The use of graded finite elements in the study of elastic wave propagation in continuously nonhomogeneous materials

Santare, Michael H.; Thamburaj, Priya; Gazonas, George A.

doi:10.1016/s0020-7683(03)00315-9

Cited by 74 publications

(34 citation statements)

References 12 publications

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“…Using conventional finite element formulations such that the property field is constant within an individual element for dynamic problems leads to significant discontinuities and inaccuracies. 38 These inaccuracies will be more significant in 2D-FGM cases. On the other hand, by using graded finite element in which the material property field is graded continu- Figure 1.…”

Section: -7mentioning

confidence: 99%

Free Vibration Analysis of Functionally Heterogeneous Hollow Cylinder Based on Three Dimensional Elasticity Theory

Asgari¹

2017

IJAV

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A two-dimensional functionally heterogeneous thick hollow cylinder with a finite length is considered and its natural modes and frequencies are determined. Since mode shapes of a thick cylinder are three-dimensional, even with axisymmetric conditions, three-dimensional theory of elasticity implemented for problem formulation. The axisymmetric conditions are assumed for the cylinder. The material properties of the two-dimensional functionally graded material (2D-FGM) cylinder are varied in the radial and axial directions with power law functions. Effects of volume fraction distribution on the different types of anti-symmetric mode shape configuration and vibrational behaviour of a simply supported cylinder are analyzed. Three-dimensional equations of motion are used and the eigen value problem is developed based on direct variational method. The study shows that the 2D-FGM cylinder exhibit interesting vibrational characteristics and mode shapes when the constituent volume fractions are varied.

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Section: -7mentioning

confidence: 99%

Free Vibration Analysis of Functionally Heterogeneous Hollow Cylinder Based on Three Dimensional Elasticity Theory

Asgari¹

2017

IJAV

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“…In equation (4), the dynamic stiffness block matrices are formulated by taking into account the continuous variation of the shear modulusḠ (x, ✓) in ⌦ i s . The stochastic shear modulus G (✓) is first evaluated at the finite element nodes and subsequently interpolated at any point of domain ⌦ i s by using the same FE shape functions as for the interpolation of the displacements [17].…”

Section: Stochastic Subsoil Modelingmentioning

confidence: 99%

The Influence of Imperfectly Known Local Subsoil Conditions on the Prediction of Ground-Borne Vibrations in Buildings

Παπαδόπουλος¹,

François²,

Degrande³

et al. 2017

Proceedings of the 6th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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Abstract. This paper examines the influence of imperfectly known local subsoil conditions on the response prediction of buildings to ground-borne environmental vibration. A probabilistic finite element-perfectly matched layers model is developed for the analysis of the dynamic soil-structure interaction problem where the shear modulus of the soil is modeled as a conditional random field. An incident wave field is propagated through the finite element-perfectly matched layers model by decomposing the displacement field of the soil in accordance with the subdomain formulation developed for the dynamic soil-structure interaction problem. Monte Carlo simulation is used to propagate the uncertainty on the subsoil properties to the response of a building. A parametric study is performed with respect to the spatial correlation length of the random field representing the shear modulus of the subsoil, and the foundation type of the building. The uncertain subsoil properties affect both the incident wave field exciting the building and the dynamic stiffness of the coupled soil-building system. The uncertainty of the building response varies over frequency bands but as a general trend increases with frequency.

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“…Finite element method with graded material characteristics, within each element of the structure, is used for solution. Using conventional finite element formulations such that the property field is constant within an individual element for dynamic problems leads to significant discontinuities and inaccuracies [23]. These inaccuracies will be more significant in 2-D FGM cases.…”

Section: Introductionmentioning

confidence: 99%

Two Dimensional Functionally Graded Material Finite Thick Hollow Cylinder Axisymmetric Vibration Mode Shapes Analysis Based on Exact Elasticity Theory

Asgari¹

2015

Journal of Theoretical and Applied Mechanics

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Abstract. A thick hollow cylinder with finite length made of twodimensional functionally graded material (2D-FGM) is considered and its natural modes are determined, based on great importance of mode shapes information in order to understand vibration behaviour of structures. Three dimensional theory of elasticity implemented for problem formulation, since mode shapes of a thick cylinder are three dimensional even with axisymmetric conditions. The axisymmetric conditions are assumed for the 2D-FGM cylinder. The material properties of the cylinder are varied in the radial and axial directions, with power law functions. Effects of volume fraction distribution on the different types of symmetric mode shapes configuration and vibration behaviour of a simply supported cylinder are analyzed. Three dimensional equations of motion are used and the eigen value problem is developed, based on direct variation method.

show abstract

The use of graded finite elements in the study of elastic wave propagation in continuously nonhomogeneous materials

Cited by 74 publications

References 12 publications

Free Vibration Analysis of Functionally Heterogeneous Hollow Cylinder Based on Three Dimensional Elasticity Theory

Free Vibration Analysis of Functionally Heterogeneous Hollow Cylinder Based on Three Dimensional Elasticity Theory

The Influence of Imperfectly Known Local Subsoil Conditions on the Prediction of Ground-Borne Vibrations in Buildings

Two Dimensional Functionally Graded Material Finite Thick Hollow Cylinder Axisymmetric Vibration Mode Shapes Analysis Based on Exact Elasticity Theory

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