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TECHNICAL PAPERS

Isoparametric Graded Finite Elements for Nonhomogeneous Isotropic and Orthotropic Materials

[+] Author and Article Information
Jeong-Ho Kim, G. H. Paulino

Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, Newmark Laboratory, 205 North Mathews Avenue, Urbana, IL 61801

J. Appl. Mech 69(4), 502-514 (Jun 20, 2002) (13 pages) doi:10.1115/1.1467094 History: Received July 02, 2001; Revised November 14, 2001; Online June 20, 2002
Copyright © 2002 by ASME
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References

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Figures

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Homogeneous versus graded finite elements. (a) Property variation along one coordinate axis; (b) homogeneous elements; (c) graded elements. Notice that the property of the homogeneous element corresponds to the property at the centroid of the graded element.
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FGM link bar (units: N, mm): (a) geometry and boundary conditions; (b) symmetric model
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Stress distribution (σyy) using Q4 elements for tension loading applied perpendicular to the linear material gradation
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Stress distribution (σyy) using Q8 elements for tension load applied perpendicular to the linear material gradation
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Isotropic FGM plate with material variation in the x-direction: (a) geometry, boundary conditions and material properties; (b) tension load perpendicular to material gradation; (c) bending load; (d) tension load parallel to material gradation. The finite element mesh (9×9 quads: either Q4 or Q8) is illustrated in parts (b) through (d) with a representative Q4 element at the upper left hand corner
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Stress distribution (σyy) using Q4 elements for fixed grip0=Δ/H) load applied perpendicular to the exponential material gradation
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Displacements (ux and uy) using Q4 elements for fixed grip load applied perpendicular to the exponential material gradation in isotropic FGMs
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Stress distribution (σyy) using Q4 elements for tension load applied perpendicular to the exponential material gradation
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Stress distribution (σyy) using Q4 elements for bending load applied perpendicular to the exponential material gradation
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Stress distribution (σyy) using Q8 elements for bending load applied perpendicular to the exponential material gradation
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Stress distribution (σyy) using Q8 elements for tension load applied perpendicular to the exponential material gradation
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Stress distribution (σyy) using Q4 elements for bending load applied perpendicular to the linear material gradation
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Stress distribution (σyy) using Q8 elements for bending load applied perpendicular to the linear material gradation
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Stress distribution (σxx) using Q4 elements (9×9 mesh) for tension load applied parallel to the exponential or linear material gradation
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Stress distribution (σxx) using Q8 elements (9×9 mesh) for tension load applied parallel to the material gradation
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Strain distribution (εxx) using Q4 elements (either 9×9 and 18×18) for tension load applied parallel to the material gradation (either exponential or linear)
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Orthotropic FGM plate with material variation in the x-direction: (a) geometry, boundary conditions and material properties; (b) tension load perpendicular to material gradation; (c) bending load; (d) tension load parallel to the material gradation. The finite element mesh (Q4 or Q8 elements) is illustrated in parts (b) through (d) with a representative Q4 element at the upper left hand corner
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Stress distribution (σyy) using Q4 elements for tension loading applied perpendicular to the exponential material gradation in orthotropic FGMs (E110=1,E220=0.1,G120=0.5,ν12=0.3)
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Stress distribution (σyy) using Q8 elements for tension loading applied perpendicular to the exponential material gradation in orthotropic FGMs (E110=1,E220=0.1,G120=0.5,ν12=0.3)
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Displacements (ux and uy) along y=1 using Q4 and Q8 elements for tension load applied perpendicular to the exponential material gradation in orthotropic FGMs (E110=1,E220=0.1,G120=0.5,ν12=0.3)
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FGM link bar under unit axial tension (units: N/mm2): (a) mesh configuration with 1000 graded Q8 elements; (b) σxx stress distributions for homogeneous link bar (both TiB and Ti); (c) σxx stress distributions for FGM bar (TiB/Ti)
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An isotropic or orthotropic functionally graded plate: (a) geometry and material properties—the shaded portion indicates the symmetric region of the plate used in this analysis; (b) fixed grip loading with a schematic of the corresponding stresses at the end points of the plate; (c) tension loading; (d) bending loading
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Generalized isoparametric formulation for isotropic or orthotropic FGMs
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Displacements (ux and uy) along y=1 using Q4 and Q8 elements for bending load applied perpendicular to the exponential material gradation in orthotropic FGMs (E110=1,E220=0.1,G120=0.5,ν12=0.3)

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