TEST CASE 10.2 HINGED-ROD SYSTEM №2
Reference:
Dm. Nazarov. Review of modern programs for finite element analysis. — CAD and graphics. — 2000. — №2. (pp. 52-55).
Problem description:
The hinged-rod system consists of four linear elastic bars of different stiffness. A vertical concentrated force P is applied at point D. Determine the horizontal displacements of the points D u_{D} and E u_{E}, the vertical displacements of the points D w_{D} and E w_{E}, as well as the longitudinal forces N in the bars.
Problem sketch:
Type of created problem:
Plane truss or beam-wall (X, Z).
Geometric characteristics:
а = 3.5 m; b = 10 m.
Material properties:
Bar stiffness АD and ВD: EА_{1} = EА_{2} = 1000 tf;
Bar stiffness DЕ and СЕ: EА_{3} = EА_{4} = 2000 tf.
Boundary conditions:
Points А, В and С: X = Z = 0.
Loads:
Distributed force per unit length, is applied to the bars АD and ВD: q_{1} = q_{2} = 0.001 tf/m;
Distributed force per unit length, is applied to the bars DE and CE: q_{3} = q_{4} = 0.002 tf/m;
P = 190 tf.
Model description:
The system is modeled by 4 bar geometrically nonlinear finite elements of the “string” type (FE type is 304). Automatic selection of loading applying step with the search of new equilibrium shapes for nonlinear problem solution is used, minimum number of iterations 300.
Calculation results:
Target value |
Analytical solution |
LIRA 10 |
Deviation, % |
u_{D}, m |
0.54 |
0.5288 |
2.07 |
u_{E}, m |
0.256 |
0.26614 |
3.96 |
w_{D}, m |
-8.24 |
-8.244 |
0.05 |
w_{E}, m |
-7.62 |
-7.6264 |
0.08 |
N_{АD}, tf |
-245.0 |
-245.35 |
0.14 |
N_{BD}, tf |
-320.0 |
-319.0 |
0.31 |
N_{DE}, tf |
116.0 |
115.95 |
0.04 |
N_{CE}, tf |
116.0 |
115.99 |
0.01 |
Note:
The system loses stability at load P = 187.66 tf.
Horizontal displacements values u, m
Vertical displacements values w, m
Longitudinal forces N, tf