东北大学毕业设计（论文） 第2章 界面力学的基本理论
_???A1??B1?C1?A2??B2?C2_????B1??A1?D1?B2??A2?D2????? (2.25) ??(kA?B1?D1)?kA?B2??D222?11????????(kB?A1??C1)?k2B2?A2??C2?11_?i(??1)?1?i(??1)?1i(??1)?1A?e?Be?Ce?011?1_?i(??1)?2?i(??1)?2i(??1)?2A?e?Be?Ce?02?22????_ (2.26) ?B?ei(??1)?1?A1e?i(??1)?1?Dei(??1)?1?01?1???_??B?i(??1)?2?i(??1)?2i(??1)?1?A2e?D2e?0?2e为了同时求得待定系数间的关系，进而确定具体的应力场和位移场，我们采用以下方法化简式子(2.26)：
??e?2i?1?C1??????2i??1?D1??e??e2i?2?C2???????2i??2?D2??e式子(2.26)可以整理为：
e?2i??1??A1?? (2.27) 2i?1???e??B1?e2i??2??A2?? (2.28) ?2i?2??B?e??2???1??A1??C1???1??A2??C2??1???B???D???1???B???D? (2.29) ???1??1????2??2??C1????k2??A2??C2????k1??A1???????????????? (2.30) ???k1????B1??D1??k2????B2??D2?利用Dundur参数，为了简化其形式，采用变量替换：
?`?k2?1??(k1?1)???`?k2?1??(k1?1)? (2.31) ?`?k2?1??(k1?1)??由(2.31)式可得：
k2?1?(?`??`)/2?(k1?1)?(?`??`)/2 (2.32) 1???(?`??`)/2
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东北大学毕业设计（论文） 第2章 界面力学的基本理论
方程两边同除以γ`，则Dunders异材参数即为：???`/?`,???`/r`
利用它们之间的关系，可以将工程材料常数的影响改写为Dundurs参数表示的形式：
?1????A1????????1????A2??C1??0??????????? (2.33) ?????????????B1?0??B2??D1??1???1??1????A2??01????A1?????????1????A2??0???? (2.34) ?????1????B??1????????01??0????B2?????1????B2?将(2.27)，(2.28)代入式子(2.34)，得到：
?A1?1????B1?1???1????????e?2i??2????????1?e?2i?2???A????2? (2.35) ?????????1?e2??2?1????????e?2??2??B2???将(2.35)带入(2.33)，为了方便引入中间函数：
?????1?e2i? K(x)?sin2(?x)??2sin2x
得到：
????2????1?????2??????????????1???????????1?????????????2?????????????????????12????????1??????????????????2?1?????????1?