嵌在弹性半空间的刚性变直径圆轴的扭转*

本文用线载荷积分方程法(LLIEM)研究嵌在弹性半空间的刚性变直径圆轴的轴对称扭转.利用将“半空间的点环力偶”(PRCHS)这一虚的基本载荷沿对称轴的圆轴区间中分布就能使本问题归结为一个一维的非奇异的Ferdholm第一种积分方程,且很易用数值求解.文中给出刚性圆锥,圆柱,圆锥柱嵌在弹性半空间的扭转的数值计算的例并和他人的已知结果相比较.文中也给出了刚性半球嵌在弹性半空间的扭转的精确解.     

Solution of a Contact Elasticity Problem with a Rigid Inclusion

Computational Mathematics and Mathematical Physics - An equilibrium problem for an elastic body containing a rigid inclusion is solved. There is a delamination crack on a portion of the interface...     

Contact Problem for a Pneumatic Tire Interacting with a Rigid Foundation

Based on mixed finite-element approximations, a numerical algorithm is developed for solving a geometrically nonlinear contact problem for a prestressed multilayered Timoshenko-type shell undergoing arbitrarily large displacements and rotations. As unknowns, six displacements of faces of the shell are taken, which allows one to use principally new relationships for components of the Green–Lagrange strain tensor in curvilinear orthogonal coordinates, exactly representing arbitrarily large displacements of the shell as a rigid body. As an example, a tire interacting with a rigid foundation is considered.     

包含—受扭迴转轴的半空间的性质*

本文研究包含有一根部份嵌入的迴转轴的半空间的性质.不用知道一给定的嵌入的轴的扭转问题的精确解,这些性质能指出此半空间的位移或应力场的某些特点并且有时可以用来检查数值解.文中给出嵌入半空间的受扭的刚性圆柱的轴的表面上的正确的应力分布的检查的例子.     

半空间中一类调和函数的例外集

利用Whitney方体的相关性质, 给出了一类调和函数在半空间中无穷远点处的增长估计, 且刻画了其 例外集的几何性质. 本文推广了张艳慧和邓冠铁在半空间中的相关结果.     

半空间中一类次调和函数的增长性质

在Rn的半空间{x∈Rn,xn>0}中,得到了具有Dirichlet数据的Poisson积分在自然的积分收敛条件下满足增长性质u(x)=o(|x|),这里|x|→∞,这一性质对于半空间中满足一定条件的次调和函数仍然成立.该结果把复平面C中解析函数的增长性质推广到了n-维Euclidean半空间,并且推广了n-维Euclidean半空间中某些经典的结果.     

弹性薄板和薄扁壳及其在半空间上接触问题解的唯一性证明

用Laplace方程的第一种内边界问题不可能有两个不同的解这一定理,证明了弹性薄板和薄扁壳及其在半空间上接触问题解的唯一性问题。第二类内边界问题唯一性也得到证明。     

Sharp Growth Estimates for Modified Poisson Integrals in a Half Space

For continuous boundary data, including data of polynomial growth, modified Poisson integrals are used to write solutions to the half space Dirichlet and Neumann problems in Rⁿ. Pointwise growth estimates for these integrals are given and the estimates are proved sharp in a strong sense. For decaying data, a new type of modified Poisson integral is introduced and used to develop asymptotic expansions for solutions of these half space problems.     

Asymptotic of the Solution of the Contact Problem for a Thin Elastic Plate and a Viscoelastic Layer

The contact problem for a thin elastic rigid plate described by the elasticity equations and a viscoelastic layer is solved. The ratio of the thicknesses of the plate and the layer is a small parameter, while the ratio of the Young’s moduli of the layer and the plate is proportional to the cube of this parameter. The asymptotic expansion of the solution is constructed. A theorem on the estimate of the error of asymptotic approximation is formulated. Such problem appears in geophysics, in modeling of the Earth crust–magma interaction.     

A Contact Problem for a Half-Space and a Rigid Base with an Axially Symmetric Recess

An axially symmetric problem of frictionless contact interaction of an elastic half-space and a rigid base that has a small surface recess is considered. A corresponding problem of elasticity theory is formulated. The problem is solved by the method of double integral equations. The contact pressure, the surface shape of the half-space after compression, and the size of the gap are found in closed form.     

Classification of Positive Solutions to a Divergent Equation on the Upper Half Space

In this paper we classify the positive solutions of the divergent equation with Neumann boundary on the upper half space ■by the method of moving spheres and Kelvin transformations, where n≥1, α>0, β>-1,n-1/n+1β ≤α<β+2, and f :(0, ∞) →(0, ∞) is non-negative continuous function satisfying some conditions.This equation arises from a weighed Sobolev inequality involving divergent operator div(t~α?u) on the upper half space.