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1 (* chapter 'Biegelinie' from the textbook: |
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2 Timischl, Kaiser. Ingenieur-Mathematik 3. Wien 1999. p.268-271. |
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3 author: Walther Neuper |
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4 050826, |
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5 (c) due to copyright terms |
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6 |
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7 remove_thy"Biegelinie"; |
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8 use_thy"Knowledge/Biegelinie"; |
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9 use_thy_only"Knowledge/Biegelinie"; |
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10 |
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11 remove_thy"Biegelinie"; |
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12 use_thy"Knowledge/Isac"; |
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13 *) |
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14 |
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15 Biegelinie = Integrate + Equation + EqSystem + |
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16 |
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17 consts |
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18 |
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19 q_ :: real => real ("q'_") (* Streckenlast *) |
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20 Q :: real => real (* Querkraft *) |
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21 Q' :: real => real (* Ableitung der Querkraft *) |
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22 M'_b :: real => real ("M'_b") (* Biegemoment *) |
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23 M'_b' :: real => real ("M'_b'") (* Ableitung des Biegemoments *) |
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24 y'' :: real => real (* 2.Ableitung der Biegeline *) |
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25 y' :: real => real (* Neigung der Biegeline *) |
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26 (*y :: real => real (* Biegeline *)*) |
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27 EI :: real (* Biegesteifigkeit *) |
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28 |
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29 (*new Descriptions in the related problems*) |
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30 Traegerlaenge :: real => una |
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31 Streckenlast :: real => una |
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32 BiegemomentVerlauf :: bool => una |
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33 Biegelinie :: (real => real) => una |
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34 Randbedingungen :: bool list => una |
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35 RandbedingungenBiegung :: bool list => una |
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36 RandbedingungenNeigung :: bool list => una |
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37 RandbedingungenMoment :: bool list => una |
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38 RandbedingungenQuerkraft :: bool list => una |
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39 FunktionsVariable :: real => una |
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40 Funktionen :: bool list => una |
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41 Gleichungen :: bool list => una |
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42 |
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43 (*Script-names*) |
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44 Biegelinie2Script :: "[real,real,real,real=>real,bool list, |
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45 bool] => bool" |
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46 ("((Script Biegelinie2Script (_ _ _ _ _ =))// (_))" 9) |
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47 BiegelinieScript :: "[real,real,real,real=>real,bool list,bool list, |
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48 bool] => bool" |
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49 ("((Script BiegelinieScript (_ _ _ _ _ _ =))// (_))" 9) |
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50 Biege2xIntegrierenScript :: "[real,real,real,bool,real=>real,bool list, |
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51 bool] => bool" |
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52 ("((Script Biege2xIntegrierenScript (_ _ _ _ _ _ =))// (_))" 9) |
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53 Biege4x4SystemScript :: "[real,real,real,real=>real,bool list, |
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54 bool] => bool" |
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55 ("((Script Biege4x4SystemScript (_ _ _ _ _ =))// (_))" 9) |
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56 Biege1xIntegrierenScript :: |
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57 "[real,real,real,real=>real,bool list,bool list,bool list, |
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58 bool] => bool" |
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59 ("((Script Biege1xIntegrierenScript (_ _ _ _ _ _ _ =))// (_))" 9) |
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60 Belastung2BiegelScript :: "[real,real, |
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61 bool list] => bool list" |
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62 ("((Script Belastung2BiegelScript (_ _ =))// (_))" 9) |
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63 SetzeRandbedScript :: "[bool list,bool list, |
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64 bool list] => bool list" |
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65 ("((Script SetzeRandbedScript (_ _ =))// (_))" 9) |
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66 |
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67 rules |
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68 |
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69 Querkraft_Belastung "Q' x = -q_ x" |
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70 Belastung_Querkraft "-q_ x = Q' x" |
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71 |
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72 Moment_Querkraft "M_b' x = Q x" |
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73 Querkraft_Moment "Q x = M_b' x" |
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74 |
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75 Neigung_Moment "y'' x = -M_b x/ EI" |
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76 Moment_Neigung "M_b x = -EI * y'' x" |
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77 |
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78 (*according to rls 'simplify_Integral': .. = 1/a * .. instead .. = ../ a*) |
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79 make_fun_explicit "Not (a =!= 0) ==> (a * (f x) = b) = (f x = 1/a * b)" |
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80 |
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81 end |
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82 |