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A variational inequality describing an elastic body with a finite set of rigid inclusions is considered. The Signorini condition is imposed on a part of the boundary of the body. On the other part a homogeneous Dirichlet boundary condition is specified. The inclusions are arranged such that distance between any two inclusions is not less than a given positive number. All inclusions are located at a nonzero distance from the outer boundary. An inverse problem is investigated, which consists in identification of positions of the rigid inclusions from the measurement of displacements on an observation boundary. Continuous dependency of the solution of the forward problem on parameters of inclusions' location and rotation is established. This provides existence of a solution for the inverse identification problem. [ABSTRACT FROM AUTHOR]

A new mathematical model describing an equilibrium of an elastic Kirchhoff-Love plate is proposed. We suppose that the plate may come into contact on the side edge with a rigid obstacle. On a given part of the closed curve corresponding to the plate side edge we impose clamping conditions and on the rest part of the curve we consider a nonpenetration condition of the Signorini type. The rigid obstacle is defined by cylindrical surface with generators normal to the plate midplane. In addition, the plate has a flat rigid inclusion (stiffener) on the side edge. The inclusion also defined by a cylindrical surface. The peculiarity of the problem is related to the partial delamination of the inclusion on the contact surface. Boundary conditions of an inequality type ensure nonpenetration of the plate points and the obstacle as well as for points of an elastic matrix and inclusion points. Solvability of the problem is proved. Under the assumption that the solution of the variational problem is smooth enough, optimality conditions on the contact boundary are found. [ABSTRACT FROM AUTHOR]

Poorly soluble zinc ethylenediaminetetraacetate zincate Zn[ZnL] reacts with sodium Na4L, potassium K4L, ammonium (NH4)4L, 2-ammonioethanol (H3NCH2CH2OH)4L, and hexamethylene-1,6-diammonium {H3N(CH2)6NH3}2L salts of ethylenediaminetetraacetic acid H4L to give readily soluble sodium Na2[ZnL], potassium K2[ZnL], ammonium (NH4)2[ZnL], 2-ammonioethanol (H3NCH2CH2OH)2[ZnL], and hexamethylene-1,6-diammonium {H3N(CH2)6NH3}[ZnL] ethylenediaminetetraacetate zincates. The reaction of tetrakis(triethylammonium) salt {(C2H5)3NH}4L with Zn[ZnL] does not give the expected bis(triethylammonium) ethylenediaminetetraacetate zincate {(C2H5)3NH}2[ZnL], but gives instead mono(triethylammonium) ethylenediaminetetraacetate zincate, {(C2H5)3NH}H[ZnL]; in aqueous solution, this product generates poorly soluble zinc ethylenediaminetetraacetate H2[ZnL(H2O)]·2H2O, which was studied by X-ray diffraction (CCDC no. 2172274). [ABSTRACT FROM AUTHOR]

A new variational problem on the equilibrium of a thermoelastic heterogeneous Kirchhoff-Love plate is considered in a domain with a cut. The cut corresponds to an interfacial crack located on a part of the boundary of a rigid inclusion. We suppose that the plate is under the special loads for which the configuration of crack's edges is known a priori. This assumption allows us to rewrite the well known nonpenetration condition for Kirchhoff-Love plates in a refined form, which, in turn, leads to new relations describing the possible mechanical interaction of opposite crack edges. Displacements on the rigid inclusion satisfy special constraints having a linear form. Solvability of the problem is proved, an equivalent differential statement is found. [ABSTRACT FROM AUTHOR]