Solvability of geometrically nonlinear boundary-value problems for shallow shells of Timoshenko type with pivotally supported edges

Solvability of One Nonlinear Boundary-value Problem for a System of Differential Equations of the Theory of Shallow Timoshenko-type Shells

“…These questions have not been clarified yet. There are a number of works devoted to the solvability of nonlinear problems in the framework of the Timoshenko displacement model [6][7][8][9][10]. The method used in these studies is based on the integral representations of the desired solution of system (8) that contain arbitrary holomorphic functions.…”

“…At the present time, existence theorems of solutions of nonlinear problems for Timoshenko-type shell with rigidly clamped edges [6,7] and with free edges [8,9] are obtained. Method developed in [6][7][8][9] was applied to system (8) with boundary conditions w 1 = w 3 = ψ 1 = 0 that describe the state of equilibrium of Timoshenko-type shell with simply supported edges [10]. The study presented in this paper develops results obtained in [10].…”

“…Method developed in [6][7][8][9] was applied to system (8) with boundary conditions w 1 = w 3 = ψ 1 = 0 that describe the state of equilibrium of Timoshenko-type shell with simply supported edges [10]. The study presented in this paper develops results obtained in [10]. The more complicated case of boundary conditions w 1 = ψ 1 = 0 is considered.…”

Stress state of hinged supported thin-wall elastic structures

“…Vorovich [10] and remained open until recently. To date, there are a number of works [18][19][20][21][22][23][24] devoted to the study of the stress-strain state in the framework of the Timoshenko shear model. The research in [18][19][20][21][22][23][24] is based on integral representations for generalized displacements containing arbitrary holomorphic functions that are found in such a way that the generalized displacements satisfy the given boundary conditions.…”

“…The first approach is based on the application of explicit representations of solutions to Riemann -Hilbert problems for holomorphic functions in the unit circle. Therefore, a flat region homeomorphic to the median surface of the shell is either assumed to be a unit circle from the very beginning [18][19][20], or conformally mapped to a unit circle [22], [24]. In the second approach, the theory of onedimensional singular integral equations is used to determine holomorphic functions [21], [23].…”