Table 3 Theoretical and LCP results of impulsively loaded beam with bending shear interaction.
| Â | Theoretical solution, Jones34 | Numerical solution (100 uniform mass elements) | Numerical solution (100 uniform mass elements) | Error (100 lumped mass elements) (%) | Error (100 uniform mass elements) (%) |
|---|---|---|---|---|---|
Final displacement \(\overline{W}_{f} = \left( {W_{f} /L} \right)\left( {mL} \right)M_{p} /I^{2}\) | 0.08333 | 0.08352 | 0.08345 | -0.22801 | -0.14401 |
Time when shear-sliding ceases \(\overline{t}_{1} = M_{p} t_{1} /IL\) | 0.06322 | 0.06286 | 0.06325 | 0.56944 | -0.04745 |
Time when hinges coalesce \(\overline{t}_{2} = M_{p} t_{2} /IL\) | 0.08333 | 0.08020 | 0.08198 | -0.07200 | 2.65211 |
Cessation time \(\overline{t}_{3} = M_{p} t_{3} /IL\) | 0.25 | 0.25 | 0.25 | 0 | 0 |
