Axisymmetric Body Force Research Articles

Response of bimaterials with interfacial tension subjected to axisymmetric body force

This paper presents an analytical treatment of the boundary value problem of an isotropic elastic bimaterial full space with interfacial tension subjected to an axisymmetric body force. The interfacial tension is modeled as the residual stress in the pre-tensed interfacial atom membrane on the basis of Gurtin and Murdoch’s surface theory. The generality of the present model is justified with several degenerated cases (e.g. classical bimaterials with bonded and unsinkable interface, homogeneous full space with interfacial tension, and half space with surface tension). By virtue of classical Hankel or Fourier transforms, the unconventional boundary value problems are addressed in a concise and systematic manner. The final solutions are all given in the form of a semi-infinite line integral. Particularly, the solutions for the interfacial response induced by interfacial point load can be obtained in exact closed form in terms of Struve and Bessel functions. Numerical results are presented to show the influence of interfacial tension on the induced responses. It is shown that the existence of interfacial tension can significantly influence the induced elastic fields and reduce the point load singularity. The results presented in this paper are useful and meaningful to the studies of nanocomposites, soft solids, and biological tissue, where the effects of surface/interface tension could be dominant.

Unsteady axisymmetric deformation of an elastic space with a spherical cavity under the action of body forces

A homogeneous elastic isotropic space with a spherical cavity is considered. Unsteady axisymmetric body forces are exerted on this space. Disturbances are absent at the boundary of the cavity. Series expansions in Legendre polynomials and their derivatives as well as the Laplace time transform are used. The solution is represented in an integral form with kernels in the form of Green’s functions. The structure of these kernels is determined and their originals are found. Numerical results are discussed.

1407 弾性円すい棒と剛体円すい孔の界面応力 : 等分布圧力を受ける場合(OS14-2 締結・接合部のプロセスと信頼性評価-接着接合-)

This paper is concerned with the interface stresses between a rigid conical-form hole and an elastic conical-form solid subjected to an uniform pressure. A body force distribution method is used to obtain the interface stresses. The method of solution is said to be a method of fundamental solution. We apply Green's functions for axisymmetric body force problems of an elastic half space. Influences of the tapered angle of the conical-form solid on the interface stress are considered and the results are compared with that subjected to a concentrated force at the center of surface of the conical-form solid.

21509 半球ピットに埋め込まれた半球状剛体をもつ半無限弾性体の界面応力(一般講演 機械材料・材料科学(2))

This paper deals with the interface stresses and the stress singularity of a hemispherical rigid body embedded in a hemispherical pit of an elastic half space. It is assumed that the interface is perfectly bonded and the hemispherical rigid body is subjected to a displacement in the axial direction. A body force distribution method is used to obtain the interface stresses. The method of solution is said to be a method of fundamental solution. We apply Green's functions for axisymmetric body force problems of an elastic half space.

OS0106 横等方性弾性円柱の軸対称熱応力(弾性数理解析とその応用,オーガナイズドセッション)

A method of fundamental solution is presented for axisymmetric thermal stress problems of a transversely isotropic elastic circular solid cylinder. We apply fundamental solutions for axisymmetric thermal stress problems and axisymmetric body force problems of transversely isotropic elastic solids. Thermal stresses and temperature distributions of a solid cylinder subjected to a heat distribution at the end surface are considered by numerical calculations.

10402 球状弾性介在物をもつ弾性円柱の引張り(材料(1))

This paper deals with a stress concentration problem of an elastic circular solid cylinder with an elastic spherical inclusion under tension. Effects of Poisson's ratio, especially effects of negative Poisson's ratio, on the stress concentrations are investigated. Lakes has shown that there are materials with negative Poisson's ratios. A method of solution is presented for the problem by applying Green's functions for axisymmetric body force problems of infinite circular solid cylinder and fundamental solutions for axisymmetric problems of elasticity.

A Boussinesq's Problem of an Elastic Half Space with an Elastic Spherical Inclusion

The problem of determing of stresses and displacements of an elastic half space subjected to a concentrated force acting at a point of the plane surface is called Boussinesq's problem. This paper deals with Boussinesq's problems of an elastic half space with an elastic spherical inclusion. We use a body force distribution method for the stress concentration problem. For this purpose, we apply the Green's functions for axisymmetric body force problems of an elastic half space and the fundamental solution for axisymmetric body force problems of elasticity. The problem is formulated by an integral equation with unknown functions corresponding to the intensities of distributed body forces. Stress distributions around the inclusion are shown by numerical calculations and influences of elastic moduli on the stresses are also investigated.

球状剛体介在物をもつ弾性円柱の表面圧力による応力集中(OS3-4 応力集中、最適設計他,OS3 先端機能性構造材料の力学的挙動に関する数理解析とマルチスケールアナリシスへの進展)

This paper deals with a stress concentration problem of an elastic circular solid cylinder with a rigid spherical inclusion under uniform surface pressures. A method of solution is presented for the problem by using Green's functions for axisymmetric body force problems of an elastic solid cylinder. Stress distributions around the inclusion are investigated.

Stress Concentrations of a Hollow Circular Cylinder with a Semicircular Notch under Internal Pressure.

This paper deals with the stress concentration problem of a hollow circular thick walled elastic cylinder with a semicircular groove under internal pressure. A method of solution is presented for the problem by applying Green's functions for axisymmetric body force problems of a thick plate. The Green's functions are defined as solutions for a thick plate subjected to axisymmetric body forces acting along a circle in the interior of the plate. A principle of the method of solution is to imagine a hollow cylinder with a notch and to distribute axisymmetric body forces in the thick plate so as to satisfy the boundary conditions of the hollow cylinder. The problem is formulated by an intergral equation with unknown functions of body forces. Stress concentrations at the notch are investigated by numerical calculations and stress distributions near the notch and form factors are shown. The maximum stress appears at the bottom of notch or the inner boundary of smallest cross section depending on the inner radius of cylinder and the notch radius.

836 球状弾性体介在物をもつ半無限弾性体の Boussinesq の問題

The problem of determing of stresses and displacements of an elastic half space subjected to a concentrated force acting at a point of the plane surface is called Boussinesq's problem. This paper deals with Boussinesq's problems of an elastic half space with an elastic spherical inclusion. We use a body force distribution method for the stress concentration problem. For this purpose, we apply the Green's functions for axisymmetric body force problems of an elastic half space and the fundamental solution for axisymmetric body force problems of elasticity. The problem is formulated by an integral equation with unknown functions corresponding to the intensities of distributed body forces. Stress distributions around the inclusion are shown by numerical calculations and influences of elastic moduli on the stresses are also investigated.

618 球状剛体介在物をもつ半無限弾性体の Boussinesq の問題 : 続, すべり境界の場合

This paper deals with the problem of determing of stresses and displacements of an elastic elastic half space with a rigid spherical inclusion in case of sliding interface. It is assumed that the half space is subjected to a concentrated normal force at a point on the plane surface of the half space. A method of solution is presented for the problem by using the Green's functions for axisymmetric body force problems of an elastic half space. Stresses and displacements around the inclusion are shown by numerical calculations and compared with the perfect bonding case. Influnces of Poisson's ratio on stresses and displacements are shown.

502 球状剛体介在物をもつ半無限弾性体の Boussinesq の問題

This paper deals with the problem of the determing of the stress and the displacement of an elastic half space with a rigid spherical inclusion. It is assumed that the half space is subjected to a concentrated normal force at a point on the plane surface of the half space. A method of solution is presented for the problem by using the Green's functions for axisymmetric body force problems of an elastic half space. The problem is formulated by an integral equation with unknown functions of the intensities of distributed body forces. Stresses and displacements around the inclusion of the half space are shown by numerical calculations.

123 半円切欠きみぞをもつ厚肉円筒の内圧による応力集中(GS-1 構造解析・応力解析(1))

This paper deals with the stress concentration problem of a hollow circular thick walled elastic cylinder with a semicircular groove under internal pressure. A method of solution is presented for the problem by applying Green's functions for axisymmetric body force problems of a thick plate. The Green's functions are defined as solutions for a thick plate subjected to axisymmetric body forces acting along a circle in the interior of the plate. A principle of the method of solution is to imagine a hollow cylinder with a notch and to distribute axisymmetric body forces in the thick plate so as to satisfy the boundary conditions of the hollow cylinder. The problem is formulated by an intergral equation with unknown functions of body forces. Stress concentrations at the notch are investigated by numerical calculations and stress distributions near the notch and form factors are shown. The maximum stress appears at the bottom of notch or the inner boundary of smallest cross section depending on the inner radius of cylinder and the notch radius.

K-0729 内壁に半円形環状切欠きをもつ厚肉円筒のねじり(G03-10 解析・シミュレーション)(G03 材料力学部門一般講演)

A stress concentration problem is considered for the torsion problem of an elastic thick walled circular cylinder with a semicircular notch at the inner surface. A method of solution is presented for the problem by applying Green's functions for torsional body force problems of an elastic thick walled circular cylinder. The Green's functions are defined as a solution for an elastic thick walled circular cylinder subjected to a axisymmetric torsional body force acting along a circle in the interior of the cylinder. Influences of the inner radius of the cylinder and of the radius of the notch on stress concentrations are investigated in this paper.

Green's Functions for Axisymmetric Body Force Problems of an Elastic Thick Infinite Plate and Their Application. Compression of a Thick Plate with a Spherical Cavity.

Green's functions are shown for axisymmetric body force problems of an elastic thick infinite plate. The Green's functions are defined as solutions to the problem of an elastic thick infinite plate subjected to axisymmetric body forces acting along a circle in the interior of the plate. The axisymmetric body forces considered here are a radial force and an axial force in cylindrical coordinates. Green's functions for torsional body force problems have been shown in a previous paper. In order to obtain the Green's functions, we apply stress functions for axisymmetric problems of elasticity. As an example of application of the Green's functions shown, we consider a stress concentration problem of a thick plate with a spherical cavity. It is assumed that a uniform pressure acts on the plane surfaces of the plate with a spherical cavity. The problem is formulated by an integral equation with unknown body forces. By numerical calculations, stress distributions around the cavity are shown. The results are compared with the exact solution for an infinite elastic solid with a spherical cavity.

251 等分布圧力を受ける半球ピットをもつ無限弾性厚板

This paper deals with the stress concentration problem of an elastic infinite thick plate with a hemispherical pit subjected to uniform pressure. The problem of an elastic half space with a hemispherical pit has been already inbestigeted. The present results for the thick plate are compared with the results for the half space. A method of solution is presented for the problem of a thick plate with a hemispherical pit by applying Green's functions for axisymmetric body force problems of an elastic infinite thick plate. The Green's functions are defined as solutions to the problem of an elastic infinite thick plate subjected to axisymmetric body forces acting along a circle in the interior of the plate.

370 部分はく離をもつ円柱状剛体介在物を有する無限弾性体の熱応力

This paper deals with the thermal stress problem of an elastic solid with a rigid circular cylindrical inclusion under a uniform temperature change. It is assumed that the end faces of the inclusion are semispherical form and there are partially debonded interfaces at the end faces of the inclusion. A method of solution is presented for the thermal stress problem by applying the fundamental solutions for axisymmetric body force problems of elasticity. Stress distributions around the inclusion are shown by numerical calculations.

838 部分はく離のある球状剛体介在物を有する無限弾性体の熱応力

This paper deals with the thermal stress problems of an elastic solid with a rigid spherical inclusion under a uniform temperature change. It is assumed that there are partially debonded interfaces between the surfaces of the inclusion and the matrix. We use a body force distribution method for the stress concentration problem. For this purpose, we apply the fundamental solution for axisymmetric body force problems of elasticity. The thermal stress fields are expressed by the elastic field due to temperature and the elastic filed due to body forces. Stress distributions around the inclusion are shown, and compared with the results for an elastic solid with a partially debonded rigid sphericaal inclusion under tension.

Tension of a Dissimilar Elastic Solid with a Spherical Cavity.

This paper deals with the stress concentration problem of a dissimilar elastic solid with a spherical cavity under tension. A method of solution is presented for the problem by applying Green's functions for axisymmetric problems of a dissimilar elastic solid. The Green's functions are defined as solutions to the elastic problem of a dissimilar solid subjected to axisymmetric body forces acting along a circle. The principle of the method of solution is to distribute body forces so as to satisfy boundary conditions for a spherical cavity. The problem is formulated by an integral equation with unknown body forces. Performing numerical calculations, influences of the elastic modulas of the dissimilar solid on the stress distributions on the interface and around the cavity are shown.

Torsion of an Elastic Solid Cylinder Embedded in an Elastic Half Space.

The stress transfer between an elastic solid cylinder under axially symmetric torsion and an elastic half-space in which the cylinder is partially embedded is investigated. A method of solving the problem is obtained by using Green's functions for axisymmetric torsional body force problems of an elastic half-space and the fundamental solution for torsion problems of an elastic solid. The Green's functions and the fundamental solution are defined as solutions to a half-space and a full space subjected to a torsional body force acting along a circle, respectively. Effects of the shear moduli of elasticity on the stress distributions at the interface are shown. A method of solution is investigated to obtain stress singularity factors at the interface.