超奇异积分方程及其在多孔弹性材料中的应用
Hypersingular Integral Equations and Applications to Porous Elastic Materials
AI总结：
本文提出了一种高效的直接数值配置法处理超奇异积分方程，并将其应用于Cowin-Nunziato模型描述的多孔弹性材料中的裂纹问题，研究了应力集中因子与材料孔隙率的关系。
摘要：
本文介绍了超奇异积分方程的处理方法，这些方程在具有混合边界条件的波动力学、弹性力学和流体力学等许多问题中具有重要应用。本研究的主要目标是开发一种高效的直接数值配置法。工作的第二部分致力于将该方法应用于多孔弹性材料。这部分涉及经典问题：在由Cowin-Nunziato模型描述的特定多孔弹性材料中位错的裂纹。通过应用傅里叶积分变换，问题被简化为一些积分方程。对于平面应变问题，我们采用直接数值处理超奇异积分方程。我们还研究了应力集中因子，并探讨了其随材料孔隙率的变化行为。最后，我们探讨了将结果推广到热弹性情况的可能性。
英文摘要：
In this paper a treatment of hypersingular integral equations, which have relevant applications in many problems of wave dynamics, elasticity and fluid mechanics with mixed boundary conditions, is presented. The main goal of the present work is the development of an efficient direct numerical collocation method. The second part of the work is devoted to the application of the method to the porous elastic materials. This part deals with classical problem for cracks dislocated in a certain very specific porous elastic material, described by a Cowin-Nunziato model. By applying Fourier integral transform the problem is reduced to some integral equations. For the plane-strain problem we operate with a direct numerical treatment of a hypersingular integral equation. We also study stress-concentration factor, and investigate its behaviour versus porosity of the material. At the end we investigate the possibility to extend the results in the thermoelastic case.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
