing plane sections to rotate during bending, thereby introducing shear strains. This leads to a more accurate representation of the displacement field and stress distribution, particularly in thicker structures or when large deflections are involved. The theory introduces two additional degrees of freedom per node compared to Kirchhoff plate theory, representing the rotations about the in-plane axes.

Key to the theory are the shear correction factors, which are empirical or semi-empirical coefficients used to reconcile the simplified shear strain assumptions with more rigorous elasticity solutions. The introduction of shear deformation leads to a system of coupled differential equations, which are generally more complex to solve than those arising from Kirchhoff theory. Despite this increased complexity, the Mindlin-Timoshenko theory provides a more physically realistic description of the behavior of thick plates and shells and is widely used in structural engineering and mechanical design applications.