2. Benchmark solution#
2.1. Calculation method used for the reference solution#
The reference solution is the one given in sheet SSLS27 /89 of guide VPCS:
Displacement of point \(C\): \(w=35.37{10}^{-7}m\)
Resulting of integration efforts (\(\mathit{AD}\)) following \(\mathit{DZ}\): \({\mathit{RESULT}}_{Z}\mathrm{=}0\)
Moment associated with the result of the efforts to embed in the middle of \(\mathit{AD}\):
\({\mathit{MOMENT}}_{X}\mathrm{=}\mathrm{-}1\)
\({\mathit{MOMENT}}_{Y}\mathrm{=}0\)
Forces in the same direction perpendicular to the plate [bib3]
The Euler beam formulation gives an approximate solution for a different Poisson’s ratio \(\nu\).
Move all the nodes to the \(\mathrm{BC}\) side:
Resulting of integration efforts (\(\mathit{AD}\)) following \(\mathit{DZ}\): \({\mathit{RESULT}}_{Z}\mathrm{=}\mathrm{-}2\)
Moment associated with the result of the efforts to embed in the middle of \(\mathit{AD}\):
\({\mathit{MOMENT}}_{X}\mathrm{=}0\)
\({\mathit{MOMENT}}_{Y}\mathrm{=}24\)
2.2. Benchmark results#
Move points \(B\), \(C\), and \(E\). Resulting from embedding along \(\mathit{AD}\), embedding moment with respect to axes \(X\) and \(Y\) in the middle of \(\mathit{AD}\).
2.3. Uncertainty about the solution#
Analytical solution.
2.4. Bibliographical references#
ROBINSON « Evaluation element. A set of assessment parts and standard tests » Proceedings of Finite Element Methods in the Commercial Environment, Vol. 1, (October 1978).
J.L. BATOZ, M.B. TAHAR « Evaluation of new quadrilateral thin plate boundary element » International Journal for Numerical Methods in Engineering, Vol. 18, John Wiley & Sons (1982).
R.J. ROARK, W.C. YOUNG « Formulas for Stress and Strain » New York: McGraw-Hill, 5th edition, p 96.