Transient Analysis

Problem Description

Transient analysis of a cantilever beam having uniform cross section is performed to calculate the dynamic response from time varying load.

Geometry

A cantilever beam of length 1m , having rectangular cross section is studied.

Mesh Generation

We model the beam using 2D plane stress quadrilateral element.

Import Mesh

Now import the mesh file saved in file 2DPlaneBeam.m which is exported from GMSH.

Define Analysis Settings

Select type of analysis as transient and using the analysis settings dialog box , define load steps and sub steps for the analysis.

Analysis Settings > Define Load Steps

Load steps is used to define loading conditions for time varying loads. We can also specify Rayleigh damping coefficients to include damping. Newmark time integration is used as solver.

Define Material Properties

Select material of beam from material editor. We can also add new materials from the editor.

Define Element Properties

We define the behavior of 2D 4 node quadrilateral elements as plane stress.

Now we define the formulation of quadrilateral elements as Enhanced Assumed Strain
Select the stiffness and mass matrix integration rule as 2x2.
Specify the thickness as 40 mm.

Apply Boundary Conditions

The beam is fixed at its left end using boundary ID 4.

Apply Loads

Time varying load is applied at the corner of the beam at node Id 3.
We apply load of 500 N for time step 1 and 2 then force is reduced to zero.
After applying the force we can cross check the FORCES array in the Scilab console to check the applied load.

Solve

Start solver to solve the model. Due to large no.of time steps , the solving time of the analysis will be higher.

Post Process Results

Using the post processor tab, we can plot the required results.

Using the post processor tab, we can plot the graph of any result quantity to study the dynamic response. To change the plot, select the type of results from results dropdown box.

dynamic response of tip of cantilever beam

Summary

In this tutorial we have prepared the geometry and the mesh in GMSH. The mesh is then imported in SCIFESOL to perform linear transient analysis. Damping is not included in the analysis , hence the dynamic response of the beam is similar to response of undamped spring mass system.

Transient Analysis tutorial pdf