Mathematical Control of Space-Based Kinetic Energy Weapons Based on Partial Differential Equations and Evaluation of Their Destructive Effects

Abstract

This paper presents an in-depth study and analysis of the mathematical control of space-based kinetic energy weapons and the evaluation of the damaging effect by partial differential equations. The spectral element discrete format of the optimal control problem is constructed, the a priori error estimate of the control problem solution is proved theoretically, the posteriori error estimator is constructed, and the adaptive solution algorithm is designed. The posteriori error estimator is used as the encryption criterion to guide the local encryption of the grid so that the distribution of the dissection nodes is denser where the function regularity is poor. In the case of a compartment subjected to a shell attack, the effect of different factors on the structural damage of a single compartment under two explosions is investigated by varying the explosive mass, the location of the blast point, and the interval between the two explosions. In this paper, the problem of implosion in the cabin is studied, and the main factors affecting the response of the implosion structure are analyzed using dimensionality. The data of various simulation conditions are counted, and the dimensionless damage number is fitted with the deformation results of the bulkhead under each damage mode. It is still difficult to obtain the acceleration information of the target. Experimental studies were conducted on the composite honeycomb sandwich structure penetrated by fragmentation at different velocities and angles, and the accuracy of the theoretical model and the fragmentation residual formula was verified based on the test results. The analysis found that the antidamage performance of the composite honeycomb sandwich structure is better than the existing honeycomb sandwich body structure, and the energy absorption per unit volume of the structure is 27.2%–84.2% higher than that of the existing structure in the range of different penetration velocities. The average error between the theoretical calculation results and experimental results of the remaining velocity of the broken piece is within 6%, the error with the numerical simulation is about 8%, and the composite honeycomb sandwich structure with the best energy absorption characteristics and structural parameters is obtained.