The word I've seen for "tent" in koine is σκηνή, but this word doesn't seem to occur in Homer. The Greeks' shelters on the shore of Troy are κλισίαι, which Cunliffe translates as "hut or cabin," and derives from κλίνω, to lie.
Is there some other word in the Homeric dialect that means a tent, i.e., a fabric structure with poles, as opposed to a rigid structure? Or is κλισίη actually as general as implied by the etymology, just a place to lay your head, which could be translated as "tent?"
Your latter alternative is the right one; the general interpretation.
I agree @brianpck 's comment is as good as an answer. Κλισίη(α) is typically the hut where a shepherd spends the summer in the uplands pasture... These guys wouldn't spend a decade in movable tents (January averages 98mm of rainfall there). I am not sure the epic fighters knew about tents, a desert contraption designed for mobility.
Iliad 24.448 seq. is pretty clear on this:
ἀλλ᾽ ὅτε δὴ κλισίην Πηληϊάδεω ἀφίκοντο ὑψηλήν, τὴν Μυρμιδόνες ποίησαν ἄνακτι δοῦρ᾽ ἐλάτης κέρσαντες: ἀτὰρ καθύπερθεν ἔρεψαν λαχνήεντ᾽ ὄροφον λειμωνόθεν ἀμήσαντες: ἀμφὶ δέ οἱ μεγάλην αὐλὴν ποίησαν ἄνακτι σταυροῖσιν πυκινοῖσι: θύρην δ᾽ ἔχε μοῦνος ἐπιβλὴς εἰλάτινος, ...
(But when they were come to the hut of Peleus' son, the lofty hut which the Myrmidons had builded for their king, hewing therefor beams of fir —and they had roofed it over with downy thatch, gathered from the meadows; and round it they reared for him, their king, a great court with thick-set pales; and the door thereof was held by one single bar of fir ...)
The Perseus translation is so weird, that I'd indulge in Fagles'
Now, at last, they approached royal Achilles' shelter, the tall, imposing lodge the Myrmidons built their king, hewing planks of pine, and roofed it with thatch, gathering thick shaggy reeds from the meadow banks, and round it built their king a spacious courtyard fenced with close-set stakes. A single pine beam held the gates, ...
