1. Benchmark solution

The law of behavior DASHPOTlie, at each calculation moment \({t}_{i}\), the nodal force \(F({t}_{i})\) at the displacement increment \({\mathrm{\Delta }}_{x}({t}_{i})\) in the following way: \(F({t}_{i})=K{\mathrm{\Delta }}_{x}({t}_{i})\) where \(K\) is a stiffness parameter provided by the user.

In this test, the following on-the-go loading is required: \(U(t)=\mathrm{sin}(\mathrm{\omega }t)\).

The analytical solution for force is therefore expressed as follows: \(F(t)=K\mathrm{\omega }{\mathrm{\Delta }}_{t}\mathrm{cos}(t)\) where \({\mathrm{\Delta }}_{t}\) is the time increment.