Earthquake Opensees

This benchmark verifies Ashes' earthquake simulation capabilities against OpenSees 3.7.1 , an open-source finite element software widely used for earthquake engineering simulations. The test compares the dynamic response of a cantilever beam structure subjected to various ground motion scenarios.

1 Test Description

The test model consists of a cantilever beam representing a simplified wind turbine tower structure. The beam is fixed at the base and free at the top, where a concentrated mass is applied.

1.1 Model Geometry and Properties

The cantilever beam has the following characteristics:
  • Height: 100 m
  • Cross-section: Uniform circular hollow section
  • Outer diameter: 4 m
  • Wall thickness: 30 mm
  • Top mass: 150 t
  • Discretization: 10 beam elements of equal length
The model is shown in the image below:

Vertical cantilever beam with 10 elements

1.2 Simulation Settings

The simulation is configured with the following parameters:
  • Analysis type: Linear dynamic analysis
  • Damping: Stiffness-proportional damping with 5% damping ratio on the first mode (4.39 s)
  • Duration: 70 seconds
  • Solver: Time-domain integration

1.3 Load Cases

Five different ground motion scenarios are simulated to verify the earthquake response across various loading conditions:
  1. Constant acceleration in X direction: Uniform ground acceleration of 1 m/s2 applied in the global X direction
  2. Constant acceleration in Y direction: Uniform ground acceleration of 0.5 m/s2 applied in the global Y direction
  3. Sinusoidal acceleration in X direction: Harmonic ground motion of amplitude 10 m/s2 and period 3 s in the X direction
  4. Sinusoidal acceleration in Y direction: Harmonic ground motion of amplitude 5 m/s2 and period 1 s in the Y direction
  5. Northridge earthquake: Real earthquake record with acceleration time histories in X, Y, and Z directions

2 Comparison Methodology

The verification compares the dynamic response between Ashes and OpenSees at two critical locations:

2.1 Top Node Kinematics

At the top node of the cantilever beam, the following quantities are compared in all three global directions (X, Y, Z):
  • Displacement time histories
  • Velocity time histories
  • Acceleration time histories

2.2 Bottom Node Internal Loads

At the base of the cantilever beam, the internal loads are compared for all six degrees of freedom:
  • Axial force (Fz)
  • Shear forces (Fx, Fy)
  • Torsional moment (Mz)
  • Bending moments (Mx, My)

3 Acceptance Criteria

The benchmark test is considered passed if the relative difference between Ashes and OpenSees results is within 0.5% for all compared quantities. The relative error is calculated as:
$$\text{Relative Error} = \frac{|\text{Ashes} - \text{OpenSees}|}{|\text{OpenSees}|} \times 100\%$$
This criterion ensures that Ashes accurately reproduces the earthquake response predicted by OpenSees, verifying the implementation of:
  • Ground motion input and application
  • Dynamic time integration schemes
  • Stiffness-proportional damping formulation
  • Structural dynamics calculations for beam elements
  • Multi-directional earthquake loading

4 Results

The comparison between Ashes and OpenSees can be viewed on this link:
https://www.simis.io/downloads/open/benchmarks/current/Earthquake Opensees.pdf

This benchmark provides confidence in using Ashes for earthquake analysis of wind turbine structures, where seismic loads may be a critical design consideration in certain geographical regions.