Technical Brief

Effective Convergence Checks for Solution Verification of Finite Element Stresses at Three-Dimensional Stress Concentrations

[+] Author and Article Information
Jeffrey R. Beisheim

Development Department, ANSYS Inc., Canonsburg, PA 15317

Glenn Sinclair

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

Patrick J. Roache

Consultant, 1215 Apache Drive, Socorro, NM 87801

1Corresponding author.

ASME doi:10.1115/1.4042515 History: Received July 05, 2018; Revised January 10, 2019


Current computational capabilities facilitate the application of finite element analysis to three-dimensional geometries to determine peak stresses. The three-dimensional stress concentrations so quantified are useful in practice provided the discretization error attending their determination with finite elements has been sufficiently controlled. Here we provide some convergence checks and companion a posteriori error estimates that can be used to verify such three-dimensional finite element analysis, and thus enable engineers to control discretization errors. These checks are designed to promote conservative error estimation. They are applied to twelve three-dimensional test problems that have exact solutions for their peak stresses. Associated stress concentration factors span a range that is larger than that normally experienced in engineering. Error levels in the finite element analysis of these peak stresses are classified in accordance with: 1-5%, satisfactory; 1/5-1%, good; and <1/5%, excellent. The present convergence checks result in 111 error assessments for the test problems. For these 111, errors are assessed as being at the same level as true exact errors on 99 occasions, one level worse for the other 12. Hence stress error estimation that is largely reasonably accurate (89%), and otherwise modestly conservative (11%).

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