Mindlin's Theory for thin plate is a mathematical model that describes the behavior of thin plates under various loading and boundary conditions. It takes into account the effects of both bending and shear deformation, making it more accurate than previous plate theories.
The key assumptions of Mindlin's Theory for thin plate are that the plate is thin compared to its other dimensions, that it has a constant thickness, and that it is made of a homogeneous and isotropic material. It also assumes that the plate is subjected to small deformations and that the strains are small.
Mindlin's Theory for thin plate has many practical applications, including in the field of structural engineering for the design of bridges, buildings, and aircraft components. It is also used in the analysis of thin shell structures, such as pressure vessels and pipelines.
Mindlin's Theory for thin plate is not suitable for thick plates or plates with large deformations. It also does not take into account the effects of plastic behavior or nonlinear materials. Additionally, it may not accurately predict the behavior of plates with complex geometries or boundary conditions.
Some recommended books on Mindlin's Theory for thin plate include "Theory of Plates and Shells" by S. Timoshenko and S. Woinowsky-Krieger, "Advanced Mechanics of Solids" by L. Srinath, and "Engineering Mechanics of Solids" by E. Popov. Websites such as ResearchGate, ScienceDirect, and SpringerLink also have numerous articles and research papers on Mindlin's Theory for thin plate.