Isoparametric finite element analysis for solid rocket motors

Abstract

Several large scale finite element computerprograms have been written for the stress analysis of solid propellant rocket motors during the past several years. The displacement formulation is employed, and continuum and shell elements are coupled together along the idealized interface of the grain or insulation and the motor case. However, since the continuum elements exhibit a linear variation in displacements along each edge, and the shell elements have a cubic variation in displacements along their length, gaps can develop at the common interface of a coupled continuum and shell element. This incompatibility may lead to errors in stress predictions at a very important area in the solid rocket motor, the case/liner or case/ grain bondline. In this present paper, the problem of grain/case finite element incompatibility is addressed within the framework of the conventional displacement formulation. Both the shell elements and the continuum elements are derived from the same quadratic isoparametric shape function, yielding finite element idealizations which are totally compatible along the interface of a continuum and shell element. A numerical example is presented which shows the differences between the present compatible formulation and the conventional incompatible formulations.