Investigation by the Method of Integral Equations of the Stress State of the Implant an Intervertebral Disk at Axisymmetric Loading

Abstract

The stress state of an anisotropic ring disk of an implant of the intervertebral disk at complex axisymmetric loading is investigated in the work. The method of the integral equations is applied to the calculation of a stresses in a disk. The resolving system of integral equations is removed for the problem of an axisymmetric bend of an anisotropic ring disk of the variable thickness lying on the elastic basis of Vinkler. The received system of integral equations is tackled by the method of successive approximations. The exact solution of a flat task of the theory of elasticity is given for the calculation of the stretching stresses in the disk with the sedate law of change of its thickness testing the action of "the hydrostatic pressure" on the internal contour. A tangent stresses in a disk arising from the action of the constant torque on an external contour is calculated on known formulas. The offered mathematical model of calculation of the stress state of an implant of an intervertebral disk under the influence of the complex axisymmetric loading rather precisely describes its mechanical deformation.

Keywords

• an implant of an intervertebral disk
• an anisotropic disk
• integral equations
• a method of successive approximations