A special application of Bassali's solution for transverse flexure of thin elastic plates supported at several points is presented for the case of symmetrical bending. Equations for moments , shearing forces. and stresses are developed which may be useful for design purposes. The ex perim e ntal results although limit ed in quantity are in good a.greement with the theoretical predic tion s.

(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...

A method is p rescn tcd for computing the comprcss iv e buckling load of a simply supported elastic rectangula r p latc having a central ci rc ular hole rcinforced by a circular doubler platc . Num erical res ults are presented for six square plates having hol e diamc ters up to onc-half of the platc le ngt h. Comparison of t hese res ults with t hose computed for platcs wit hout holes shows th a t an unreinforced ci rcular hole causcs a re Jati\'cly small rcduction in buck lin g load , and reinforcem ent of a circular holc by a doubler plate c au~es a s ub tan tial increase in buckling load .

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Finite element computer programs were developed for the planform analysis and the longitudinal cross-section analysis of metal sheet reinforced by adhesively bonded overlays of composite material. The analyses articulate the separate responses of the metal sheet, the composite overlays, and the adhesive layers. All materials are assumed to be orthotropic and linear elastic, with the provision that nonlinear interlaminar shear deformation can be approximated by a series of stepwiselinear solutions. The computer programs were developed specifically for the study of three general configurations: (1) a sheet with a reinforced cutout; (2) a sheet with a reinforced cutout with two symmetrical transverse cracks, within the sheet, radiating away from the cutout edge; and (3) a sheet with a reinforced transverse crack. The programs are also suitable for the study of bonded lap joints. The principal output of the computer programs is a set of contour plots of stress and strain fields throughout the sheet, the overlays, and the adhesive layers. A series of laboratory tests was conducted to demonstrate the validity of the analyses. Strains measured on the surfaces of specimens representing the general configurations studied were, for the most part, in good agreement with strains predicted by the finite element analyses. Significant correlations between certain failure modes and the stresses computed by the finite element analyses were apparent. Similarities between the modes of failure under static and fatigue loading were also evident.