TEST CASE 10.3 FIXED CIRCULAR ARCH
Reference:
- D. Landau, E. M. Lifshits Theory of elasticity, M.: "Nauka", 1987, p. 107.
Problem description:
The fixed circular arch is loaded with a vertical concentrated force P. Determine the vertical displacement of point 3.
Problem sketch:
Type of created problem:
Spatial structure (X, Y, Z, UX, UY, UZ).
Geometric characteristics:
Arch radius: R = 41 m;
Arch section width: b = 0.5 m;
Arch section height: h = 0.5 m.
Material properties:
Elastic modulus: E = 3·10^{7} tf/m^{2};
Density: γ = 2 tf/m^{3}.
Boundary conditions:
Points А and B: X = Y = Z = UX = UY = UZ = 0.
Loads:
P = 2000 tf.
Model description:
The system is modeled via 180 geometrically nonlinear elements of tight bend bar (FE type is 309). 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, % |
w_{3}, m |
-66.07 |
-66.093 |
0.04 |
Note:
The system loses stability at load P = 1947.8 tf (displacement: w_{3} = 19.583 m).
Vertical displacements distribution w, m