The Halacha prohibits “Bitul Keli MeHechano”-neutralizing a vessel from functioning on Shabbat. That is, one may not perform an action that would render an otherwise permitted vessel Mukse. The classic example is placing a bowl underneath a hen to catch her egg. The egg is Mukse as “Nolad”-an item that came into being on Shabbat. Once the egg falls in the bowl, the bowl becomes Mukse as a “Ba'sees”-a base for Mukse. Putting the bowl under the hen is inherently prohibited, even if one has no intention of moving it after the egg falls there. Rashi seems to understand the root of the prohibition as "Soter"-destroying" a vessel. A vessel can be destroyed not only by shattering it, but by rendering it useless, as well.
The Ben Ish Hai (Rav Yosef Haim of Baghdad, 1833-1909), at the end of Parashat Mikes (the second year) brings a more common application of this prohibition. He prohibits placing empty nut shells on an empty plate on Shabbat. According to him, doing so constitutes “Bitul Keli MeHechano.” Since the shells are inedible to humans and animals, they are Mukse; therefore, placing them on the plate renders it useless. He offers a solution to place another item of value, such as the nuts or another food, on the plate. That way, the empty shells don't render the plate Mukse, since it is a base for non-Mukse items as well.
Hacham Ovadia, in Hazon Ovadia, takes issue with this ruling of the Ben Ish Hai. He argues that placing empty shells on a plate is not “Bitul Keli MeHechano,” for two reasons. First, “Bitul Keli MeHechano” is only when the intention is to leave the Mukse item on the vessel for the duration of Shabbat. He bases this on the opinion of the Meiri and the Ran, as cited by the Shilteh Giborim. In the case of the nut shells, a person generally wants to discard the shells once he finishes eating. Hacham Ovadia brings a proof to this from the Mishna Berura (Rav Yisrael Meir Kagan of Radin, 1839-1933) who cites the Magen Abraham (Rabbi Abraham Gombiner, Poland, 1637-1682) who permits catching dripping wax from candles in a plate. Even though Maran prohibits catching dripping oil, the Mishna Berura differentiates between the cases, since the oil is valuable and is meant to be kept in the vessel, whereas the wax will be discarded. This proves that there is no problem when the Mukse will not remain in the vessel.
Secondly, Hacham Ovadia argues that “Bitul Keli MeHechano” does not apply to a case such as the shells, which are so insignificant. Only an item of value, such as an egg, can neutralize the vessel.
Interestingly, several pages later (p. 219) in Hazon Ovadia, Hacham Ovadia seems to contradict this lenient ruling. Surprisingly, he quotes the ruling of the Ben Ish Hai verbatim that one should not put empty shells in a plate, seemingly agreeing with his position. The latest volume of the Mishna Berura Tiferet (Siman 310, note 15) points out this apparent contradiction. He reconciles the problem by explaining that the stricter position is brought as a Humra-stringency, but the basic Halacha is lenient.
The Menuhat Ahaba (Rabbi Moshe Halevy, Israel, 1961-2001) extends the stringent position of the Ben Ish Hai. He rules that one may not throw the shells in an empty garbage can, because that too is “Bitul Keli MeHechano.”
Hacham Ovadia (Hazon Ovadia Shabbat Vol. 3) disagrees and brings an additional lenient factor. Since the vessel of the garbage can is designated to receive refuse, it is not being taken out of its original function.
One may rely on the lenient opinions and place empty nut shells in a plate or in a garbage can on Shabbat, although it is praiseworthy to refrain from doing so.