Test 1.1 Space frame with elastic supports

Verification of the LIRA-FEM software / Test 1.1 Space frame with elastic supports / Analytical solution: M. Laredo,Sistance des matriaux, Paris, Dunod, 1970, p. 165.

Linear static problems for rod systems, plates and shells, three-dimensional problems

Analytical solution: M. Laredo, sistance des matriaux, Paris, Dunod, 1970, p. 165.

Geometry:

L = 2 m;
Iy = Ix = I = 10^-6 m⁴;
J = 2.0 x 10^-6 m⁴;
A = 0.001 m².

Material characteristic: Isotropic elastic, E=2.1 С… 10¹¹ Pa, G=7.875 x 10¹⁰ Pa.

Boundary conditions:
At point A: _y=0, u_A=w_A=0; Р_Сѓ=52500 N/m (compressive-tensile stiffness);
Rx=Rz=52500 Nm/rad (torsional stiffness).
At point B: _X=0, v_B=w_B=0; Р_С…=52500 N/m (compressive-tensile stiffness);
Ry=Rz=52500 Nm/rad (torsional stiffness).
At point H: the hinge.

Loads:

F = -10000 Рќ.

CALCULATION RESULTS:

Point	Desired value	Analytical solution	Calculation results (LIRA)	Accuracy,%
A	Moment РњС…, Nm	-8437,5	-8437,6	0,001
A	Moment РњСѓ, Nm	-1562,5	-1562,4	0,006
A	Moment Рњz, Nm	3125,0	3124,8	0,006
B	Moment РњС…, Nm	1562,5	1562,4	0,006
B	Moment РњСѓ, Nm	8437,5	8437,6	0,001
B	Moment Рњz, Nm	3125,0	3124,8	0,006
A	Moving v_A, m	-0,029762	-0,02976	0,006
A	Turning angle Оё_AX, rad	0,16071	0,16071	0
D	Moving w_D, Рј	-0,37004	-0,37004	0

Preview image: Array

Note: To build the scheme, FE 10 (bar FE) and FE 51 (single-node FE) are used. Number of nodes:5. Number of elements:10.

FILES

Test 1.1 Space frame with elastic supports

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