Partitioned schemes of the finite-element method for dynamic problems of acoustoelectroelasticity

Abstract

To cite this version:A. Belokon', V. Eremeyev, A. Nasedkin, A. Solov'Yev. Partitioned schemes of the finite-element method for dynamic problems of acoustoelectroelasticity.

Finite element dynamic analysis of anisotropic elastic solids with voids

“…We show that this damping model with the modes superposition method enables to split the system of finite element equations into separate scalar equations. These approaches for dynamic problems are similar to those suggested for the theory of piezoelectricity [10,12]. We also propose FEM for numerical solution of eigenvalue problems for elastic media with voids [11].…”

“…We note, that several effective block algorithms for this finite element eigenvalue problems with partial coupling similar algorithms for piezoelectric modal problems are described in [10]. We remark that from Eq.…”

“…The matrix K in (45) is symmetric and positive defined by virtue of properties (7)- (10). Thus, problem (44) possesses the main calculating properties of finite element matrices for the elasticity theory, and therefore it can be solved by the same effective algorithms as the analogous problems for ordinary elastic media.…”

Nonlinear finite element modeling of vibration control of plane rod-type structural members with integrated piezoelectric patches

“…Let us note that in the piezoelectricity these matrices may have special properties which can be used for numerics, see, e.g., [96,[98][99][100][101].…”

Multiscale computer design of piezomagnetoelectric mixture composite structures

“…Let h h be a region filled by the finite element mesh, , h } at the finite element mesh h h in the form (14) and analogous representations for projecting functions into the weak setting of the piezomagnetoelectric problem (1) - (7) for h h , we get the finite element system Note that similarly to [14,15] we can use an effective algorithm with symmetric quasidefinite matrices for solving finite element system (15) -(17) with (18) -(21). All the procedures that we need in finite element manipulations (the degree of freedom rotations, mechanical and electric boundary condition settings, etc.)…”