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首页> 外文期刊>Zeitschrift fur Angewandte Mathematik und Mechanik >Transient response of a thermoelastic half-space to mechanical and thermal buried sources
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Transient response of a thermoelastic half-space to mechanical and thermal buried sources

机译：热弹性半空间对机械和热掩埋源的瞬态响应

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摘要

With the aid of a complete set of two scalar potential functions, the transient responses of an isotropic thermoelastic half-space subjected to time dependent tractions and heat flux applied to a finite patch at an arbitrary depth below a free surface are derived. Using the displacements- and temperature-potential function relationships, the coupled equations of motion and energy equation are uncoupled, resulting in two (6th and 2nd order) partial differential equations in the cylindrical coordinate system, which are solved with the aid of Fourier series expansion and joint Hankel-Laplace integral transforms. The solutions are also investigated in details for tractions varying with time in terms of a Heaviside step function and heat flux as a Dirac delta function, which may be used as a kernel in any integral based method for more complicated thermoelastodynamic initial-boundary value problems. Due to the complexity of the integrands involved in the general case, the integrals cannot be resolved analytically and thus an appropriate numerical algorithm is used for the inversion of the Laplace and Hankel integral transforms. To demonstrate the pattern of deformations as well as the distribution of change of temperature at the free surface of the half-space, numerical evaluations for these functions are presented for an isotropic material.
机译：借助于两个标量势函数的完整集合，得出各向同性热弹性半空间的瞬态响应，这些半空间受到时间依赖的牵引力，并在自由表面以下的任意深度处将热通量应用于有限的斑块。利用位移和温度势函数的关系，运动和能量方程的耦合方程解耦，从而在圆柱坐标系中产生两个（六阶和二阶）偏微分方程，借助傅立叶级数展开法求解以及汉克-拉普拉斯联合积分变换。还针对Heaviside阶跃函数和作为Dirac delta函数的热通量随时间变化的牵引力对解决方案进行了详细研究，该方法可在任何基于积分的方法中用作内核，以解决更复杂的热弹性动力学初值问题。由于一般情况下涉及的被积物的复杂性，无法解析地解析积分，因此使用适当的数值算法对Laplace和Hankel积分变换进行求逆。为了证明半空间自由表面的变形模式以及温度变化的分布，对各向同性材料提供了这些函数的数值评估。

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