Particularities of mathematical modeling of deformation processes for arched and panel designs of composites with large displacements and rotation angles

Abstract

In aerospace systems and automotive industry flexible elastic and thin-walled structures are widely used. The adequate mathematical models are in the process of development as well as numerical algorithms for examination of the features of processes of deformation of panel and arch designs with large displacements and arbitrary angles of rotation of the normal. For the discretization of the original continuum problem in spatial variables, the finite difference method can be used with the replacement of differential operators by finite-difference second-order approximations. The computational algorithm for solving a substantially nonlinear boundary-value problem is constructed on the basis of adaptation of the calculation method with construction of an explicit two-layer difference scheme in time of the second order of accuracy. The influence of the boundary conditions on the features of subcritical and supercritical behavior of the elastic arch structure under the influence of the surface load of the “tracking” type is considered.

Numerical Analysis of Deformation Characteristics of Elastic Inhomogeneous Rotational Shells at Arbitrary Displacements and Rotation Angles

“…When constructing the discrete analog of the original continuum problem ( 1)-( 13), FDM [3,4] is used to discretize the spatial variables. Two grids are introduced in the area of continuous variation of the argument s: a main grid with integer indices i and an auxiliary grid with indices i ± 1/2, the nodes of which are positioned in the middle between the nodes of the main grid i ± 1 (Figure 4).…”

“…21 within the m-layer [9][10][11]. The equilibrium equations of the deformed element of a rotational shell have the following form (11) [4,5,8]:…”

“…For a single-layer structure, the mid-surface of the shell is taken as the coordinate surface (datum surface); for a multi-layer structure, the mid-surface of one of the layers or the contact surface of the layers can be taken as the coordinate surface. To describe the deformation processes of elastic rotational shells at large displacements of coordinate surface points and unlimited rotation angles of the normal to it, the changes of Cartesian coordinates x, y are taken as unknowns, which allows for the considered variant of geometrically nonlinear deformation of thin-walled constructions to greatly simplify the structure of initial differential equations in comparison with using traditional components of tangential u and normal w displacements [4,5].…”

Effect of High Velocity Deformation on Strength of ArmoredComposite Materials

“…During loading, a material subjected to high-rate deformation may change its mechanical properties, in comparison with the properties found as a result of static tests [1][2][3][4][5][6][7][8]. To calculate the structures under consideration, it is necessary to assess the effect of the strain rate on the properties of the materials used [9][10][11][12][13][14][15][16].…”

Application of Magnetically Controlled Sorbents for Detoxication

“…As is known, the rates of the establishment of adsorption-desorption equilibrium in carbon coatings of small thickness are significantly increased, which provides a high speed of the specified method. The same effects were applied for creation and modelling of composite materials of various nature [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]. It should be noted that the total area of the adsorbing surface is so large that desorption practically does not reduce the surface density of the reagent.…”