It is developed a new approach to analyze the induced fission of heavy nuclei, which takes into account the nuclear dissipation phenomenon and the shell structure of nuclei in determination of fission barriers. The approach is based on the combined dynamical and statistical simulations. In the framework of this approach the method of calculation the fission fragment angular distributions in a wide energy range is discussed. The ability of the method is demonstrated in the simultaneous description of the experimental data of the fission probabilities on the Am and Pu nuclei, yields of the spontaneous fission of isomers for the α + 238U reaction at Eα = (20 - 32) MeV and the d + 242,240Pu reactions at Ed = (20 - 30) MeV, the fission times for the α + 238U reaction and angular distribution of fission fragments for the α + 238U, 237Np reactions at Eα = (20 - 100) MeV. A further information on the value of the nuclear dissipation at low excitation energies is obtained. In addition, it is demonstrated that the influence of the shell effects on the deformation potential energy holds up to excitation energies of about (50 - 60) MeV.