Two-Dimensional Circular Truss-Arch Snapthrough

Author: Mahmoud Zidan

Kratos version: 7.0

Source files: Two-Dimensional Circular Truss-Arch Snapth rough

Problem definition

The two different non-linear solutions, namely displacement control and load control, are demonstrated on this example, introduced by (Crisfield, 1997). The problem consists of a two-dimensional arch made of a truss system, where a load is applies at the apex, and the load factor vs. the vertical displacement is studied,

Static System [1]

with E = 5E9, A = 0.01, and F=1.

Results

This structure is solved using the non-linear truss element in the two following approaches:

Load Control

Incrementally prescribing the load factor and solving for the apex vertical displacement.

Non-linear snap through: Load-control

Displacement Control

Incrementally prescribing the apex vertical displacement and solving for the load factor.

Non-linear snap through: Displacement-control

The following figure shows the load displacement curve for the two approaches.

Load Displacement curve.

References

1. Crisfield, M. A., 1997. Non-Linear Finite Element Analysis of Solids and Structures. Volume 2: Advanced Topics. pp 407-410.