TEST CASE 1.3 FLAT HINGED-ROD SYSTEM UNDER CONCENTRATED FORCE
Reference:
S. Rao, The finite element method in engineering, 4 ed, Elsevier science end technology books, 2004, p. 313.
Problem description:
The flat hinged-rod system consists of four inclined rods. The rods of the AC and BC have a common node (point C) and are hinged at support points, the rods CD and BC have a common node (point D). Concentrated force is applied to node D F. Determine the horizontal u and vertical w displacements of the common nodes C and D.
Problem sketch:
Type of created problem:
Plane truss or beam-wall (X, Z).
Geometric characteristics:
Cross-sectional area of bars AC and BC: A_{AC} = A_{BC} = 2·10^{-4} m^{2};
Cross-sectional area of bars CD and BD: A_{CD} = A_{BD} = 1·10^{-4} m^{2}.
Material properties:
Elastic modulus: E = 2·10^{10} Pa.
Boundary conditions:
Points A and B: X = Z = 0.
Loads:
F = 1000 N.
Model description:
The system is modeled by four finite elements of truss bar (FE type is 4). The number of nodes in the calculation scheme is 4.
Calculation results:
Target value |
Analytical solution |
LIRA 10 |
Deviation, % |
u_{C}, mm |
0.26517^{} |
0.26517 |
0.00 |
w_{C}, mm |
0.08839 |
0.08839 |
0.00 |
u_{D}, mm |
3.47903 |
3.47903 |
0.00 |
w_{D}, mm |
-5.60035 |
-5.60035 |
0.00 |