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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