Research on optimization method of spacecraft stiffness based on variable section Timoshenko beam

Abstract

Thin-walled cylindrical or truncated conical structures are main load support segments in spacecrafts and rockets (including upper stages). The stiffness of these structures has to meet the requirements especially to avoid resonance with fundamental frequencies which may cause catastrophic destruction during the launch and aviation, limiting the reduction of the structure weight. Unlike cylindrical structures, the stiffness matrix of a truncated conical structure is strongly correlated to the variation of the cross section geometries. Timoshenko beam theory with variable cross section was applied to obtain an analytical solution of the stiffness matrix of a thin-walled truncated cone as a function of material and geometrical parameters. Considering a structure consisted of connecting thin-walled cylinders and truncated cones, the overall stiffness matrix was assembled by each of its sub-components and was used, together with the overall mass matrix, to calculate the fundamental frequencies rapidly. We verified the correctness of our analytical model by finite element analyses, showing a small deviation of less than 5.2%. With the preceding frequency-calculation method based on variable-cross-section Timoshenko beam theory, we proposed an optimization process by tuning geometrical parameters including thickness, height, diameters of cylindrical and truncated conical parts, aiming at minimizing the structural weight under given restrained fundamental frequencies. In a launch mission with an upper stage carrying two satellites, we applied the optimization with the particle swarm algorithm (PSO) and obtained optimal thicknesses for each sub-components. Several cases with different initial conditions showed consistent results, demonstrating the robustness of the optimization process. We believe it tends to be a potential and powerful tool for accelerating the structural prototype design of spacecrafts and rockets.