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Now you have me lost. Where is there a circular part with 3 legs and a something going upwards?I assume that you mean the circular part with three attached "legs". I don't think an analysis has to be very complicated but it depends on the loading and if the circular part is supported upwards.
There is something going upwards above the circle, can that be a support? If it is and the loading is the same in the three legs, and the circle has a reasonable stiffness, and the dome in the circle has no structural function. Then it shouldn't be to complicated.