TEST CASE 7.1 CURVILINEAR CANTILEVER BEAM UNDER THE ACTION OF CONCENTRATED FORCES AT A FREE END
Reference:
R. H. Macneal, R. L. Harder, A proposed standard set of problems to test finite element accuracy, North-Holland, Finite elements in analysis and design, 1, 1985, p. 3-20.
Problem description:
Curvilinear isotropic cantilever beam of rectangular cross section is subjected to concentrated transverse forces P_{y} and P_{z} at the free end (bending in and out of the plane of the longitudinal axis of the beam).
Problem sketch:
Type of created problem:
Spatial construction (X, Y, Z, UX, UY, UZ).
Geometric characteristics:
R = 4.22 m; b = 0.1 m; h = 0.2 m; α = 90°.
Material properties:
Isotropic elastic: E = 1·10^{7} kPa; μ = 0.25.
Boundary conditions:
Rigid restraint at the end: X = Y = Z = UX = UY = UZ = 0.
Loads:
P_{y} = P_{z} = 1000 N.
Model description:
The system is modeled by 6 shell elements (FE type is 44).
Calculation results:
Target value |
Analytical solution |
LIRA 10 |
Deviation, % |
v, mm |
-88.536 |
-86.839 |
1.92 |
w, mm |
454.527 |
441.150 |
2.94 |