Viscoelastic Stresses in the Plates Containing Inclusions with Cracks
Journal Article
·
· Journal of Mathematical Sciences
- Ukrainian National Academy of Sciences, Pidstryhach Institute for Applied Problems in Mechanics and Mathematics (Ukraine)
We study viscoelastic stresses in the plates containing inclusions weakened by cracks by the method of boundary integral equations and the Laplace integral transformation. The case in which the rheological relations between stresses and strains are written in the differential form is analyzed in detail. To solve the boundary problem of viscoelasticity, we use the well-known approach in which the corresponding problem of the theory of elasticity is studied by replacing the differential operators with constant quantities. The solution of the auxiliary problem is obtained by the method of boundary integral equations reduced to a system of algebraic equations. After replacing the elastic quantities in this system by the corresponding differential operators, we solve the system obtained as a result by using the Laplace integral transformation and then applying the improved numerical-analytic inversion formula adapted to this class of problems.
- OSTI ID:
- 22771483
- Journal Information:
- Journal of Mathematical Sciences, Journal Name: Journal of Mathematical Sciences Journal Issue: 3 Vol. 229; ISSN JMTSEW; ISSN 1072-3374
- Country of Publication:
- United States
- Language:
- English
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