The Solutions of Elastostatics Derived from the Wave Modes : Two-dimensional Problems in Rectangular Domains

Abstract

This paper deals with the theory of obtaining the solutions of elastostatics from the solutions of elastodynamics, namely, wave modes. A harmonic wave in an elastic strip consists of P and S waves. These two waves fall into linear dependence at zero frequency. But, as the frequency of the wave tends to zero, the limits of the P or S wave and of a linear combination of the P and S waves become independent solutions of the static equation. There are innumerable pairs of such solutions. The general solution for a rectangular plate may be constructed in the form of a series of these solutions with unknown coefficients. Some problem are calculated numerically as application examples.