The free vibration of curvilinearly stiffened shallow shells is investigated by the Ritz method. Based on the first-order shear deformation shell theory and three-dimensional (3D) curved beam theory, the strain and kinetic energies of the stiffened shells are introduced. The stiffener can be placed anywhere within the shell, without the need for having the stiffener and shell element nodes coincide. Numerical results with different geometrical shells and boundary conditions and different stiffener locations and curvatures are analyzed to verify the feasibility of the presented Ritz method for solving the problems. The results show good agreement with those using other methods, e.g., using a converged set of results obtained by Nastran.

In this paper, first, the meso-debonding process of a GAP/CL20/AP composite solid propellant under uniaxial tension was analyzed using the advantages of the material point method (MPM) and the finite element method (FEM) for the first time; then, the numerical simulation results were compared with the experiments. Based on the basic principle of modeling with the material point method, grains of different sizes were generated quickly and efficiently. Next, the grains were dispersed into particles, and the position information of the particles was mapped onto the background grid, so the background grids were used to determine the position of the grains. After that, the generated AP and CL20 grains were imported into the commercial software Abaqus through python scripting codes for numerical calculation. Based on macro-mechanical tests and a micro-numerical simulation, this paper studies the micro-internal mechanism that affects the macro-mechanical properties of composite solid propellants. Three interface parameters needed to be determined by parameter inversion, and the value of the objective interpolation function $\min R$ was 0.05078%. From a comparison, it was found that the numerical simulation results are in good agreement with the experimental results in the aspects of micro-crack cracking characteristics and the nominal stress–strain curve of propellants. After that, the influence of interface parameters on the stress–strain curve are discussed. The research in this paper has high scientific value and engineering application value and can provide important reference and guidance for the design of composite solid propellants and its mechanical property analyses, so as to solve the structural integrity problem of solid rocket motor charges.