Three-dimensional grain stress analysis based on the boundary integral equation method. Volume 1: Analytical formulation

The theory is presented of the three-dimensional grain stress analysis program based on the boundary integral equation method, which is based on a surface integral representation of the theory of elasticity for isotropic and linearly elastic solids. The boundary integral equation method was extended to include body forces which are derivable from a potential function. Particular boundary solutions are generated within the strain potential approach which are combined with the prescribed boundary conditions to define a homogeneous problem. Cyclic symmetry considerations are included in the analysis. The numerical results are compared with those of the finite element analysis for typical solid propellant grain configurations. Theoretical and numerical formulations are presented.