The coil spring plays an important role in absorbing the external forces and energy with deformation and releasing them after unloading. The coil spring in automobiles serves as a component to suspend the body of the automobiles. Since the coil spring requires to endure the several kinds of heavy loads without any damages during the all life-time, it is very important to obtain the exact deformation characteristics with stress distributions of the coil spring. The analysis of coil springs can be carried out with analytic solutions such as Wahl‘s equations based on the fundamental elasticity theory and numerical solutions by finite element method using continuum elements or beam elements.
In this study, computerized multi-level substructuring methods were developed and applied to analysis of springs. The purpose of substructuring methods is to reduce capacity of computer memory and computational time by multiple level reduction of the degrees of freedom of large size problems which are modeled by continuum elements. The finite element program developed is applied to some simple problems of tension, torsion, and bending of a bar with rectangular or circular cross section. The purpose of examples is to verify the accuracy and efficiency of the multi-level substructuring method schemes. The applications to the coil spring analysis demonstrate the validity of the multi-level substructuring method and the efficiency in computing time and memory.