Many theoretical and experimental investigations on reinforced rectangular plate have beenpublished. The former has two ways. One of them is to solve the partial differential equationof reinforced rectangular plate in equilibrium under the required boundary conditons, andthe other is by the method of strain energy.
In either case, we must solve simultaneous equations in final calculation. Especially inthe former case, simultaneous equations with infinite unknowns must be solved. Of course, we calculate simultaneous equations with finite unknowns approximately, but more termsare required for more accuracy in accordance with rigidity of reinforcement. And in thelatter case, that is to say, strain energy method, we meet similar difficulties.
The author proposed the following equation for rectangular plate with reinforcement at y-direction,
D(∂4w/∂x4+2∂4w/∂x2∂y2+∂4w/∂y4)=P-∑iEIiδ(x-xi)d4w/dy4x=xi
where w: deflexion of plate, D: rigidity of plate,
P: lateral load on plate, Ii: moment of inertia of i-th reinforcement,
δ(x-xi) Dirac's impulse function,
and he gave its solution as follows,
w=∑<m>n[a°mn-1/{(mπ/a)2+(nπ/b)2}2∑jAj∑<α>a°αnsinαπxj/a]sinmπx/asinnπy/b
where a°mn=4/abD1/{(mπ/a)2+(nπ/b)2}2∫a0∫b0P(ξ, η)sinmπξ/asinnπη/bdξdη
In case of the plate with one or two edges (opposite each other) clamped,
lim xj→0oraγj→∞ amn is taken for above amn,
where γj=2EIj/Da
From the results, he reduced the formulae for rectangular plate with clamped edges and without reinforcement.
Moreover, the author proposed a new calculation methodd of rectangular plate with concentrated load, by expressing the load in Dirac's impulse function. In this way, concentrated load is handled like uniformly distributed load.
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