基于分数阶Kelvin黏弹性模型的固体推进剂药柱应力分析

利用黏弹性材料本构关系的Laplace变换与弹性材料的形式相似性,得到了分数阶Kelvin黏弹性模型弹性模量和泊松比的Laplace变换解.将固体推进剂药柱视为黏弹性介质,并利用分数阶Kelvin本构模型来描述其应力-应变关系.在推进剂药柱应力弹性解的基础上,运用弹性-黏弹性对应原理得到了分数阶Kelvin黏弹性模型描述的推进剂药柱在均布内压作用下内力的拉氏解,通过Laplace逆变换求得了其时域解.研究结果表明:推进剂药柱径向应力总是压应力,而环向应力总是拉应力,分数阶Kelvin黏弹性模型的解可以退化到经典Kelvin黏弹性模型的解,分数导数的阶数越大,应力的绝对值越大.

Stress Analysis of Solid Propellant Grain Based on Fractional Derivative Kelvin Viscoelastic Model

Using the similarity between the transformation of viscoelastic materials constitutive relation and elastic materials,the Laplace transform solutions of elastic modulus and Poisson's ratio of fractional Kelvin viscoelastic model were obtained.The solid propellant grain was regarded as viscoelastic medium,and the stressstrain relationship of solid propellant grain was described by the fractional derivative Kelvin constitutive model.The Laplace solutions of the stress of solid propellant grain described by fractional derivative viscoelastic model under uniform internal pressure were obtained by using the elastic-viscoelastic correspondence principle based on the elastic solution of stress,and the solutions in time domain were also got by the inverse Laplace transform.The results indicated that the radial stress is always compressive stress and the circumferential stress is always pulling stress,and the solution of fractional derivative Kelvin viscoelastic model can be degenerated to the solution of classic Kelvin viscoelastic,and the absolute value of stress will be greater if the order of fractional derivative is greater.