Table 1 Comparison between theoretical solution and numerical LCP solution at phase transition.
From: An Improved Linear Complementarity Solver for the Dynamic Analysis of Blast Loaded Structures
Theoretical solution | Numerical Lumped mass | Error Lumped mass (%) | Numerical Continuous mass | Error Continuous mass (%) | |
|---|---|---|---|---|---|
\({P}_{0}=1.5{P}_{c}\) | |||||
Hinge position \({\xi }_{*}/L\) | 0.58579 | 0.59000 | − 0.72 | 0.58500 | 0.1349 |
Displacement at the end of motion \({\bar{W}}_{1}=({W}_{1}/L)(mL){M}_{p}/{I}^{2}\) | 0.13471 | 0.13429 | 0.31 | 0.13456 | 0.1114 |
Cessation time \(\overline{t }={M}_{p}T/IL\) | 0.30463 | 0.30444 | 0.06 | 0.30784 | − 1.0537 |
\({P}_{0}=2.5{P}_{c}\) | |||||
Hinge position \({\xi }_{*}/L\) | 0.58579 | 0.59000 | − 0.72 | 0.58500 | 0.1349 |
Displacement at the end of first phase \({\bar{W}}_{1}=({W}_{1}/L)(mL){M}_{p}/{I}^{2}\) | 0.43885 | 0.43576 | 0.7 | 0.43615 | 0.6152 |
Displacement at the end of second phase \({\bar{W}}_{2}=({W}_{2}/L)(mL){M}_{p}/{I}^{2}\) | 0.48008 | 0.47692 | 0.66 | 0.47706 | 0.6291 |
Cessation time \({\bar{t}}_{2}={M}_{p}T/IL\) | 0.34315 | 0.34308 | 0.02 | 0.3450 | − 0.5391 |