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Table 6 Strain energy (\(U_{\mathrm {strain}}\)) and bending energy (\(U_{\mathrm {bending}}\)) for different load cases and load intensities

From: Introducing the Logarithmic finite element method: a geometrically exact planar Bernoulli beam element

Load case Moderate load intensity Strong load intensity
\(\varvec{U_{\mathrm {strain}}}\) (J) \(\varvec{U_{\mathrm {bending}}}\) (J) \(\varvec{{U_{\mathrm {strain}}}/{U_{\mathrm{int}}}}\) (%) \(\varvec{U_{\mathrm {strain}}}\) (J) \(\varvec{U_{\mathrm {bending}}}\) (J) \({\varvec{U_{\mathrm {strain}}}/\varvec{U_{\mathrm{int}}}}\) (%)
A 451 2108 17.6 10,284 26,541 27.9
B 509 1885 21.3 11,891 9724 55.0
C 264 2299 10.3 9469 27,909 25.3
D 380 808 32.0 6375 3500 64.6
E 95 818 10.4 3946 5416 42.1
F 8 464 1.6 1405 6366 18.1
  1. \(U_{\mathrm{int}}\) denotes the internal energy, which is given as the sum of the strain energy and the bending energy