appendices:a10
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appendices:a10 [2019/06/21 13:02] helene |
appendices:a10 [2020/08/25 15:46] (current) |
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| | \[= 0\] | \[\Delta X = 0\] |Most effective choice| | | \[= 0\] | \[\Delta X = 0\] |Most effective choice| | ||
| | \[= 1\] | \[\Delta X = \dot{V}_0 \Delta t + \ddot{V}_0 \frac{\Delta t^2}{2}\] |Central difference method| | | \[= 1\] | \[\Delta X = \dot{V}_0 \Delta t + \ddot{V}_0 \frac{\Delta t^2}{2}\] |Central difference method| | ||
| - | | \[= 2\] | \[\Delta X = \dot{V}_0 \Delta t + \frac{1}{2} \ddot{V}_0 \Delta t^2 \left(1-\frac{2 \beta}{\gamma}\right)\] |Central difference method| | + | | \[= 2\] | \[\Delta X = \dot{V}_0 \Delta t + \frac{1}{2} \ddot{V}_0 \Delta t^2 \left(1-\frac{2 \beta}{\gamma}\right)\] |Newmark's algorithm with $ \dot{V}_1=\dot{V}_0$| |
| + | | \[= 3\] | \[\Delta X = \dot{V}_0 \Delta t \left(1-\frac{\beta}{\gamma}\right) + \frac{1}{2} \ddot{V}_0 \Delta t^2 \left(1-\frac{2 \beta}{\gamma}\right)\] |Newmark's algorithm with $ \dot{V}_1=0$| | ||
| + | | \[= 3\] | \[\Delta X = \dot{V}_0 \Delta t + \frac{1}{2} \ddot{V}_0 \Delta t^2 \left(1-2 \beta\right)\] |Newmark's algorithm with $ \ddot{V}_1=0$| | ||
| + | With: | ||
| + | * $\dot{V}_0$ = speeds at the beginning of the step | ||
| + | * $\ddot{V}_0$ = accelerations at the beginning of the step | ||
| + | * $\dot{V}_1$ = speeds at the end of the step | ||
| + | * $\ddot{V}_1$ = accelerations at the end of the step | ||
appendices/a10.1561114968.txt.gz · Last modified: 2020/08/25 15:33 (external edit)
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