耦合热弹性动力学的统一变分原理族
A FAMILY OF UNIFIED CLASSICAL VARIATIONAL PRINCIPLES IN COUPLED THERMOELASTO DYNAMICS
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摘要: 对耦合热弹性动力学问题，迄今文献中只建立了Ｇｕｒｔｉｎ型合卷积的统一变分原理，其缺点是只适用于常系数的线性问题，且因含卷积而使实际数值离散和求解复杂化．文中首次成功地建立了耦合热弹性动力学问题经典型（不含卷积）统一变分原理族，其关键是建议了动态差分变换和初终值条件的新处理法．该方法可以推广到各向异性材料以及非线性问题上去，同时在应用有限元法离散和求解上都比较简便．Abstract: The variational principle (VP) of classical type (excluding the Blot's VP, the Gurtin'sVP, the least square VP & various constrained VP, in which some unknown variables are frozenduring the variation operation) for the entitled problem is extremely difficult to establish, so that upto now all VP for this problem, to more or less degree, are constrained VP with the only exception ofthe Grutin's VP. However, the Gurtin's VP posesses the following two essential short-comings: 1) itis confined only to linear di...
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