He did, once, in 2012, for three hours.
Before he found out that one of the survivors was Sarah Conner’s great grandmother?
Apart from what Shelly Duvall claimed, what other actor did he mistreat?
"It is certainly not true that chefs … commonly scream abuse at their employees, "
Gordon Ramsey
In “reality” shows, and even then in specific ones.
No actually, most directors are not abusive and violent. I’m certainly not and the mere accusation is extremely ignorant and offensive to me. The directors job is the guide the actors and the crew to get a specific vision across on screen. They are not there to do whatever it takes, and psychologically fuck up people whatever the cost in order to make it happen. Steven Speilberg certainly would take umbridge with that and so probably would George Lucas.
Ah, but are most directors able to read a calendar?
I think it was fairly common for filmmakers to do that in the past. If memory serves me, Judy Garland was treated like that in one of her films, and it’s well known that Gene Kelly was excessively harsh on Debbie Reynolds. I’m pretty sure there are plenty more examples. Drive ‘em to tears to bring out their best acting, and I guess give ‘em a good stiff slap if they won’t stop blubbering. 
Kubrick strikes me as anything but well adjusted, but maybe he thought he was just doing his job.
Out of interest I checked Shelley Duvall’s Wikipedia page, which has a side note to the Dr Phil episode and her recollections of Kubrick:
The interview refered to is on the Hollywood Reporter website.. (edited to add:) I quickly skimmed the interview, it provides much more detailed recollections of Kubrick, confirming the general impression in this thread but also seems not to have left a general traumatic memory on Duvall.
Commenting on the infamous Scatman Crothers multi-take - there are numerous things going on in the “Danny ice-cream” scene other than Scatman’s performance. Maybe Kubrick was getting those right as well as Scatman’s dialogue and it took a lot of takes to get everything synchronised and perfect. Lining up the knives above Danny’s head for instance, and yes, even things like reflections and lights on Scatman. There is a lot to the lights in The Shining.
Don’t forget that when Jackie Cooper was a child actor, director Norman Taurog got an emotional performance out of him by having a security guard take Cooper’s dog off the set and pretend to shoot it. And Norman Taurog was Jackie Cooper’s UNCLE for cryin’ out loud.
(An adult Jackie Cooper titled his autobiography about his career Please Don’t Shoot My Dog.)