In this paper,for the solution of the torsion problem about the equation Δu=-2 with homogeneous Dirichlet boundary conditions in a bounded convex domain in Rn,we find a superharmonic function which implies the strict...In this paper,for the solution of the torsion problem about the equation Δu=-2 with homogeneous Dirichlet boundary conditions in a bounded convex domain in Rn,we find a superharmonic function which implies the strict concavity of u ^(1/2) and give some convexity estimates.It is a generalization of Makar-Limanov’s result(Makar-Limanov(1971))and Ma-Shi-Ye’s result(Ma et al.(2012)).展开更多
This paper deals mainly with the dynamic response of a rigid disc bonded to the surface of a layered poroelastic half-space. The disc is subjected to time-harmonic torsional moment loadings. The half space under consi...This paper deals mainly with the dynamic response of a rigid disc bonded to the surface of a layered poroelastic half-space. The disc is subjected to time-harmonic torsional moment loadings. The half space under consideration consists of a number of layers with different thickness and material properties. Hankel transform techniques and transferring matrix method are used to solve the governing equations. The continuity of the displacement and stress fields between different layers enabled derivation of closed-form solutions in the transform domain. On the assumption that the contact between the disc and the half space is perfectly bonded, this dynamic mixed boundary-value problem can be reduced to dual integral equations, which are further reduced to Fredholm integral equations of the second kind and solved by numerical procedures. Selected numerical results for the dynamic impedance and displacement amplitude of the disc resting on different saturated models are presented to show the influence of the material and geometrical properties of both the saturated soil-foundation system and the nature of the load acting on it. The conclusions obtained can serve as guidelines for practical engineering.展开更多
The solution of dynamic Point-Ring-Couple at the origin, on z=0 plane, in an elastic space is presented and its properties are discussed. Let shocking loads be uniformly distributed, along the direction of circumferen...The solution of dynamic Point-Ring-Couple at the origin, on z=0 plane, in an elastic space is presented and its properties are discussed. Let shocking loads be uniformly distributed, along the direction of circumference, at a circle, on z=0 plane, with radius a and centered at the origin. Then, the solution of our problem is obtained via integral calculation for a 0. When the intensity of this dynamic Point-Ring-Couple is varied with sincot, the cones in the elastic space with apex at the origin and the z-axis be its symmetric axis, become zero stressed surfaces at any time instance. The solution of dynamic torsion problem of revolution solids with these cones as boundary under the application of torque varied with sincot is found.展开更多
基金supported by National Key Research and Development Project (Grant No. SQ2020YFA070080)National Natural Science Foundation of China (Grant Nos. 11871255 and 11721101)supported by National Natural Science Foundation of China (Grant Nos. 11971137 and 11771396)
文摘In this paper,for the solution of the torsion problem about the equation Δu=-2 with homogeneous Dirichlet boundary conditions in a bounded convex domain in Rn,we find a superharmonic function which implies the strict concavity of u ^(1/2) and give some convexity estimates.It is a generalization of Makar-Limanov’s result(Makar-Limanov(1971))and Ma-Shi-Ye’s result(Ma et al.(2012)).
基金Project (No. 50079027) supported by the National Natural ScienceFoundation of China
文摘This paper deals mainly with the dynamic response of a rigid disc bonded to the surface of a layered poroelastic half-space. The disc is subjected to time-harmonic torsional moment loadings. The half space under consideration consists of a number of layers with different thickness and material properties. Hankel transform techniques and transferring matrix method are used to solve the governing equations. The continuity of the displacement and stress fields between different layers enabled derivation of closed-form solutions in the transform domain. On the assumption that the contact between the disc and the half space is perfectly bonded, this dynamic mixed boundary-value problem can be reduced to dual integral equations, which are further reduced to Fredholm integral equations of the second kind and solved by numerical procedures. Selected numerical results for the dynamic impedance and displacement amplitude of the disc resting on different saturated models are presented to show the influence of the material and geometrical properties of both the saturated soil-foundation system and the nature of the load acting on it. The conclusions obtained can serve as guidelines for practical engineering.
基金Project supported by Natural Science Foundation of Guangdong Province
文摘The solution of dynamic Point-Ring-Couple at the origin, on z=0 plane, in an elastic space is presented and its properties are discussed. Let shocking loads be uniformly distributed, along the direction of circumference, at a circle, on z=0 plane, with radius a and centered at the origin. Then, the solution of our problem is obtained via integral calculation for a 0. When the intensity of this dynamic Point-Ring-Couple is varied with sincot, the cones in the elastic space with apex at the origin and the z-axis be its symmetric axis, become zero stressed surfaces at any time instance. The solution of dynamic torsion problem of revolution solids with these cones as boundary under the application of torque varied with sincot is found.
