本文探討多個異質物體的接觸問題，根據材料性質分為異向性彈性/黏彈性/壓電/磁電彈材料，並通過整理基本方程式可以整理成相同的數學表示式，對於壓電與磁電彈材料，我們利用材料系數的矩陣維度擴張，將適用於異向性彈性問題的史磋公式，拓展至壓電與磁電彈問題，處理黏彈性問題時則是使用彈性-黏彈性對應原理與時間步進法，前者透過Laplace轉換，將基本方程式轉換成通用表達式，求解完後再透過Laplace反轉換得到黏彈解，後者則是將問題分成兩個部分，分別是初始時間與各個步進時間，兩個部分均可整理成通用表達式，藉由初始時間與各個步進時間的疊加得到黏彈解。通過這種通用的數學式，無論考慮哪種材料，都可以利用彈性系統求解。
將傳統用於求解具有指定曳引力和/或指定位移邊界條件的二維異向性彈性固體問題的邊界元素法擴展到多體摩擦接觸問題。一個完整的線性方程組是由邊界積分方程式和接觸約束關係構成的。通過迭代檢查邊界條件是否滿足接觸準則，最終得到接觸解。
為了證明所提方法的有效性，本文提供了幾個數值例子，並利用商用有限元軟體ANSYS比對，並進一步討論了摩擦係數、材料異向性和孔洞等等對接觸的影響。

We consider the contact problem of multiple heterogeneous solids. According to the material properties, it is divided into anisotropic elastic / viscoelastic / piezoelectric / magneto-electro-elastic materials and can be organized into the same mathematical expression by sorting out the basic equations. For piezoelectric and magneto-electro-elastic materials, we extend the Stroh formalism for anisotropic elastic problems to piezoelectric materials and magneto-electro-elastic materials by expanding the related matrix dimension. For viscoelastic materials, we use the elastic-viscoelastic correspondence principle and the time-stepping method. The former uses Laplace transformation to convert the basic equation into a unified expression. After the solution is completed, the viscoelastic solution is obtained through Laplace inversion. The latter divides the problem into two parts, the initial time and each time step. Both parts can be organized into a unified expression, and the viscoelastic solution is obtained by the superposition of the initial time and each time step. With this unified expression, elastic systems can be used to solve whatever material is considered.
The traditional boundary element method for solving the two-dimensional anisotropic elastic solid problem with prescribed traction and/or prescribed displacement boundary conditions is extended to the multiple bodies friction contact problem. A complete system of linear equations is constructed by boundary integral equations and contact constraint relations. By iteratively checking whether the boundary conditions satisfy the contact criterion, the contact solution is finally obtained. Several numerical examples prove the effectiveness of the proposed methods and further discuss the influence of friction coefficient, material anisotropy, and holes on contact.

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