A New Approximate Solution in Boundary Value Problems by the Use of Orthogonal Curvilinear Coordinates

1948 ◽  
Vol 3 (1) ◽  
pp. 33-40 ◽  
Author(s):  
Shigeo Uchida
Keyword(s):  
Approximate Solution ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Curvilinear Coordinates ◽  
Orthogonal Curvilinear Coordinates

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.

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