Wave propagation and dynamic analysis of smoothly graded heterogeneous continua using graded finite elements

Abstract

The dynamic behavior of smoothly graded heterogeneous materials is investigated using the finite element method. The global variation of material properties (e.g., Young's modulus, Poisson's ratio and mass density) is treated at the element level using a generalized isoparametric formulation. Three classes of examples are presented to illustrate this approach and to investigate the influence of material inhomogeneity on the characteristics of wave propagation pattern and stress redistribution. First, a cantilever beam example is presented for verification purposes. Emphasis is placed on the comparison of numerical results with analytical ones, as well as modal analysis for beams with different material gradation profiles. Second, wave propagation patterns are explored for a fixed-free slender bar considering homogeneous, bi-material, tri-layered and smoothly graded materials (steel/alumina), which also provide further verification of the numerical procedures. Comparison of stress histories in these samples indicates that the smooth transition of material gradation considerably alleviates the stress discontinuity in the bi-material system (with sharp interface). Third, a three-point-bending epoxy/glass graded beam specimen is investigated for validation purposes. The beam is graded along the height direction. Stress evolution history at a location of interest is analyzed in detail, which not only reveals the dependence of stress evolution on material gradation direction, but also provides information predictive of potential material failure time for graded beams with different material gradation profiles. Jointly, these three classes of examples provide proper verification and validation for the present numerical techniques.

Application of the spectral nite element method for elastic wave propagation problems in functionally graded materials

“…Zhang and Paulino [8] developed the so-called Generalized Isoparametric Formulation that consists in incorporating the material property variation at the element by employing the same shape functions adopted to interpolate the unknown displacement field. In their study, the use of this strategy results in smoother and more accurate solutions when conpared to the homogeneous element strategy.…”

“…Functionally graded materials are widely used in contemporary science due to their distinct properties [8] and, thus, the development and study of numerical methods for the solution of problems that adopt such type of material is of great importance. Hence, the behavior of these materials in the context of elastic wave propagation problems is investigated here using the SFEM and then compared with other material models.…”

İki Malzemeli Kompozit Bir Kirişin Serbest ve Zorlanmış Titreşimlerinin İncelenmesi

“…[5] epoksi/çelik malzemelerinden yapılmış iki malzemeli bir kirişin artık gerilmelerini deneysel olarak incelemişlerdir. Zhang ve Paulino [6] fonksiyonel derecelendirilmiş ve iki malzemeli kirişlerin dinamik ve dalga yayılımlarını sonlu elemanlar yöntemi ile incelemiştir. Della ve Shu [7] delaminasyonlu iki malzemeli bir kirişin serbest titreşim analizini araştırmışlardır.…”

Dynamic and static analysis of FGM skew plates with 3D elasticity based graded finite element modeling

“…The graded finite element method (GFEM) is a relatively new numerical technique in structural analysis. Kim and Paulino (2002), and Zhang and Paulino (2007) developed a GFEM approach for modeling the nonhomogeneous structures. They compared results of the graded versus conventional homogeneous elements under various loading conditions.…”