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101.
102.
将弹性细杆的"Kirchhoff动力学比拟"方法推广到弹性薄壳,使弹性薄壳的变形在物理概念上和刚体的运动对应, 在数学表述上等同,从而可以用刚体动力学的理论和方法研究弹性薄壳的变形,为连续的弹性薄壳提供新的离散化方法. 在直法线假设下,在弹性中面上构筑空间正交轴系, 此轴系沿坐标线"运动"的角速度构成两自变量的弯扭度. 沿两个坐标线的弯扭度表达了弹性薄壳的变形和位形,证明了弯扭度之间以及弯扭度与中面切矢间的相容关系. 用Euler角和Lam$\acute{e}$系数表达了非完整约束和中面位形的微分方程,用弯扭度和Lam$\acute{e}$系数表达了应变和应力以及内力及其本构方程.导出了用分布内力集度表达的弹性薄壳在变形后位形上的平衡偏微分方程组,方程的形式与刚体动力学的Euler方程和弹性细杆的Kirchhoff方程具有相似性,实现了Kirchhoff动力学比拟对弹性薄壳的推广.总结了弹性薄壳静力学和刚体动力学以及弹性细杆静力学在概念上的比拟关系.最后给出了一个算例. 为研究弹性薄壳的变形和运动提供新的建模方法和研究思路.也可进一步推广到弹性薄壳动力学. 相似文献
103.
An effective method is developed and used to investigate the antiplane problem of a rigid line in a confocal elliptic inhomogeneity
embedded in an infinite medium. The analytical solution is obtained. The proposed method is based upon the use of conformal
mapping and the theorem of analytic continuation. Special solutions which are verified by comparison with existing ones are
provided. Finally, the characteristics of stress singularity at the tip of the rigid line inhomogeneity are analyzed and the
extension forces for the crack and the rigid line inhomogeneity are derived.
The project supported by the National Natural Science Foundation of China, the State Education Commission Foundation and the
Failure Mechanics Lab of SEdC. 相似文献
104.
105.
Time-dependent natural convective heat transfer in a closed rectangular domain with heat-conducting boundaries of finite thickness is investigated numerically in the case of local heating on the inner side of the vertical wall. Convection-radiation heat transfer takes place on one of the outer boundaries of the solution domain. The inhomogeneous temperature distribution in the gas cavity is clearly manifested when the Grashof number Gr > 106. Circulation flows can be distinguished in various zones of the solution domain on the basis of the numerical investigations carried out. These flows are due to the effect of the heat-release source, the propagation of perturbations induced by elements of the rigid wall, and the dynamics of conductive heat transfer in the solid material. The scales of the effect of the Grashof number on the hydrodynamic and thermal characteristics are indicated. 相似文献
106.
Some exact results basic to the linearized Boltzmann equations for a binary mixture of rigid spheres
R. D. M. Garcia C. E. Siewert 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2006,57(6):999-1010
Six exact solutions (related to the conservation of number, energy and momentum) of the linearized Boltzmann equations for
a binary mixture of rigid spheres, for the case of isotropic scattering in the center-of-mass system, are reported. The verification
of the reported exact solutions (collisional invariants) is based on a recently reported explicit formulation of the linearized
Boltzmann equation for a binary mixture of rigid spheres. Elementary analysis is used also to establish a basic flow condition. 相似文献
107.
The exact expression for the electrostatic interaction between an ionpenetrable sphere and an ion-impenetrable rigid sphere is derived on the basis of the linearized Poisson-Boltzmann equation without recourse to Derjaguin's approximation. 相似文献
108.
Paul Gartside David Gauld Sina Greenwood 《Proceedings of the American Mathematical Society》2008,136(9):3363-3373
All metaLindelöf, and most countably paracompact, homogeneous manifolds are Hausdorff. Metacompact manifolds are never rigid. Every countable group can be realized as the group of autohomeomorphisms of a Lindelöf manifold. There is a rigid foliation of the plane.
109.
Lattice models (on a hypercubic lattice of dimension larger than or equal to three) with spins attaining a finite number of values and finite-range interactions at low temperatures are considered. The existence of rigid interfaces as well as of surface tension under appropriate conditions is proven and the properties of corresponding Gibbs states are investigated. 相似文献
110.