Absolutely. Her %health damage works much better off of penetration than off of AP, so that's the offensive itemization you want to focus on. Outside of that, you just want tank stats. If you want a clearer picture of why stacking AP on her isn't really a good idea, try playing a match with her built as a straight AP assassin. Her damage output can ramp up rather severely from a combination of high AP and high penetration, but you'll quickly find that she starts losing steam during the lategame as she's entirely too easy to take down without sufficient bulk to back her up. She might not deal as much damage playing off of a meager amount of AP combined with stacked penetration, but she'll be able to deal that damage for much longer and make herself overall much more useful.
To give some reference, a standard build for her in S4 was Ancient Golem, Sorc Boots/Merc Treads depending on the enemy team, a Liandry's Torment, and then situational from there. A lot of people favored Rylai's Crystal Scepter, myself included, for the addition of a slow to her kit, making her spells deal double burn from the Liandry's, and the extra health. The 80 AP didn't exactly go to waste either, as her spider form deals AP based magic damage on hit, her spiderlings heal based partially on her AP, and her human form W still has a decent AP scaling. Abyssal Scepter was pretty popular if you needed some MR due to the fact that i made her W/autos a slight bit more potent, but the main draw was that amazing aura that just flat reduced MR around her by 20 while considerably buffing her own.
In general, she works a bit better as somewhat of a health tank than as a standard tank. You want her to be survivable enough to hop around a fight, but she probably shouldn't be the main source of tank for a team. She fits a kind of odd role as an AP bruissassin; in smaller skirmishes she serves as a decent tank, able to safely outlast one or two squishier foes, in slightly longer ones she can hop around disrupting the enemy while weakening the squishies, and in 1v1 situations she's an amazing duelist. An Elise usually won't be able to 100-0 burst someone, so she isn't an assassin in the vein of a high AD Rengar or an AP assassin like Kat, Akali, or Diana, but more along the lines of a Nocturne style assassin. If you're alone, she's going to kill you, it's just going to be a slightly more drawn out process consisting of you attempting to run away and her whittling you down while you try to. The best items for an Elise are ones that give a mix of durability and offenses, hence the focus on Liandry's/Rylai's as main offensive items, and items like Abyssal Scepter for defensive options. You don't want to focus on one to the exclusion of the other, but you have to know when to strike what balance and where. Elise is a VERY varied champion, and her standard build can be swapped out pretty freely as needed. I've seen, although I wouldn't suggest, builds centered around her spider form utilizing Nashor's Tooth, and I've seen builds that focus on CDR and tank stats so she can hit you more often with her W and Q in spider form to outlast you that way.
That being said, building tank items isn't the worst choice you can make. A Spirit Visage will increase the healing she's getting from her spiders hitting something, which can actually add up with 5 spiders up and her W maxed out. A Randuin's Omen applies an undeniably nifty slow that can help with disengages, disruptions, or slowing a fleeing enemy if you don't have any spells available to get that Rylai's proc off. Banshee's Veil lets her dive into enemy teams with relative impunity, although she should probably be followed up by a beefier tank if she didn't go in at the same time.
Your build's use of tank items isn't terrible, but the tank should come after her core items like Liandry's Torment unless your team just needs a dedicated tank and you're the only viable option. Her excellent ganks usually suffuse the need for building tank early on as cooperation between her and laners can allow for easy, quick kills, so she isn't taking all that much damage through the early game. Try to remember that you're comparing her to champions like Vi, Wukong, and JIV, all of whom have AoE CC available and incredibly powerful engagement options. An Elise has a stun... and that's about it. She isn't meant to dive headlong into enemy teams like that as her utility is meant for repositioning to either escape or put herself in a favorable position to take out a carry if possible. She shouldn't be the one running into a fight the way a JIV would E Q into one, or a Wukong would E R into one. She serves a different purpose and should be treated differently, even if their roles appear to be similar from a cursory glance.
I actually used to HATE Elise, half because she was a spider and half because I found her kit a bit odd and clunky. I didn't like it from a mechanical standpoint, but I sat down one day about half a year ago and committed myself to learning her. More I played her the more I found that her movements and abilities actually flow together pretty well once you've got a handle on her, and her clear speeds in season 4 were absolutely insane. Once I learned her better I was routinely outpacing the spawn timers. Elise is a great champ if you can learn her to the point that using her is half instinct and half trained response. I wish you the best of luck and I hope I was at least a bit helpful!