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Civil-Comp Proceedings
ISSN 1759-3433 CCP: 73
PROCEEDINGS OF THE EIGHTH INTERNATIONAL CONFERENCE ON CIVIL AND STRUCTURAL ENGINEERING COMPUTING Edited by: B.H.V. Topping
Paper 88
Sensitivity of Inverse Boundary Element Techniques to Errors in Photoelastic Measurements P. Wang, A.A. Becker, I.A. Jones and T.H. Hyde
School of Mechanical, Materials, Manufacturing Engineering and Management, University of Nottingham, United Kingdom Full Bibliographic Reference for this paper
P. Wang, A.A. Becker, I.A. Jones, T.H. Hyde, "Sensitivity of Inverse Boundary Element Techniques to Errors in Photoelastic Measurements", in B.H.V. Topping, (Editor), "Proceedings of the Eighth International Conference on Civil and Structural Engineering Computing", Civil-Comp Press, Stirlingshire, UK, Paper 88, 2001. doi:10.4203/ccp.73.88
Keywords: boundary element method, photoelasticity, stress separation, inverse problem.
Summary
The application of computational mechanics techniques to inverse problems has
been receiving increasing attention in various branches of science and engineering.
In solid mechanics it may provide non-destructive evaluation tools which can be
used to identify unknown variables at the surface, such as the stress distribution in a
contact region between contacting bodies.
Photoelastic readings provide information regarding the differences of the
principal stresses and their orientations at interior points. However, it is often
difficult to separate the individual Cartesian stress components from the photoelastic
data The BE technique is an ideal companion to photoelastic analysis since, unlike
the finite element (FE) method, the interior solutions can be represented by
unconnected points rather than discretised elements.
This paper presents an inverse boundary element (BE) technique to reconstruct the boundary conditions in the unknown regions using photoelastic measurements taken from the photoelastic isochromatic fringe order and the isoclinic angle at interior points. The separate individual Cartesian stress components are then obtained using the forward BE method The BE approach is based on two integral equations: a surface (boundary) integral equation relating displacements and tractions on the surface, and an interior integral equation relating the stresses at the interior points to the surface displacements and surface tractions. The surface (boundary) integral equation is as follows:
where ![]() ![]() ![]() ![]() where ![]() ![]() ![]() where ![]() ![]() ![]() ![]() Previous research has shown that inverse BE methods relying on the interior kernels only cannot be used to obtain the solution, and that it is necessary to use both interior integral equation 88.4 and surface integral equation 88.2. In the unknown region ![]() ![]() ![]() Subscript ![]() ![]() ![]() ![]() ![]() where
and
The Singular Value Decomposition (SVD) method is used to solve equation 88.7. It is clear that once ![]() ![]() ![]() ![]() ![]() ![]()
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