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Finite-element method of solving problems of thermoelectroviscoelasticity for solids of revolution under harmonic loading. (English. Russian original) Zbl 0632.73064

Sov. Appl. Mech. 22, 606-613 (1986); translation from Prikl. Mekh., Kiev 22, No. 7, 9-17 (1986).
The paper is devoted to the numerical solution of thermoelectroviscoelastic problems for solids of revolution made of materials exhibiting the piezoelectric effect under harmonic loading. In the first part of the paper, the authors discuss the governing equations and some simplified forms of them. Afterwards they give the variational formulation of the coupled field problems and apply the finite element method for the discretization of the field problems. The resultant system of nonlinear finite element equations is solved by some linearization method such as the Newton method and its variants, or variants of the method of variable parameters and others. The axisymmetric case is discussed in detail. Here linear triangular finite elements are used to approximate the coupled boundary value problem. Finally, the dynamic behavior of a hollow, circular, piezoceramic cylinder of length L with an inside surface which is free of mechanical loads was simulated on the computer. The numerical results obtained by the use of 50 triangular elements only show that the algorithm proposed in the paper works well.
Reviewer: U.Langer

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74D99 Materials of strain-rate type and history type, other materials with memory (including elastic materials with viscous damping, various viscoelastic materials)
74F15 Electromagnetic effects in solid mechanics
74S30 Other numerical methods in solid mechanics (MSC2010)
74A15 Thermodynamics in solid mechanics
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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