Research Papers

On the Detection of Stress Singularities in Finite Element Analysis

[+] Author and Article Information
G. B. Sinclair

Department of Mechanical Engineering,
Louisiana State University,
Baton Rouge, LA 70803

J. R. Beisheim

Development Department,
Canonsburg, PA 15317

A. A. Kardak

OPENSO Engineering,
Edwardsville, IL 62025

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received September 8, 2018; final manuscript received October 16, 2018; published online December 3, 2018. Assoc. Editor: Shaoxing Qu.

J. Appl. Mech 86(2), 021005 (Dec 03, 2018) (18 pages) Paper No: JAM-18-1518; doi: 10.1115/1.4041766 History: Received September 08, 2018; Revised October 16, 2018

Finite element analysis (FEA) has become the method of choice for the stress analysis of many of the complex configurations encountered in practice. Such configurations can contain stress singularities. Then, it is critical for the necessarily finite estimates from finite elements to be rejected as valid results for the infinite stresses present. There is an extensive literature devoted to the asymptotic identification of stress singularities that can often, but not always, provide a means for such rejection. The present study seeks to offer a further means of rejection: mesh refinement with divergence checks. These divergence checks are a natural counterpart to the convergence checks of ASME. The two are used together on 265 finite element stresses at 32 different singularities: all of these finite element stresses are thus rejected.

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Fig. 1

Dovetail blade attachment in a gas turbine, with a close-up showing an undercut

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Fig. 2

Simulation configuration for undercutting contact and initial finite element mesh

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Fig. 3

Bicycle wrench configuration: (a) geometry and coordinates and (b) initial finite element mesh around the rightmost bolt hole

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Fig. 4

Clamped block under pressure

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Fig. 5

Clamped plate under shear and initial finite element mesh

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Fig. 6

Plate indented by a rigid wedge and initial finite element mesh

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Fig. 7

Half-space indented by a rigid cone: (a) genesic configuration and (b) initial finite element mesh for actual configuration (rotated through 90 deg about the y-axis)

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Fig. 8

Elliptical plate with an elliptical hole under tension (a/b = 18 7/16)

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Fig. 9

Elliptical plate with hyperbolic notches under tension (Δ = 0.99)

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Fig. 10

Ellipsoid with a hyperbolic notch under tension (Δ = 0.99)



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