that makes the prediction of viscoelastic relaxation moduli easy . the numerical example was presented in the end of this paper 給出的單向纖維復(fù)合材料的粘彈性松弛模量預(yù)測的數(shù)值算例驗證了該方法的有效性。
the viscoelastic relaxation moduli in time domain are obtained by the inverse laplace transform of the curve-fitted formulae . the method takes advantage of rational curve-fitted formulae and avoids complicated numerical inverse laplace transform 該方法利用合理的曲線擬合函數(shù)避開了復(fù)雜的數(shù)值laplace逆變換,使得單向纖維增強復(fù)合材料的粘彈性性能的確定變得容易。
by laplace transforming the governing equation of the problem of unidirectional fiber reinforced composite materials, the formulae for predicting the viscoelastic relaxation moduli in laplace transformed domain are obtained . according to correspondence principle of viscoellastic mechanics and elastic, mechanics, the results of effective moduli for several s are obtained by using the finite element method of the homogenization . then effective relaxation moduli should be curve-fitted, according to the viscoelastic relaxation modulus formulae of many viscoelastic materials 首先對單向纖維增強復(fù)合材料粘彈性問題的控制方程進行l(wèi)aplace變換,在像空間s中利用均勻化理論建立宏觀松弛模量的laplace變換泛函形式,根據(jù)粘彈性-彈性對應(yīng)原理,用均勻化問題的有限元方法預(yù)報單向纖維增強復(fù)合材料在相空間中多個離散點的本構(gòu)關(guān)系,然后根據(jù)典型粘彈性材料的松弛模量具有的函數(shù)形式進行曲線擬合,再通過對擬合出的函數(shù)進行l(wèi)aplace逆變換,從而再回到時間t域,就得到了單向纖維增強復(fù)合材料的松弛模量。
by laplace transforming the governing equation of the problem of unidirectional fiber reinforced composite materials, the formulae for predicting the viscoelastic relaxation moduli in laplace transformed domain are obtained . according to correspondence principle of viscoellastic mechanics and elastic, mechanics, the results of effective moduli for several s are obtained by using the finite element method of the homogenization . then effective relaxation moduli should be curve-fitted, according to the viscoelastic relaxation modulus formulae of many viscoelastic materials 首先對單向纖維增強復(fù)合材料粘彈性問題的控制方程進行l(wèi)aplace變換,在像空間s中利用均勻化理論建立宏觀松弛模量的laplace變換泛函形式,根據(jù)粘彈性-彈性對應(yīng)原理,用均勻化問題的有限元方法預(yù)報單向纖維增強復(fù)合材料在相空間中多個離散點的本構(gòu)關(guān)系,然后根據(jù)典型粘彈性材料的松弛模量具有的函數(shù)形式進行曲線擬合,再通過對擬合出的函數(shù)進行l(wèi)aplace逆變換,從而再回到時間t域,就得到了單向纖維增強復(fù)合材料的松弛模量。
and then the brief description of the researches in micro-mechanics is presented . ( see chapter 1 ) 2 . the basic conception of the homogenization theory is given, and then by laplace transforming, the formulae for predicting the viscoelastic relaxation moduli in laplace transformed domain are obtained from the governing equation of the problem of composite materials (詳見第一章)2、在簡要介紹細觀多尺度均勻化方法的基本理論的基礎(chǔ)上,通過復(fù)合材料粘彈性問題的控制方程的laplace變換,并利用對應(yīng)原理,在像空間中導(dǎo)出了利用均勻化理論預(yù)測宏觀松弛模量的laplace變換泛函形式。