[[alternative]]Transient Response of a Permeable Crack in a Functionally Graded Piezoelectric Strip under Electromechanical Impacts

計畫編號：NSC100-2221-E032-021-MY2 研究期間：20110801~20120731 研究經費：435,000[[abstract]]本兩年期計畫將探討含可滲透裂紋之功能性梯度壓電材料(FGPM)受動力機電載 荷之暫態效應。第一年擬先研究含裂紋之功能性梯度壓電長條板於上、下自由表面受 「反平面」均佈應力與平面均佈電位移負載之動力破壞問題，透過於裂紋面反加拉普 拉斯轉換域中之應力來求得應力強度因子於轉換域中之解，最後可以獲得奇異積分方 程式，再求解此積分方程並做拉普拉斯數值逆轉換以求得本暫態問題的應力強度因子 時域解。第二年擬解析含裂紋之功能性梯度壓電長條板於上、下自由表面受「平面」 均佈應力與平面均佈電位移載荷之動力破壞問題，此問題因為乃承受平面應力，問題 將變得十分複雜、困難，本計畫同樣擬利用於裂紋面反加拉普拉斯轉換域中之應力可 求得應力強度因子於轉換域中之解，接著做拉普拉斯數值逆轉換以求得暫態時域解。 最後，並將對各年度之所有結果與相關文獻作詳細的比較與討論。[[abstract]]The two-year proposal is to investigate the transient response of a permeable crack in a functionally graded piezoelectric material (FGPM). The work of the first year studies the dynamic fracture problem of a FGPM strip subjected to “anti-plane” mechanical impact and in-plane electric displacement impact. The integral transform and the Cauchy singular integral equation methods are applied to obtain the solutions in the Laplace transformed domain. Durbin’s method is used to carry out the numerical inversion of Laplace transform. The accuracy is examined through some specified functions and the applicable numerical parameters are suggested respectively by the experience of calculation. In the second-year proposal, the transient analysis of the same FGPM strip as the first year, but subjected to “in-plane” mechanical impact and in-plane electric displacement impact is performed. The solution procedures are based on the use of integral transforms and singular integral equations. The solutions for the dynamic stress intensity factors will be derived and numerical results will be evaluated and discussed in detail for both years.[[sponsorship]]行政院國家科學委員