We examine the profile of second harmonic generation (SHG) for GaAs/GaAlAs spherical quantum dots (QDs) of Woods-Saxon (WS) plus attractive inversely quadratic (AIQ) potential under the joint influence of additional factors (pressure and temperature) and structural parameters (strengths and radius). The energies and wave functions in GaAs/GaAlAs spherical QDs under WS-AIQ limiting potential are calculated using parametric Nikiforov-Uvarov (NU) method. Depending on the calculated energies and corresponding wave functions, the SHG coefficient is examined by the iterative procedure in the density matrix method for this system. Finally, the calculated results display that a strong SHG coefficient response, and red shift or blue shift energy can be acquired by adjusting parameters.