Boundary–Value Problems: Cylindrical Coordinates

Representation of Solutions of Some Boundary Value Problems of Elasticity by a Sum of the Solutions of Other Boundary Value Problems

Georgian Mathematical Journal ◽

10.1515/gmj.2003.257 ◽

2003 ◽

Vol 10 (2) ◽

pp. 257-270

Author(s):

N. Khomasuridze

Keyword(s):

Boundary Value Problems ◽

Boundary Value ◽

Cognitive Significance ◽

Cylindrical Coordinates ◽

Classical Elasticity ◽

Representation Of Solutions ◽

Elasticity Problems ◽

Lamé Coefficients

Abstract Basic static boundary value problems of elasticity are considered for a semi-infinite curvilinear prism Ω = {ρ 0 < ρ < ρ 1, α 0 < α < α 1, 0 < 𝑧 < ∞} in generalized cylindrical coordinates ρ, α, 𝑧 with Lamé coefficients ℎ ρ = ℎ α = ℎ(ρ, α), ℎ𝑧 = 1. It is proved that the solution of some boundary value problems of elasticity can be reduced to the sum of solutions of other boundary value problems of elasticity. Besides its cognitive significance, this fact also enables one to solve some non-classical elasticity problems.

Download Full-text

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

Georgian Mathematical Journal ◽

10.1515/gmj.2004.495 ◽

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.

Download Full-text