Boundary nonlinearity

Boundary nonlinearity occurs if the boundary conditions change during the analysis. Consider the cantilever beam, shown in Figure 1, that deflects under an applied load until it hits a “stop.”

Figure 1. Cantilever beam hitting a stop.

The vertical deflection of the tip is linearly related to the load (if the deflection is small) until it contacts the stop. There is then a sudden change in the boundary condition at the tip of the beam, preventing any further vertical deflection, and so the response of the beam is no longer linear. Boundary nonlinearities are extremely discontinuous: when contact occurs during a simulation, there is a large and instantaneous change in the response of the structure.

Another example of boundary nonlinearity is blowing a sheet of material into a mold. The sheet expands relatively easily under the applied pressure until it begins to contact the mold. From then on the pressure must be increased to continue forming the sheet because of the change in boundary conditions.

Boundary nonlinearity is covered in Contact.