为了对不均匀介质中物理场进行更有效的多尺度模拟,提出一种称为有限点集-网格元法的数值方法(finite point-grid element method,FPGEM).FPGEM是对传统有限元方法的改造,它把网格与节点分离成独立的两套覆盖,采用离散的有限点集对物理场进行多尺度逼近,同时采用网格剖分作为介质分布的几何载体;点集和网格各自扮演不同的角色,发挥不同的功能.FPGEM主要的优点是:由于其节点和网格分离,对场的非均匀性及介质非均匀分布具有双重的多尺度模拟的优势,为一些地球物理问题中的多尺度模拟提供了一种更加灵活、自然的计算框架.
Dynamic contact stiffness at the interface between a vibrating rigid sphere and a semi-infinite transversely isotropic viscoelastic solid is investigated. An oscillating force superimposed onto a static compressive force in the vertical direction excites the vibration of a rigid sphere, which causes variable contact radius and contact pressure distribution in the contact region. The assumption of a sufficiently small oscillating force yields a dynamic contact-pressure distribution of a constant contact radius, which gives dynamic contact stiffness at the interface between the rigid sphere and the semi-infinite solid. Numerical calculations show the influence of vibration frequency of the sphere, and elastic constants of the transversely isotropic solid on dynamic contact stiffness, which benefits quantitative evaluation of elastic constants and orientation of single hexagonal grains by resonance-frequency shifts of the oscillator in resonance ultrasound microscopy.
