三边夹紧一边自由的矩形厚板的弯曲
The Bending of a Thick Rectangular Plate with Three Clamped Edges and One Free Edge
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摘要: 利用厚板的Reissner理论中的广义简支边概念[1]得到了三边夹紧一边自由受均布横向载荷作用的矩形厚板的精确解.研究和考察了板的厚度对弯曲的影响及薄板弯曲的Kirchhoff理论的适用范围.Abstract: The exact solution of the bending of a thick rectangular plate with three clamped edges and one free edge under a uniform transverse load is obtained by means of the concept of generalized simply-supported boundary[1] in Reissner's theory of thick plates. The effect of the thickness h of a plate on the bending is studied and the applicable range of Kirchhoffs theory for bending of thin plates is considered.
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[1] Cheng Chang-jun(程昌钧) and Duan Da-ming(段大鸣),Concept of generalized simply-supported boundary in theory of thick plates,KEXUE TONGBAO,33,6(1988),472-477. [2] Reissner,E.,The effect of transverse shear deformation on the bending of elastic plates,J.Appl.Mech.,12(1945),69-86. [3] Reissner,E.,On bending of elastic plates,Quart.Appl.Math.,5(1947),55-68. [4] Salerno,V.and M.A.Goldberg,Effect of shear deformation on the bending of rectangular plates,J.Appl.Mech.,27(1960),54. [5] 程昌钧、尚新春,计及横向剪切变形效应的矩形板的弯曲,兰州大学学报(自然科学报),18,4(1982), 16-29. -
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