Abstract: This problem is solved by dividing the quadratic yielding criterion into two linear partial differential equations. With the help of Cauchy’s integral, these two linear equations can be easily solved. An example is given to show the calculation of the stress components in the plastic domain and the determination of equation of the boundary line between the plastic and elastic domains.

Key words: asymmetric system, nonlinear normal mode, localization of vibration, bifurcation of normal mode, nonlinear dynamics