models/johnpye/beam.a4c

REQUIRE "atoms.a4l";

(* a parameterised simply-supported beam model *)

MODEL beam_parameterised(
	n WILL_BE integer_constant;
	E WILL_BE youngs_modulus;
	I WILL_BE second_moment_of_area;
	L WILL_BE distance;
);
	v[1..n] IS_A distance;
	x[1..n] IS_A distance;
	
	P IS_A force;
	a,b IS_A distance;
	a + b = L;

	isrightp[1..n] IS_A boolean_var;
	
	FOR i IN [1..n] CREATE
		v_left[i]: v[i] = P*b/(6*E*I*L)*((L^2 - b^2)*x[i] - x[i]^3);
		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 );
	END FOR;
	
	CONDITIONAL
		FOR i IN [1..n] CREATE
			isright[i]: x[i] > a;
		END FOR;
	END CONDITIONAL;

	FOR i IN [1..n] CREATE
		isrightp[i] == SATISFIED(isright[i]);

		WHEN (isrightp[i])
			CASE TRUE:
				USE v_right[i];
			CASE FALSE:
				USE v_left[i];
		END WHEN;
	END FOR;
METHODS
METHOD specify;
	FIX P, a, x[1..n];
END specify;
METHOD values;
	a.upper_bound := 100 {m};
	b.upper_bound := 100 {m};
	L.upper_bound := 100 {m};
END values;

END beam_parameterised;

(*
	Model of a simply-supported beam of length L
	with a single vertical point load P at 0 < a < L
*)

MODEL beam;
	n IS_A integer_constant;
	n :== 1;
	E IS_A youngs_modulus;
	I IS_A second_moment_of_area;
	L IS_A distance;
	B IS_A beam_parameterised(n,E,I,L);

	P ALIASES B.P;
	a ALIASES B.a;
	b ALIASES B.b;
	
	x ALIASES B.x[1];
	v ALIASES B.v[1];
	
METHODS
METHOD specify;
	FIX E, I, L;
	FIX P, a;
	FIX x;
END specify;

METHOD values;
	E := 200 {GPa}; (* approx, for steel *)
	I := 142e6 {mm^4}; (* AISC Universal Beam 360UB50.7 *)
	L := 3.5 {m};
	P := 14.0 {kN};
	a := 1.75 {m};
	x := 2.0 {m};
END values;

METHOD on_load;
	RUN reset;
	RUN values;
END on_load;

END beam;

1	johnpye	838	REQUIRE "atoms.a4l";
2
3			(* a parameterised simply-supported beam model *)
4
5			MODEL beam_parameterised(
6			n WILL_BE integer_constant;
7			E WILL_BE youngs_modulus;
8			I WILL_BE second_moment_of_area;
9			L WILL_BE distance;
10			);
11			v[1..n] IS_A distance;
12			x[1..n] IS_A distance;
13
14			P IS_A force;
15			a,b IS_A distance;
16			a + b = L;
17
18	johnpye	839	isrightp[1..n] IS_A boolean_var;
19	johnpye	838
20			FOR i IN [1..n] CREATE
21			v_left[i]: v[i] = Pb/(6EIL)((L^2 - b^2)x[i] - x[i]^3);
22			v_right[i]: v[i] = Pb/(6EIL)((L^2 - b^2)x[i] - x[i]^3 + (L/b)*(x[i]-a)^3 );
23	johnpye	839	END FOR;
24
25			CONDITIONAL
26			FOR i IN [1..n] CREATE
27	johnpye	838	isright[i]: x[i] > a;
28	johnpye	839	END FOR;
29			END CONDITIONAL;
30	johnpye	838
31	johnpye	839	FOR i IN [1..n] CREATE
32	johnpye	838	isrightp[i] == SATISFIED(isright[i]);
33
34			WHEN (isrightp[i])
35			CASE TRUE:
36			USE v_right[i];
37			CASE FALSE:
38			USE v_left[i];
39			END WHEN;
40			END FOR;
41	johnpye	839	METHODS
42			METHOD specify;
43			FIX P, a, x[1..n];
44			END specify;
45			METHOD values;
46			a.upper_bound := 100 {m};
47			b.upper_bound := 100 {m};
48			L.upper_bound := 100 {m};
49			END values;
50	johnpye	838
51			END beam_parameterised;
52
53			(*
54			Model of a simply-supported beam of length L
55			with a single vertical point load P at 0 < a < L
56			*)
57
58			MODEL beam;
59			n IS_A integer_constant;
60			n :== 1;
61			E IS_A youngs_modulus;
62			I IS_A second_moment_of_area;
63			L IS_A distance;
64			B IS_A beam_parameterised(n,E,I,L);
65
66			P ALIASES B.P;
67			a ALIASES B.a;
68			b ALIASES B.b;
69
70			x ALIASES B.x[1];
71			v ALIASES B.v[1];
72
73			METHODS
74			METHOD specify;
75			FIX E, I, L;
76			FIX P, a;
77			FIX x;
78			END specify;
79
80			METHOD values;
81			E := 200 {GPa}; (* approx, for steel *)
82			I := 142e6 {mm^4}; (* AISC Universal Beam 360UB50.7 *)
83			L := 3.5 {m};
84			P := 14.0 {kN};
85			a := 1.75 {m};
86			x := 2.0 {m};
87			END values;
88
89			METHOD on_load;
90			RUN reset;
91			RUN values;
92			END on_load;
93
94			END beam;
95