Deflection relationships between classical and third-order plate theories. (English) Zbl 0912.73027
Summary: We derive a differential relationship between the deflections of the classical Kirchhoff and third-order Reddy plate theories, and use it to determine the relationship between the deflections of polygonal plates with simply supported boundary conditions. As an example, we obtain the deflection of a simply supported rectangular plate using the third-order plate theory and the relationship developed herein. The relationship indicates that the third-order theory yields for simply supported rectangular plates virtually the same solutions as the first-order theory.
MSC:
| 74K20 | Plates |
Keywords:
Kirchhoff plate theory; third-order Reddy plate theory; polygonal plates; simply supported boundary conditionsReferences:
| [1] | Reddy, J. N.: Mechanics of laminated composite plates: theory and analysis. Boca Raton: CRC Press, 1997. · Zbl 0899.73002 |
| [2] | Reddy, J. N.: A simple higher-order theory for laminated composites plates. J. Appl. Mech.51, 745-752 (1984). · Zbl 0549.73062 · doi:10.1115/1.3167719 |
| [3] | Reddy, J. N.: Energy and variatitional methods in applied mechanics. New York: John Wiley, 1984. |
| [4] | Wang, C. M., Alwis, W. A. M.: Simply supported polygonal Mindlin plate deflections using Kirchhoff plates. J. Eng. Mech.121, 1383-1385 (1995). · doi:10.1061/(ASCE)0733-9399(1995)121:12(1383) |
| [5] | Wang, C. M., Lee, K. H.: Deflection and stress-resultants of axisymmetric Mindlin plates in terms of corresponding Kirchhoff solutions. Int. J. Mech. Sci.38, 1179-1185 (1996). · Zbl 0862.73032 · doi:10.1016/0020-7403(96)00019-7 |
| [6] | Wang, C. M.: Relationships between Mindlin and Kirchhoff bending solutions for tapered circular and annular plates. Eng. Struct.19, 255-258 (1997). · doi:10.1016/S0141-0296(96)00080-6 |
| [7] | Marcus, H.: Die Theorie elastischer Gewebe. Berlin: Springer, 1932. · JFM 58.1297.13 |
| [8] | Conway, H. D.: Analogies between the buckling and vibration of polygonal plates and membranes. Can. Aeron. J.6, 263 (1960). |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
