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題名 | A New Solution Methodology for Solving Dynamic and Static Antiplane Problem of a Layered Medium=反平面問題多層域動力與靜力分析之新方法 |
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作者 | 李艮生; 馬劍清; Lee, Genn-sheng; Ma, Chien-ching; |
期刊 | 中國機械工程學刊 |
出版日期 | 19981000 |
卷期 | 19:5 1998.10[民87.10] |
頁次 | 頁441-455 |
分類號 | 446.11 |
語文 | eng |
關鍵詞 | 反平面問題; 多層域動力; 靜力分析; 多層材料; Transient waves; Antiplane deformation; Matrix bromwich expansion; Static and dynamic analysis; |
中文摘要 | 本文將詳細探討多層材料受任意位置反平面載荷之動力與靜力解析。本文旨在發 展出一套有效的方法,以解析層板的暫態與靜力問題。對暫態解與靜力解而言,均可以矩陣 方式, 在轉換域中直接將求得的解析解作展開,而得到一由反射與透射矩陣 R 所構成的級 數解。由此暫態解與靜力解的逆轉換,可分別藉由 Cagniard 的方法與直接積出富立葉積分 式求得,而不用求逆轉換積分的殘值。本文中以一薄層覆於半無窮域之問題來進行數值計算 ,對一當時間夠長時趨向靜力載荷的衝擊加載而言,其靜力場可由暫態波場求得。 |
英文摘要 | In this study, the transient and static responses of a multilayered medium subjected to arbitrarily distributed antiplane loadings are investigated in detail. One of the objectives of this study is to develop an effective analytical method for determining transient and static full field solutions in the layered medium. A matrix method, for both transient and static solutions, is developed by expanding the matrix solution obtained directly from the boundary value problem in the transform domain into a power series of the phase-related reflection and transmission matrix R. The inverse transform is carried out, without evaluation of the residue, by the application of Cagniard's method for transient analysis and by the evaluation of the Fourier integral for static analysis. A case of a thin layer overlying a half-space is chosen for numerical examples. It is shown that the transient solution tends to the corresponding static one when time is sufficient long and the corresponding static field can be determined from the transient wave field. |
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