Probability characteristics of solutions of boundary-value problems of the dynamics of an elastic body for random loads

1976 ◽  
Vol 12 (12) ◽  
pp. 1242-1247
Author(s):  
V. M. Goncharenko
Keyword(s):  
Boundary Value Problems ◽  
Elastic Body ◽  
Boundary Value ◽  
Random Loads

scholarly journals Effective Solution of a Class of Boundary Value Problems of Thermoelasticity in Generalized Cylindrical Coordinates

2004 ◽  
Vol 11 (3) ◽  
pp. 495-514
Author(s):  
N. Khomasuridze
Keyword(s):  
Boundary Value Problems ◽  
Elastic Body ◽  
Boundary Value ◽  
Thermal Characteristics ◽  
Curvilinear Coordinates ◽  
Effective Solution ◽  
Cylindrical Coordinates ◽  
Cartesian System ◽  
Transversally Isotropic ◽  
Orthogonal Curvilinear Coordinates

Abstract A class of static boundary value problems of thermoelasticity is effectively solved for bodies bounded by coordinate surfaces of generalized cylindrical coordinates ρ, α, 𝑧 (ρ, α are orthogonal curvilinear coordinates on the plane and 𝑧 is a linear coordinate). Besides in the Cartesian system of coordinates some boundary value thermoelasticity problems are separately considered for a rectangular parallelepiped. An elastic body occupying the domain Ω = {ρ 0 < ρ < ρ 1, α 0 < α < α 1, 0 < 𝑧 < 𝑧1}, is considered to be weakly transversally isotropic (the medium is weakly transversally isotropic if its nine elastic and thermal characteristics are correlated by one or several conditions) and non-homogeneous with respect to 𝑧.

scholarly journals Solution of the problems of quasi-statics for an elastic body with double porosity

2021 ◽  
Vol 1 (3) ◽  
pp. 1-5
Author(s):  
Ivane Tsagareli
Keyword(s):  
Boundary Value Problems ◽  
Elastic Body ◽  
Boundary Value ◽  
Original System ◽  
Double Porosity ◽  
Point Of View ◽  
Static Case ◽  
Elementary Functions ◽  
The Laplace Transform ◽  
Dimensional Boundary

The construction of solutions in explicit form is especially important from the point of view of its application, since it makes it possible to effectively carry out a quantitative analysis of the problem under study. This paper investigates the processes of deformation of solids in the quasi-static case. Two-dimensional boundary value problems of Dirichlet and Neumann for an elastic body with double porosity are considered. In Using the Laplace transform, these problems are reduced to auxiliary boundary value problems. Special representations of solutions to auxiliary boundary value problems are constructed using elementary functions that allow reducing the original system of equations to equations of a simple structure and facilitate the solution of the original problems. Auxiliary boundary value problems are solved for a specific elastic body - a porous disk. Solutions to these problems are obtained in the form of series. Conditions are provided that ensure the absolute and uniform convergence of these series and the use of the inverse Laplace theorem. It is proved that the inverse transforms provide a solution to the initial problems.

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