TY - JOUR

T1 - Corner stress singularities in an FGM thin plate

AU - Huang, Chiung-Shiann

AU - Chang, M. J.

PY - 2007/5/1

Y1 - 2007/5/1

N2 - Describing the behaviors of stress singularities correctly is essential for obtaining accurate numerical solutions of complicated problems with stress singularities. This analysis derives asymptotic solutions for functionally graded material (FGM) thin plates with geometrically induced stress singularities. The classical thin plate theory is used to establish the equilibrium equations for FGM thin plates. It is assumed that the Young's modulus varies along the thickness and Poisson's ratio is constant. The eigenfunction expansion method is employed to the equilibrium equations in terms of displacement components for an asymptotic analysis in the vicinity of a sharp corner. The characteristic equations for determining the stress singularity order at the corner vertex and the corresponding corner functions are explicitly given for different combinations of boundary conditions along the radial edges forming the sharp corner. The non-homogeneous elasticity properties are present only in the characteristic equations corresponding to boundary conditions involving simple support. Finally, the effects of material non-homogeneity following a power law on the stress singularity orders are thoroughly examined by showing the minimum real values of the roots of the characteristic equations varying with the material properties and vertex angle.

AB - Describing the behaviors of stress singularities correctly is essential for obtaining accurate numerical solutions of complicated problems with stress singularities. This analysis derives asymptotic solutions for functionally graded material (FGM) thin plates with geometrically induced stress singularities. The classical thin plate theory is used to establish the equilibrium equations for FGM thin plates. It is assumed that the Young's modulus varies along the thickness and Poisson's ratio is constant. The eigenfunction expansion method is employed to the equilibrium equations in terms of displacement components for an asymptotic analysis in the vicinity of a sharp corner. The characteristic equations for determining the stress singularity order at the corner vertex and the corresponding corner functions are explicitly given for different combinations of boundary conditions along the radial edges forming the sharp corner. The non-homogeneous elasticity properties are present only in the characteristic equations corresponding to boundary conditions involving simple support. Finally, the effects of material non-homogeneity following a power law on the stress singularity orders are thoroughly examined by showing the minimum real values of the roots of the characteristic equations varying with the material properties and vertex angle.

KW - Asymptotic solutions

KW - Eigenfunction expansion method

KW - FGM thin plates

KW - Stress singularities

UR - http://www.scopus.com/inward/record.url?scp=33847760715&partnerID=8YFLogxK

U2 - 10.1016/j.ijsolstr.2006.08.024

DO - 10.1016/j.ijsolstr.2006.08.024

M3 - Article

AN - SCOPUS:33847760715

SN - 0020-7683

VL - 44

SP - 2802

EP - 2819

JO - International Journal of Solids and Structures

JF - International Journal of Solids and Structures

IS - 9

ER -