Improved three-dimensional refined plate theory - Shimpi, R.P. (Archives of Mechanics, 2025)
The paper presents improvements over an earlier developed three-dimensional refined plate theory. The improved theory removes the disadvantage of the earlier theory in that it does not properly satisfy transverse shear stress conditions, and deficiency in being suitable only for flexure problems. The improved theory is suitable for use in flexure, as well as, for vibrations and stability problems of plates. The theory is simple, easy to use and accurate. The number of unknown variables involved are the same as those associated with thin plates, viz. only one in the case of flexure and vibrations; and three in the case of stability. The theory is based on displacement. The theory, to keep it as simple as possible, uses the concept of targeted displacements (which contribute only towards specific stresses, moments, shear forces, axial forces). All the stresses are represented realistically. The theory uses all strain displacement relations, and satisfies, as accurately as possible, all constitutive relations. The moments and forces satisfy gross equilibrium equations. The theory has some noteworthy similarities with the earlier developed well known theories. Due to these similarities, the experience of dealing with the earlier developed theories can be harnessed. Illustrative examples bring out the eficacy of the theory.