Reference:

NAFEM “Benchmark tests for solution procedures in geometric non-linearity”, By M A Crisfield G W Hunt P G Duxbury, Published by NAFEMS, Ref: - P3 (Draft), Example 5.1.

Problem description:

The hinged-rod system is loaded with a horizontal concentrated force F. Determine the horizontal displacement of point A u_A, the vertical displacement of point B w_B and the force in the bar N.

Problem sketch:

Type of created problem:

Plane truss or beam-wall (X, Z).

Geometric characteristics:

L = 2500 m; αL = 25 m.

Material properties:

Bar stiffness: EА = 5·10⁷ tf;

Spring stiffness: k = EA/L = 1.5 tf/m.

Boundary conditions:

Point A: Z = 0;

Point B: X = 0;

End of spring: X = Z = 0.

Loads:

F = 4500 tf.

Model description:

The system is modeled by 1 bar geometrically nonlinear finite element of the “string” type (FE type is 304) and 1 finite element of truss bar (FE type is 4). Automatic selection of loading applying step with the search of new equilibrium shapes for nonlinear problem solution is used, minimum number of iterations 10000.

Calculation results:

Note:

The system loses stability at load P = 3503.48 tf (displacements: u_A = 57.363 m, w_B = 508.78 m).

Horizontal displacements values u, m

Vertical displacements values w, m

Longitudinal forces N, tf