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題名 | Coupled Electroelastic Fields in an Orthotropic Piezoelectric Medium Containing Ellipsoidal Inclusions=含橢球同質體之正向性壓電材料的耦合電彈場 |
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作者 | 黃錦煌; | 書刊名 | 力學 |
卷期 | 12:2 1996.06[民85.06] |
頁次 | 頁229-241 |
分類號 | 440.33 |
關鍵詞 | 同質體方法; 耦合電彈場; 耦合電彈Eshelby張量; Inclusion method; Electroelastic field; Electroelastic eshelby tensors; |
語文 | 英文(English) |
中文摘要 | 本文旨在探討一正向性壓電材料含橢球同質體之耦合電彈場。經由微觀力學之同 質體方法,耦合電彈場被一致且明確地求得,然後利用此電彈場及使用柯西留數定理,求出 一組含四個耦合電彈 Eshelby 張量; 文中特別針對橢球體的一些特殊常見形狀:如旋轉橢 球體、橢圓柱、圓柱和錢幣狀等同質體的耦合電彈 Eshelby 張量以明確式表示出。 當壓電 耦合效應忽略不計時,文中的張量與傳統等向彈性體材料的 Eshelby 張量相吻合。 所以, 本文所得到的電彈 Eshelby 張量,不僅可供壓電材料之電彈場分析, 亦可應用於不考慮壓 電耦合效應之非等向性彈性材料的彈性場分析。最後,本文亦明確地將同質體的應力與電位 移之集中因子以一單一式表示出。文中所得到的結果,可廣泛地運用於破壞力學、壓電複合 材料、熱應力及含有瑕疵之壓電材料等諸問題。 |
英文摘要 | In the present paper, the inclusion method is employed to examine coupled electroelastic fields in orthotropoic piezoelectric solids containing ellipsoidal inclusions. By utilizing this method, a unified expression for the coupled electroelastic fields is obtained explicitly. The resulting electroelastic fields are further extended by the use of Cauchy's residue theorem to obtain a set of four electroelastic tensors analogous to Eshelby tensor for elastic inclusion problems. In particular, the electroelastic Eshelby tensors for several practical types of the orthotropic inclusion problems, such as spheroid, elliptic cylinder, circular cylinder, and penny shape, are presented explicitly. It is verified that when piezoelectric coupling is absent, such tensors reduce to those of Mura [1]. for isotropic elastic solids. Therefore, the resulting tensors are applicable not only to the general ellipsoidal inclusion in a piezoelectric solid but also to the elastic anisotropic inclusion problems. Finally, the stress and electric displacement concentration factors are obtained explicitly and also expressed in a unified form. The results obtained in the present paper can be applied to fracture mechanics, piezoelectric composite materials, thermal problems and to the piezoelectric material pertaining to defects, etc. |
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