Robustness is an important requirement in nonlinear analysis. One of the requirements of a robust analysis code is that it obtains a realistic solution even with a coarse mesh. In engineering practice, the use of a coarse mesh should lead quickly to an approximate solution, especially in the case of a nonlinear analysis. There should be little need for experimenting with meshes just to obtain a realistic solution. Of course, with a robust analysis code, using a finer mesh always gives a more accurate solution.
Solving this simple example demonstrates the robustness of the ADINA System in nonlinear analyses. A spherical shell is slowly compressed between rigid surfaces in the above animations using a coarse and a fine mesh. The static solution requires the use of contact, shell elements and load-displacement control.
The following figure shows the load-displacement curves obtained for both meshes. The coarse mesh shows large fluctuations in the stiffness of the model. These fluctuations are due to the coarseness of the finite element model, which leads to the few nodes coming into and out of contact affecting the stiffness of the model. Due to the nature of the response, a force-based loading would not capture this behavior. Instead the load-displacement control algorithm commonly used for collapse analysis is used, and it succeeds in capturing the static complex response of the coarse model.
Recall that the same ADINA robustness is present in the analysis of fluid flow and fluid-structure interactions (see previous ADINA News features New FCBI Elements for Fluid Flow and Turbulent Pipe Flow). In such analyses it can also be very important to be able to solve quickly and obtain a reasonable response prediction using first a coarse mesh. Then after this coarse mesh solution has been calculated, the mesh might be refined depending on the objective of the analysis — just like in the static shell analysis shown here.
