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首页> 外文期刊>Mathematical Problems in Engineering >On Spatial Evolution of the Solution of a Nonstandard Problem in Linear Thermo-Microstretch Elasticity
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On Spatial Evolution of the Solution of a Nonstandard Problem in Linear Thermo-Microstretch Elasticity

机译：线性热微拉伸弹性非标准问题解的空间演化

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摘要

An anisotropic and nonhomogeneous compressible linear thermo-microstretch elastic cylinder is subject to zero body loads and heat supply and zero lateral specific boundary conditions. The motion is induced by a time-dependent displacement, microrotation, microstretch, and temperature variation specified pointwise over the base. Further, the motion is constrained such that the displacement, microrotation, microstretch and temperature variation and their derivatives with respect to time at points in the cylinder and at a prescribed time are given in proportion to, but not identical with, their respective initial values. Two different cases for these proportional constants are treated. It is shown that certain integrals of the solution spatially evolve with respect to the axial variable. Conditions are derived that show that the integrals exhibit alternative behavior and in particular for the semi-infinite cylinder that there is either at least exponential growth or at most exponential decay.
机译：各向异性且非均质的可压缩线性热微拉伸弹性圆柱体承受零的身体载荷和热量，零横向的特定边界条件。该运动是由与时间有关的位移，微旋转，微拉伸和在基座上逐点指定的温度变化引起的。此外，运动受到限制，使得在圆柱体上的点处以及在规定的时间处的位移，微旋转，微拉伸和温度变化及其相对于时间的导数与它们各自的初始值成比例但不相同。这些比例常数有两种不同的情况。结果表明，解的某些积分相对于轴向变量在空间上演化。得出的条件表明，积分表现出可替代的行为，特别是对于半无限圆柱体，至少存在指数增长或至多呈指数衰减。

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