Two-dimensional nonstationary contact of elastic cylindrical or spherical shells

Modeling the Unsteady Contact of Spherical Shell Made With Applying the Additive Technologies With the Perfectly Rigid Stamp

“…Based on the superposition principle [1,2,3,4] the shell normal displacements are connected with the contact pressure by the integral relationship…”

“…Taking additionally into consideration the problem symmetry relatively to horizontal plane which is in parallel to the stamps' surfaces and divides the spherical shell in halves, the problem boils down to the equivalent axial-symmetric problem of the unsteady contact interaction with the mobile stamps the velocity of each of them is V (Figure 1). For theoretical description of the shell deformation process there are used Timoshenko model movement equations [1] and [2] written in the spherical coordinate system with center on the shell axis and angle α ∈ [0, π] (dots above the characters hereinafter mean the time derivatives):…”

Bending of a Sandwich Beam by Local Loads in the Temperature Field

“…xz and σ (3) zz are components of the stress tensor. Further, we accept the kinematic boundary conditions of simple support for end faces of the beam on spatially motion-less rigid supports.…”

“…i , and σ (k) , ε (k) are the deviatoric and spherical parts of stress and strain tensors; s (3) xz and e (3) xz are the shear stresses and strains in the filler; G k (T k ) and K k (T k ) are temperature-dependent elastic moduli of the material of a kth layer, calculated by the linear Bell formula [2];…”

“…The isothermal dynamic deformation of layered (three-layer) structural elements, including those connected to an elastic foundation, under the action of continuous and local loads are investigated in [3][4][5][6][7][8][9][10][11]. The statements and solution methods of boundary-value problems on isothermal deformations, including cyclic ones, of elastoplastic composite structural elements are presented in [12][13][14][15][16][17][18][19].…”