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

Abstract

Adequate mathematical models and computational algorithms are developed in this study to investigate specific features of the deformation processes of elastic rotational shells at large displacements and arbitrary rotation angles of the normal line. A finite difference method (FDM) is used to discretize the original continuum problem in spatial variables, replacing the differential operators with a second-order finite difference approximation. The computational algorithm for solving the nonlinear boundary value problem is based on a quasi-dynamic form of the ascertainment method with the construction of an explicit two-layer time-difference scheme of second-order accuracy. The influence of physical and mechanical characteristics of isotropic and composite materials on the deformation features of elastic spherical shells under the action of surface loading of “tracking” type is investigated. The results of the studies conducted have shown that the physical and mechanical characteristics of isotropic and composite materials significantly affect the nature of the deformation of the clamped spherical shell in both the subcritical and post-critical domains. The developed mathematical models and computational algorithms can be applied in the future to study shells of rotation made of hyperelastic (non-linearly elastic) materials and soft shells.

Analytical and Numerical Investigation of Two-Dimensional Heat Transfer with Periodic Boundary Conditions

“…In order to solve the two-dimensional quasilinear parabolic problem, several numerical methods are available, such as the finite difference method [24,25], the finite element method [26,27], the finite volume method [28], and the lattice Boltzmann methods [15,29,30]. Denghan solved the one-dimensional heat diffusion equation numerically using the finite difference method [31].…”

Analytical and Numerical Investigation of two-dimensional Heat Transfer with Periodic Boundary Conditions

“…In order to solve two-dimensional quasilinear parabolic problem, there are several numerical methods, such as finite difference methods [19,20], finite element methods [21,22], finite volume methods [23], lattice Boltzmann Method [15,24,25]. Denghan solve the one-dimensional heat diffusion equation numerically with finite difference method [26].…”