The location(s) in the first picture look like typical stress singularities. Set smaller mesh sizes in the location of the max stress. If successive solutions with smaller mesh sizes cause the max stress to increase at increasing rate, it is a stress singularity. Valid max stress values will approach a constant value asymptotically with successive solutions using smaller mesh size. Stress singularities occur at corners. If the region is not of interest just scope results away from these. If it is a region of interest, make small fillets/rounds at those locations and use a small enough mesh size to model the round.
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