Abstract: SPH (smoothed particle hydrodynamics) has its natural advantages in dealing with the large deformation of the material, fracture and crack propagation due to the absence of mesh distortion. However, the tensile instability which is an inherent defect encountered in the conventional SPH, is an obstacle for further applying SPH in computational solid mechanics. TL-SPH (total Lagrangian-SPH) is an effective measure to improve the tensile instability, but it still faces some defects. For example, the accuracy may be not enough at the boundary region for the truncated supported domain of the particle. The interface conditions are difficult to be implemented strictly, and the crack propagation cannot be presented under the Total Lagrangian frame. So, first of all, TL-SPH is coupled with the high-order SPH method, which can achieve second-order accuracy. Moreover, the high-order method is simplified by reducing the number of neighbor particles to save the calculational cost, and TL-SFPM (TL-simplified finite particle method) method is proposed with a reasonable neighbor particles selection mode. Secondly, TL-SPH method is combined with the DFPM (discontinuous finite particle method), which can improve the accuracy of the interface. A contact algorithm based on the Riemann solution is proposed by establishing the Riemann model between two particles with different materials. Then the fluid-solid contact algorithm and the solid-solid contact algorithm are introduced, respectively. Moreover, to capture the damage form of the solid under external load, a particle damage model based on the total Lagrangian frame is proposed. Finally, the rationality and accuracy of the proposed TL-SFPM method, the contact algorithm and the damage model are verified by cases of the fluid-solid impact and solid-solid impact, which further extends the application of TL-SPH method in the calculation of solid impact problems. The results of the dam break with an elastic baffle and the bullet impacting target plate also demonstrate the algorithms proposed in this paper has a wide application prospect for simulation of fluid-solid interaction and solid impact problems.