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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 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:

The numerical and exact solutions are presented below:

The relative error norm versus no of spatial grid divisions is presented below verifying second order error decay.

Conclusion

· The comparisons demonstrate that the equations are solved correctly and that the numerical scheme is second order accurate (error decreases with the spacing between discrete points squared).