walther@59627
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(* Title: Knowledge/biegelinie-1.sml
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walther@59627
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Author: Walther Neuper 050826
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wneuper@59372
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(c) due to copyright terms
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*)
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"-----------------------------------------------------------------";
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"table of contents -----------------------------------------------";
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"-----------------------------------------------------------------";
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walther@59627
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"------ biegelinie-1.sml -----------------------------------------";
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"----------- the rules -------------------------------------------";
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"----------- simplify_leaf for this script -----------------------";
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walther@59627
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"----------- SubProblem (_,[setzeRandbedingungen,Biegelinien] ----";
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walther@59627
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"----------- investigate normalforms in biegelinien --------------";
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"-----------------------------------------------------------------";
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walther@59627
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"------ biegelinie-2.sml -----------------------------------------";
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walther@59627
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"----------- auto SubProblem (_,[vonBelastungZu,Biegelinien] -----";
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"----------- me SubProblem (_,[vonBelastungZu,Biegelinien] -------";
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"-----------------------------------------------------------------";
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"------ biegelinie-3.sml -----------------------------------------";
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"----------- auto method [Biegelinien,setzeRandbedingungenEin]--------------------------------";
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"----------- me method [Biegelinien,setzeRandbedingungenEin]----------------------------------";
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"-----------------------------------------------------------------";
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walther@59627
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"------ biegelinie-4.sml -----------------------------------------";
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"----------- IntegrierenUndKonstanteBestimmen2: Bsp.7.70. auto TODO investigate failure ------";
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walther@59627
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"----------- IntegrierenUndKonstanteBestimmen2: Bsp.7.70. me -----";
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"-----------------------------------------------------------------";
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"-----------------------------------------------------------------";
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"-----------------------------------------------------------------";
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val thy = @{theory "Biegelinie"};
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val ctxt = thy2ctxt' "Biegelinie";
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fun str2term str = (Thm.term_of o the o (parse thy)) str;
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fun term2s t = term_to_string'' "Biegelinie" t;
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walther@59620
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fun rewrit thm str = fst (the (rewrite_ thy tless_true e_rls true thm str));
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"----------- the rules -------------------------------------------";
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"----------- the rules -------------------------------------------";
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"----------- the rules -------------------------------------------";
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val t = rewrit @{thm Belastung_Querkraft} (str2term "- qq x = - q_0"); term2s t;
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if term2s t = "Q' x = - q_0" then ()
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else error "/biegelinie.sml: Belastung_Querkraft";
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val t = rewrit @{thm Querkraft_Moment} (str2term "Q x = - q_0 * x + c"); term2s t;
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if term2s t = "M_b' x = - q_0 * x + c" then ()
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else error "/biegelinie.sml: Querkraft_Moment";
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val t = rewrit @{thm Moment_Neigung} (str2term "M_b x = -q_0 * x^^^2/2 + q_0/2 *L*x");
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term2s t;
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if term2s t = "- EI * y'' x = - q_0 * x ^^^ 2 / 2 + q_0 / 2 * L * x" then ()
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else error "biegelinie.sml: Moment_Neigung";
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"----------- simplify_leaf for this script -----------------------";
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"----------- simplify_leaf for this script -----------------------";
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"----------- simplify_leaf for this script -----------------------";
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val srls = Rls {id="srls_IntegrierenUnd..",
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preconds = [],
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rew_ord = ("termlessI",termlessI),
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erls = append_rls "erls_in_srls_IntegrierenUnd.." e_rls
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[(*for asm in NTH_CONS ...*)
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Calc ("Orderings.ord_class.less",eval_equ "#less_"),
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(*2nd NTH_CONS pushes n+-1 into asms*)
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Calc("Groups.plus_class.plus", eval_binop "#add_")
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],
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srls = Erls, calc = [], errpatts = [],
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rules = [Thm ("NTH_CONS",num_str @{thm NTH_CONS}),
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Calc("Groups.plus_class.plus", eval_binop "#add_"),
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Thm ("NTH_NIL",num_str @{thm NTH_NIL}),
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Calc("Prog_Expr.lhs", eval_lhs "eval_lhs_"),
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Calc("Prog_Expr.rhs", eval_rhs "eval_rhs_"),
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Calc("Prog_Expr.argument'_in", eval_argument_in "Prog_Expr.argument'_in")
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],
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scr = EmptyScr};
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val rm_ = str2term"[M_b 0 = 0, M_b L = 0]";
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val M__ = str2term"M_b x = -1 * x ^^^ 2 / 2 + x * c + c_2";
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val SOME (e1__,_) = rewrite_set_ thy false srls
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(str2term "(NTH::[real,bool list]=>bool) 1 " $ rm_);
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if term2str e1__ = "M_b 0 = 0" then () else error "biegelinie.sml simplify NTH 1 rm_";
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val SOME (x1__,_) =
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rewrite_set_ thy false srls
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(str2term"argument_in (lhs (M_b 0 = 0))");
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if term2str x1__ = "0" then ()
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else error "biegelinie.sml simplify argument_in (lhs (M_b 0 = 0)";
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(*trace_rewrite := true; ..stopped Test_Isac.thy*)
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trace_rewrite:=false;
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"----------- SubProblem (_,[setzeRandbedingungen,Biegelinien] ----";
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"----------- SubProblem (_,[setzeRandbedingungen,Biegelinien] ----";
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"----------- SubProblem (_,[setzeRandbedingungen,Biegelinien] ----";
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val fmz = ["functionEq (M_b x = c_2 + c * x + -1 * q_0 / 2 * x ^^^ 2)",
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"substitution (M_b L = 0)",
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"equality equ_equ"];
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val (dI',pI',mI') = ("Biegelinie", ["makeFunctionTo","equation"],
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["Equation","fromFunction"]);
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val p = e_pos'; val c = [];
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val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
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val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
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val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
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val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
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val (p,_,f,nxt,_,pt) = me nxt p c pt;
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val (p,_,f,nxt,_,pt) = me nxt p c pt; f2str f =
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"M_b x = c_2 + c * x + -1 * q_0 / 2 * x ^^^ 2";
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val (p,_,f,nxt,_,pt) = me nxt p c pt; f2str f =
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"M_b L = c_2 + c * L + -1 * q_0 / 2 * L ^^^ 2";
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val (p,_,f,nxt,_,pt) = me nxt p c pt; f2str f =
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"0 = c_2 + c * L + -1 * q_0 / 2 * L ^^^ 2";
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val (p,_,f,nxt,_,pt) = me nxt p c pt; f2str f;
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val (p,_,f,nxt,_,pt) = me nxt p c pt; f2str f;
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if (* f2str f = "0 = c_2 + L * c + -1 * q_0 / 2 * L ^^^ 2" CHANGE NOT considered, already on leave*)
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f2str f = "0 = (2 * c_2 + 2 * L * c + -1 * L ^^^ 2 * q_0) / 2"
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then case nxt of End_Proof' => ()
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| _ => error "biegelinie.sml: SubProblem (_,[setzeRandbed 1"
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else error "biegelinie.sml: SubProblem (_,[setzeRandbed 2";
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"----------- investigate normalforms in biegelinien --------------";
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walther@59620
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"----------- investigate normalforms in biegelinien --------------";
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"----------- investigate normalforms in biegelinien --------------";
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"----- coming from integration, kept for later improvements:";
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val Q = str2term "Q x = c + -1 * q_0 * x";
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val M_b = str2term "M_b x = c_2 + c * x + -1 * q_0 / 2 * x ^^^ 2";
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val y' = str2term "y' x = c_3 + 1 / (-1 * EI) * (c_2 * x + c / 2 * x ^^^ 2 + -1 * q_0 / 6 * x ^^^ 3)";
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val y = str2term "y x = c_4 + c_3 * x +\n1 / (-1 * EI) * (c_2 / 2 * x ^^^ 2 + c / 6 * x ^^^ 3 + -1 * q_0 / 24 * x ^^^ 4)";
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(*^^^ 1 / (-1 * EI) NOT distributed - ok! ^^^^^^^^^^^^^^^^^^^^^^^*)
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