K tvarům s nulovou energií, označovaným také jako nulové tvary vlastních čísel, dochází, pokud je diskretizovaný systém nedostatečně stanoven nebo ho nelze jednoznačně vyřešit. This means that there are more degrees of freedom (unknowns) than equations available. Mathematically, zero-energy modes are special solutions of the system of equations associated with an eigenvalue of zero. Thus, this mode can be activated without energy supply and, potentially, a deformation without strain occurs.
As zero-energy modes can lead to model instability and unphysical solutions, several methods are advisable in RFEM to prevent this problem.
- Mesh Refinement: Ensure that your mesh is sufficiently refined, especially in areas with high stress gradients or complex geometry. A fine mesh can help capture the deformation more accurately and reduce the likelihood of zero-energy modes.
- Material Properties: Ensure that you have assigned suitable material properties to your model. Incorrect material properties can lead to unrealistic behavior and potentially cause zero-energy modes. Double-check the material parameters and properties.
- Boundary Conditions: Verify that your boundary conditions are correctly applied. Improper boundary conditions can cause zero-energy modes. Ensure that all degrees of freedom are correctly constrained or loaded.
- Solver Settings: Review the solver settings in RFEM. Some solvers have options to stabilize the analysis and prevent zero-energy modes. Adjust the solver settings to use stabilization techniques if available.
- Damping: Introduce damping into your analysis if necessary. Damping can help stabilize the analysis and prevent zero-energy modes. However, use damping judiciously to avoid introducing artificial damping that affects the accuracy of results.
- Check Geometry: Ensure that your model geometry is correct and free of errors. Small gaps or overlaps in the geometry can lead to numerical issues, including zero-energy modes.
- Sensitivity Analysis: Perform sensitivity analyses to identify critical parameters or areas that might be more susceptible to zero-energy modes. You can then take specific actions to address these areas.