2. Benchmark solution#

2.1. Calculation method#

The reference solution for calculating the stresses in the beam is given in [1], [2].

2.2. Reference quantities and results#

Constraints \({\sigma }_{\mathit{xx}}\), \({\sigma }_{\mathit{yy}}\) and \({\sigma }_{\mathit{xy}}\) along the \(Y\) axis.

\({\sigma }_{\mathit{xx}}(Y)\mathrm{=}\mathrm{-}\mathrm{10Y}+10\)

\({\sigma }_{\mathit{yy}}(Y)\mathrm{=}0.\)

\({\sigma }_{\mathit{xy}}(Y)\mathrm{=}0.\)

\(Y(m)\)

\({\sigma }_{\mathit{xx}}\)

\({\sigma }_{\mathit{yy}}\)

\({\sigma }_{\mathit{xy}}\)

\(0.0\)

\(10.0\mathit{Pa}\)

\(0.0\mathit{Pa}\)

\(0.0\mathit{Pa}\)

\(0.5\)

\(5.0\mathit{Pa}\)

\(0.0\mathit{Pa}\)

\(0.0\mathit{Pa}\)

\(1.0\)

\(0.0\mathit{Pa}\)

\(0.0\mathit{Pa}\)

\(0.0\mathit{Pa}\)

\(1.5\)

\(\mathrm{-}5.0\mathit{Pa}\)

\(0.0\mathit{Pa}\)

\(0.0\mathit{Pa}\)

\(2.0\)

\(\mathrm{-}10.0\mathit{Pa}\)

\(0.0\mathit{Pa}\)

\(0.0\mathit{Pa}\)

2.3. Uncertainties about the solution#

Analytical Solution

2.4. Bibliographical references#

  1. M.H. SADR - LAHIDJANI: « Modeling and analysis of thin elastic plates and shells subjected to temperature fields », Doctoral thesis UTC, 1984.

    1. PITER, HARTEL H. « Improved stress evaluation under thermal load for simple finite element », I.J.N.M.E., Vol. 15, 1507-1515, 1980.