On the mechanical interplay between Timoshenko and semirigid inclusions embedded in elastic bodies

Abstract

In the paper, an equilibrium problem for elastic bodies with a thin elastic Timoshenko inclusion and a thin semirigid inclusion is analyzed. The inclusions are assumed to be delaminated from elastic bodies, thus forming a crack between the inclusions and the elastic matrix. Nonlinear boundary conditions are imposed at the crack faces to prevent a mutual penetration between the crack faces. The inclusions have a joint point. A passage to a limit is investigated as a rigidity parameter of the elastic inclusion goes to infinity. The limit model is investigated. Junction boundary conditions are found at the joint point for the problem analyzed as well as for the limit problem.

Fictitious Domain Method for Equilibrium Problems of the Kirchhoff-Love Plates with Nonpenetration Conditions for Known Configurations of Plate Edges

“…which is analogous to (7), holds with some constant c 2 > 0 independent of η [11]. In virtue of (7) and (17), for every fixed λ we have…”

“…The method of the fictitious domain has proven useful in establishing the solvability of problems that describe equilibrium of bodies with cracks crossing the external boundary at zero angles [2,4,8,9]. In the last years, within the framework of crack models subject to non-penetration boundary conditions, numerous works have been published, see, for example, [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25].…”

The Junction Problem for Two Weakly Curved Inclusions in an Elastic Body

“…Among the articles dealing with junction we note [15][16][17][18][19][20][21][22] which consider the junction problem of elastic objects. The junction problems of elastic, rigid, and semirigid inclusions in elastic bodies in the presence of delamination with nonlinear boundary conditions on the crack faces can be found in [23][24][25][26][27][28]. Thin elastic inclusions were described there using the Euler-Bernoulli and Timoshenko beam models.…”

О Задаче Сопряжения Двух Слабо Искривленных Включений В Упругом Теле

“…Из работ, относящихся к тематике сопряжения, отметим исследования [15][16][17][18][19][20][21][22], где рассматривались задачи сопряжения упругих объектов друг с другом. Задачи сопряжения упругих, жестких и полужестких включений, расположенных в упругих телах, при наличии отслоений с нелинейными краевыми условиями на берегах трещин можно найти в [23][24][25][26][27][28]. При этом для описания тонких упругих включений использовались модели балок Бернулли Эйлера и Тимошенко.…”