Verification of Contact Stress with Surrogate Duality

DOI

10.2991/amsm-16.2016.9How to use a DOI?

Keywords

contact stress; bound; surrogate; verification; finite elements

Abstract

We present a method for verifying the contact stress of elastic bodies. An explicit formulation of the total contact force, a fraction function with the numerator as a linear function and the denominator as a quadratic convex function, is derived by using the surrogate model of quadratic optimization for the contact problem. Then a bound formulation is obtained for the sum of the nodal contact forces, which is an explicit formulation of matrices of the finite element model, derived by maximizing the fraction function under the constraint that the sum of the normalized nodal contact forces is one. The bound is solved with the problem dimensions being only the number of contact nodes or node pairs, which are much smaller than the dimension for the original problem. Next, a scheme for constructing an upper bound on the contact stress is proposed that uses the bound on the sum of the nodal contact forces obtained on a fine finite element mesh and the nodal contact forces obtained on a coarse finite element mesh. Finally, the proposed method is verified through an example to demonstrate its feasibility and robustness.

Copyright

© 2016, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Zhaocheng Xuan
PY  - 2016/05
DA  - 2016/05
TI  - Verification of Contact Stress with Surrogate Duality
BT  - Proceedings of the 2016 International Conference on Applied Mathematics, Simulation and Modelling
PB  - Atlantis Press
SP  - 36
EP  - 39
SN  - 2352-538X
UR  - https://doi.org/10.2991/amsm-16.2016.9
DO  - 10.2991/amsm-16.2016.9
ID  - Xuan2016/05
ER  -