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@@ -297,7 +297,7 @@ You get the point, even though we know thanks to [Richard Feynmann](https://en.w |
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Getting back to the case study: do we need to do FEM analysis? Well, it does not look like we can obtain the stresses of the transient cycles with just pencil and paper. But how much complexity should we add? We might do as little as axisymmetric linear steady-state conservative studies or as much as full three-dimensional non-linear transient best-estimate plus uncertainties computations. And here is where good engineers should appear: in putting their engineering judgement (call it experience or hunches) into defining what to solve. And it is not (just) because the first option is faster to solve than the latter. Involving many complex methods need more engineering time |
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1. to prepare the input data and set up the algorithms, |
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2. to cope with the many more errors that will inevitable appear during the computation, and |
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2. to cope with the many more mistakes that will inevitable appear during the computation, and |
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3. to analyse the output data and write engineering reports. |
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In the first years of the [history of computers](https://en.wikipedia.org/wiki/History_of_computing_hardware), when programs were written in decks and output results were printed in continuous paper sheets, it made sense for computer programs to calculate and write as much data as possible even if it was not needed. One would never know if it would not be needed in the future, and CPU time was so expensive that re-running engineering computations because a particular result was not included in the output was forbidden. But that is not remotely true in the XXI century anymore. Computing time is far cheaper than engineering time (result known as the [UNIX Rule of Economy](http://www.catb.org/~esr/writings/taoup/html/ch01s06.html)) that it should be neglected with respect to the time spent by a cognisant engineer searching and sorting thousands of hard-to-read floating-point numbers. |
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@@ -525,12 +525,12 @@ The loads in each cases are applied to the three remaining faces, namely “righ |
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````{=latex} |
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\rowcolors{2}{black!10}{black!0} |
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```` |
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| | | “right” | | | “back” | | | “top” | | |
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| ------------------- |:-----:|:-----:|:-----:|:-----:|:-----:|:-----:|:-----:|:-----:|:-----:| |
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| | $F_x$ | $F_y$ | $F_z$ | $F_x$ | $F_y$ | $F_z$ | $F_x$ | $F_y$ | $F_z$ | |
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| Case A, pure normal | +10 | 0 | 0 | 0 | +20 | 0 | 0 | 0 | +30 | |
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| Case B, pure shear | 0 | +15 | -15 | +25 | 0 | -5 | -15 | +25 | 0 | |
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| Case C, combination | +10 | +15 | -15 | +25 | +20 | -5 | -15 | +25 | +30 | |
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| | | “right” | | | “back” | | | “top” | | |
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| ------ |:-----:|:-----:|:-----:|:-----:|:-----:|:-----:|:-----:|:-----:|:-----:| |
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| | $F_x$ | $F_y$ | $F_z$ | $F_x$ | $F_y$ | $F_z$ | $F_x$ | $F_y$ | $F_z$ | |
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| Case A | +10 | 0 | 0 | 0 | +20 | 0 | 0 | 0 | +30 | |
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| Case B | 0 | +15 | -15 | +25 | 0 | -5 | -15 | +25 | 0 | |
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| Case C | +10 | +15 | -15 | +25 | +20 | -5 | -15 | +25 | +30 | |
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divert(-1) |
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@@ -760,8 +760,9 @@ You can get both the exponential nature of each added bullet and how easily we c |
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* The error with respect to the analytical solutions as a function of the CPU time needed to compute the membrane stress is similar for both first and second-order grids. But for the computation of the membrane plus bending stress ([@fig:error-MB-vs-cpu]), first-order grids give very poor results compared to second-order grids for the same CPU time. |
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::::: {#fig:error-vs-cpu} |
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{#fig:error-M-vs-cpu width=48%}\ |
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{#fig:error-MB-vs-cpu width=48%} |
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{#fig:error-M-vs-cpu width=90%} |
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{#fig:error-MB-vs-cpu width=90%} |
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Error in the computation of the linearised stresses vs. CPU time needed to solve the problem using FEM |
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::::: |
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@@ -1236,6 +1237,8 @@ los cufens son parecidos |
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errors and uncertainties: model parameters (is E what we think? is the material linear?), geometry (does the CAD represent the reality?) equations (any effect we did not have take account), discretization (how well does the mesh describe the geometry?) |
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garbage in - garbage out |
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do you trust your FEM program? |
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do you trust your engineering judgment? |
gtheler
6 yıl önce