Deflection of centrally loaded thin circular elastic plates on equally spaced point supports

Abstract

(Jul y 8, ] 966)Bassali 's ge ne ral th eo ry fo r the fl exure of th e thin c irc ul a r elastic pl a te suppo rted a t a n a rbitrary numbe r of points a nd subj ec ted to tran sverse load ove r a n ecce ntri c circle is spec ialized to th e case of a centrally load ed pla te s upporte d at points equally s paced on a c ircle co nce ntri c with th e ce nte r. Simplified me thod s fo r approximating th e res ults predi cted by th e more complic ated theo re ti cal ex· pressions for defl ec ti o n are prese nted along with th e ex pe rim e ntal res ult s from 138 tes ts . Both th e ex pe rimental res ults a nd th e simplifi ed equati ons a re co mp a red with the th eo ry and agree me nt is fo und to be good. Key Word s: Bassali 's th eo ry, co nce ntri c loading, circ ul a r plates, defl ec ti on, elast ic it y, exp eri · me ntal, fl exure, point supp orts, simplified app roximate soluti ons, thin plates. Introducti onThe de termination of the defl ec tion of a centrally loaded circular plate supported at points equally spaced on a circle concentric with the center has long bee n an important structural analysis proble m. In the past th e analysis of thi s problem was us ually limited by the assumption that th e point s upports were numerou s e nough to co ns titute a simple co ntinuous line support. Nadai [1] J presented a theory for the deformation of a circ ular plate s upported at several points with central point load or uniform load whic h was an improveme nt in that it recognized the errors involved in the afore me ntioned assumption. Unfortunately, Nadai's point s upports were located alon g the circumference of the plate. To some exte nt thi s limited the utility of the theory, as this me thod of support is unus ually diffic ult to realize in practi cal s tru ctures .More recently, Bassali [2] has give n the solution of the problem of fl exure of a thin circ ular elastic plate s upported at an arbitrary numb er of points whic h may b e located anywhere within the pl a te periphery, and loaded over a circular area lying anywhere within the boundary of the plate. Implicit in the work of Bassali is the solution of the problem of the centrally loaded plate supported at points equally spaced on a circle concentric with a central load. It may be noted . that the theory accounts for the cons training effec t of an annular region of the plate which overhangs the support circle and is otherwise free from restraint. This paper deals with the s p ecializ~ti~n of that part of the Bassali theory necessary to s· olve the particular proble m described above, and presents the rather tedious theoretical expressions for the defl ec tion at the ce nter of the plate and at a point midway between s upports locate d along the support circle. Since these expressions require considerable e ffort to e valuate, simplified methods of approximating the center d e flection may b e d esirable for d esign purposes. Therefore simplified expressions for ce nter de fl ection, based on the results of the exact theory, are given. Experim...

Symmetrical bending of thin circular elastic plates on equally spaced point supports

“…The test results presented herein were obtained from retesting specimen A of a previous investigation [3]. Since the specimens, materials, and test methods were fully described in the previous paper, it suffices here to indicate that the dead load method of testing was used, and the tangential strains were measured along the support circle (t = 0.976 and m = 3) by means of foil type electrical resistance strain gages having a gage length of 1/8 in.…”

“…In a previous paper [3] a special application of this more general solution was used to obtain a method of determining the deflection of a plate subjected to symmetrical bending with the load uniformly distributed over region 1. A c9mparison of theoretical and experimental results indicated that the theory adequately predicted the deflection of the plates over the range of geometries tested.…”

“…With regard to th e precedin g di sc ussion it was dee med desirable to extend the previous work [3] to e nco mpass moments, s hearin g forces, and stresses, for the purpose of presentin g equati ons which may be adapted to the design and analysis of structures of thi s type.…”

Deflection of thin circular elastic plates under symmetrically distributed loading

“…The theoretical expressions for the deflection of a plate were obtained from Bassali's work [2) and a previous specialization [1] of his work whic h dealt with the de fl ection of centrally loaded thin c ircular elastic plates on equally spaced point supports. The previous case considered that the point supports were located along a co ncentric circle outside of the central loaded area (in Region 2).…”

“…Figure 1 shows the concentric arrangement of the circular plate and defines Regions 1 and 2. Previously developed [1 , 2] general expressions pertaining to symm e tri cal bending are presented here as eqs (1) to (7)_ For the case considered here, the d evelopm e nt follows the same general reasoning_ The deflections of the plate in Regions 1 and 2 a re re prese nted by Po [ 1 11/ Rs (1)…”