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Test case, static non-uniform beam

Purpose

The purpose of this test case is to verify that the simulation model gives second order accuracy when applied to calculate the deflection of a non-uniform beam. (balance between normal force and rate of change in bending moment).

Method

The deflection has been computed numerically, and comparisons are made with the analytically calculated exact solution.

The bending stiffness distribution (for which the solutions are computed) is presented below:

Results

The numerical and exact solutions are presented below:

The relative error norm versus no of spatial grid divisions is presented below:

Conclusion

· The results confirm that the simulation model is second order accurate when applied to calculate the static deflection of a non-uniform beam.