The Study of the Stress-Strain State of the Downhole Packer's Jaw Teeth Based on the Initial Functions Method

Abstract

Based on the application of the method of initial functions using a decomposition approach with the division of the problem into two subtasks with the same type of load at the edges, calculation formulas for displacements and stresses in polar coordinates are obtained. The solutions of these problems are constructed in elementary (polynomial-exponential) functions in the form of a general solution of an inhomogeneous differential equation with the right side, depending on the intensity of the load along the edges of the wedge with unsupported or reinforced edges. The solution of the problem obtained by the operational method using the one-sided Laplace transform depends on the uncertain coefficients of the expansion of the general solution of the corresponding homogeneous differential equation in terms of linearly independent equations determined by the roots of the characteristic equation. For each of the problems under consideration, a method is indicated for identifying these uncertain coefficients in the presence of a load along the edges of the wedge, both in the presence and absence of a higher force applied to the top.