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Thin‐layer method: Formulation in the time domain
Author(s) -
Kausel Eduardo
Publication year - 1994
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620370604
Subject(s) - eigenvalues and eigenvectors , wavenumber , mathematics , mathematical analysis , quadratic equation , domain (mathematical analysis) , time domain , frequency domain , numerical analysis , computer science , geometry , physics , optics , quantum mechanics , computer vision
The thin‐layer method is a semi‐discrete numerical technique that may be used for the dynamic analysis of laminated solids or fluids. In its classical implementation, the method is normally formulated in the frequency domain and requires the solution of a complex‐valued quadratic eigenvalue problem; in this paper we present an alternative time‐domain formulation which can offer advantages in some cases, such as avoiding the use of complex algebra. The proposed method entails expressing the governing equations in the frequency‐wavenumber domain, solving a linear real‐valued eigenvalue problem in the frequency variable, carrying out an analytical integration over frequencies, and performing a numerical transform over wavenumbers. This strategy allows obtaining the Green's functions for impulsive sources directly in the time domain, even when the system has little or no damping. We first develop the algorithm in its most general form, allowing fully anisotropic materials and arbitrary expansion orders; then we consider a restricted class of anisotropic materials for which the required linear eigenvalue problem involves only real, narrowly banded symmetric matrices and finally, we demonstrate the method by means of a simple problem involving a homogeneous stratum subjected to an antiplane impulsive source.