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johnpye |
838 |
REQUIRE "atoms.a4l"; |
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(* a parameterised simply-supported beam model *) |
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MODEL beam_parameterised( |
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n WILL_BE integer_constant; |
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E WILL_BE youngs_modulus; |
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I WILL_BE second_moment_of_area; |
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L WILL_BE distance; |
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); |
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johnpye |
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v[1..n] IS_A deflection; |
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johnpye |
838 |
x[1..n] IS_A distance; |
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johnpye |
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P,R1,R2 IS_A force; |
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johnpye |
838 |
a,b IS_A distance; |
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a + b = L; |
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johnpye |
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(* |
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johnpye |
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isrightp[1..n] IS_A boolean_var; |
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johnpye |
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FOR i IN [1..n] CREATE |
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v_left[i]: v[i] = P*b/(6*E*I*L)*((L^2 - b^2)*x[i] - x[i]^3); |
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v_right[i]: v[i] = P*b/(6*E*I*L)*((L^2 - b^2)*x[i] - x[i]^3 + (L/b)*(x[i]-a)^3 ); |
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johnpye |
839 |
END FOR; |
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CONDITIONAL |
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FOR i IN [1..n] CREATE |
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johnpye |
838 |
isright[i]: x[i] > a; |
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johnpye |
839 |
END FOR; |
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END CONDITIONAL; |
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johnpye |
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johnpye |
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FOR i IN [1..n] CREATE |
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johnpye |
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isrightp[i] == SATISFIED(isright[i]); |
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WHEN (isrightp[i]) |
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CASE TRUE: |
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USE v_right[i]; |
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CASE FALSE: |
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USE v_left[i]; |
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END WHEN; |
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johnpye |
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END FOR; |
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*) |
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FOR i IN [1..n] CREATE |
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defl[i]: v[i] = P*b/(6*E*I*L)*((L^2 - b^2)*x[i] - x[i]^3 + (L/b)*( 0.5 * (x[i]-a + abs(x[i]-a)) )^3 ); |
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END FOR; |
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(* sum of vertical forces *) |
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R1 + P + R2 = 0 {N}; |
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(* sum of moments about left end *) |
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P * a + R2 * L = 0 {N*m}; |
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johnpye |
839 |
METHODS |
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METHOD specify; |
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FIX P, a, x[1..n]; |
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END specify; |
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johnpye |
840 |
METHOD values; |
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RUN bound_self; |
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END values; |
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METHOD bound_self; |
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johnpye |
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a.upper_bound := 100 {m}; |
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b.upper_bound := 100 {m}; |
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johnpye |
840 |
L.upper_bound := 100 {m}; |
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P.lower_bound := -2e4 {kN}; |
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P.upper_bound := 2e4 {kN}; |
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v[1..n].upper_bound := 10 {m}; |
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v[1..n].lower_bound := -10 {m}; |
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x[1..n].upper_bound := 100 {m}; |
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x[1..n].lower_bound := -100 {m}; |
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R1.lower_bound := -1e4 {kN}; |
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R1.upper_bound := 1e4 {kN}; |
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R2.lower_bound := -1e4 {kN}; |
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R2.upper_bound := 1e4 {kN}; |
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END bound_self; |
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johnpye |
838 |
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END beam_parameterised; |
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johnpye |
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(* superposition of n beams with displacements calculated at n locations *) |
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MODEL beam_superposition( |
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n WILL_BE integer_constant; |
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E WILL_BE youngs_modulus; |
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I WILL_BE second_moment_of_area; |
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L WILL_BE distance; |
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); |
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B[1..n] IS_A beam_parameterised(n,E,I,L); |
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v[1..n] IS_A deflection; |
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x[1..n] IS_A distance; |
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R1,R2 IS_A force; |
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johnpye |
838 |
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johnpye |
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FOR i IN [1..n] CREATE |
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B[1..n].x[i], x[i] ARE_THE_SAME; |
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v[i] = SUM[B[j].v[i] | j IN [1..n]]; |
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END FOR; |
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(* displacements are calculated at the locations of the loads *) |
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FOR i IN [1..n] CREATE |
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B[i].a, x[i] ARE_THE_SAME; |
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END FOR; |
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R1 = SUM[B[i].R1 | i IN [1..n]]; |
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R2 = SUM[B[i].R2 | i IN [1..n]]; |
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METHODS |
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METHOD bound_self; |
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FOR i IN [1..n] DO |
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RUN B[i].bound_self; |
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v[i].upper_bound := 10 {m}; |
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v[i].lower_bound := -10 {m}; |
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x[i].upper_bound := 500 {m}; |
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x[i].lower_bound := -500 {m}; |
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END FOR; |
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R1.lower_bound := -1e4 {kN}; |
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R1.upper_bound := 1e4 {kN}; |
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R2.lower_bound := -1e4 {kN}; |
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R2.upper_bound := 1e4 {kN}; |
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END bound_self; |
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END beam_superposition; |
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johnpye |
838 |
(* |
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Model of a simply-supported beam of length L |
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with a single vertical point load P at 0 < a < L |
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*) |
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MODEL beam; |
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n IS_A integer_constant; |
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n :== 1; |
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E IS_A youngs_modulus; |
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I IS_A second_moment_of_area; |
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L IS_A distance; |
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B IS_A beam_parameterised(n,E,I,L); |
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P ALIASES B.P; |
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a ALIASES B.a; |
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b ALIASES B.b; |
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x ALIASES B.x[1]; |
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v ALIASES B.v[1]; |
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METHODS |
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METHOD specify; |
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FIX E, I, L; |
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FIX P, a; |
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FIX x; |
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END specify; |
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METHOD values; |
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E := 200 {GPa}; (* approx, for steel *) |
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I := 142e6 {mm^4}; (* AISC Universal Beam 360UB50.7 *) |
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L := 3.5 {m}; |
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P := 14.0 {kN}; |
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a := 1.75 {m}; |
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x := 2.0 {m}; |
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johnpye |
840 |
END values; |
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METHOD bound_self; |
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RUN B.bound_self; |
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L.lower_bound := 500 {m}; |
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L.upper_bound := 0{m}; |
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END bound_self; |
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johnpye |
838 |
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METHOD on_load; |
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johnpye |
840 |
RUN reset; |
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RUN bound_self; |
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johnpye |
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RUN values; |
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END on_load; |
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END beam; |
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