本文首先對含圓球體空穴之應力問題，以Trefftz法各項之係數及其應力散射場求得解集，其次利用扁橢圓球座標之波動方程式(兩組漢姆荷茲方程式)之Trefftz解集，又叫橢圓球波動函數(Spheroidal Wave Functions)，直接求得含橢圓球空穴之彈性體，受平面簡諧入射波入射所產生之應力散射場與位移場，由於此散射場為級數和，其各項級數之係數，可由橢圓體空穴邊界面上無應力之邊界條件所求得。並對當橢圓很扁宛如一圓碟形之裂縫時之應力場加以探討，並與其它文獻作比較。 最後並對求解所需之橢圓體波動函數之求法加以研究，並延伸至較高頻率之情況，本文提出之方法可求得準確之特徵值。 The stress fields for a spherical cavity were solved first. Then, the Trefftz solution sets of those governing equations (two sets of Helmholtz equations), which were also called spheroidal wave functions, were then applied to a scattering field from a plane harmonic compression wave, impinging on a elastic solid with a oblate spheroidal cavity. Since the scattering field is a sum of a series, the coefficient of each term was obtained by the traction-free boundary conditions on the surfaces of the spheroidal cavity. The problem when the oblate spheroidal cavity is very flat as a penny-shaped crack was discussed, also. Finally, the methods to finding the spheroidal wave functions were also discussed the case when the multiplications of wavenumber and focus length were up to 10 for oblate spheroid. A better method to find the accurate characteristic values was suggested
