Evaluation of the Stress Concentration Near Thin Elastic and Viscoelastic Inclusions

摘要

We present a survey of the efficient approximate methods for the evaluation of the stress concentration near notches, slits, and cavities filled with elastic or viscoelastic materials. Our main attention is given to a method based on the use of solutions of the corresponding problems for bodies with mathematical cuts along the median surfaces of the concentrators. The idea of the method is to replace an inclusion with a certain volume by a surface with unknown discontinuities of stresses and/or displacements. We describe a procedure of construction of the integral equations of the corresponding boundary-value problems used to determine the indicated discontinuities. By an example of the inhomogeneities bounded by canonical surfaces, we illustrate the efficiency of construction of approximate solutions of these problems.