Finite element analysis of harmonic waves in layered and fibre‐reinforced composites

Abstract

SUMMARYThe problem of harmonic waves in layered and fibre-reinforced composites is solved by a method of finite elements. Piecewise linear approximating functions are used for the displacement and stress fields in a mixed variational formulation, recently proposed by one of the writers in the form of a new quotient. Numerical computations are made for approximate phase-velocities of harmonic waves in layered composites, where asymmetric and symmetric triangular meshes, and square meshes with interior nodes, are used. To illustrate the accuracy and effectiveness of the method, these approximate solutions are compared with those given by means of exponential test functions, and the exact ones by Rytov, etc. Calculations are also performed for harmonic waves in fibre-reinforced composites. Dispersion curves for these waves are obtained and displayed graphically.

Generalized Spatial Aliasing Solution for the Dispersion Analysis of Infinitely Periodic Multilayered Composites Using the Finite Element Method

“…In order to overcome the challenges in the analytical investigations, researchers have been employing various numerical techniques such as continuum power series method [24,25], the effective stiffness method [26,27], the mixture theory [28][29][30], the plane wave expansion method [31], the finite difference method [32], the variational method [33,34], and the finite element (FE) method [35][36][37][38][39]. In particular, the FE method offers a remarkable framework to efficiently investigate the effect of material and geometric nonlinearity on phononic dispersion relations [38,[40][41][42][43], which can be hardly done using other numerical techniques.…”

“…However, despite its superior capability to investigate the effect of nonlinearities to phononic dispersion relations, the FE method suffers from spectral distortions in the dispersion analysis of waves perpendicular to the layers in layered composites [35][36][37][38][39]. The importance of this issue regarding FE modeling and the corresponding analysis are extensively discussed in Refs.…”

“…The importance of this issue regarding FE modeling and the corresponding analysis are extensively discussed in Refs. [35] and [46]. It is worth mentioning that the spectral distortion discussed in those references is irrelevant to the effect of mesh size in FE models.…”

Refraction characteristics of phononic crystals

“…In the present paper we present a mixed variational formulation for phononic bandstructure calculations, where both the displacement and the stress fields are varied independently and hence may be approximated by any continuously differentiable set of complete base functions, even though the displacement gradients may suffer large discontinuities across interfaces of various constituents of a typical unit cell. Since the method is based on a variational principle, any set of approximating functions can be used for calculations, e.g., plane-waves Fourier series or finite elements (Minagawa et al (1981)). The method produces very accurate results and the rate of convergence of the corresponding series solution is greater than that of the displacement-based approximating functions (Babuška & Osborn (1978)).…”

Ultrasonic Dispersion in Fluid-Coupled Composite Plates

“…Therefore, much attention bas been paid by researchers over the past decade to composite materiala and their properties. One active area of endeavor bas been the topic of wave propagation studies [1][2][3][4][5][6][7][8]. Severa!…”