CRM Modal Analysis: Addressing Wingbox Deformation Issues

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CRM Modal Analysis: Addressing Wingbox Deformation Issues

Introduction

In the realm of finite element analysis, accurately predicting the modal behavior of structures is paramount. In this article, we address a specific issue encountered during a CRM modal analysis using the examples/crm/crm_frequency.py script within the TACS (Toolkit for the Analysis of Composite Structures) framework. The focus is on the simplified uCRM-9 model (CRM_box_2nd.bdf), where strange displacement patterns emerged near the root of the wingbox at higher modes. This exploration aims to dissect the problem, provide context, and offer potential solutions for researchers and engineers grappling with similar challenges.

Identifying the Issue: Strange Displacements in Higher Modes

The initial problem was observed while running the examples/crm/crm_frequency.py script to generate the first 10 modes of the simplified uCRM-9 model (CRM_box_2nd.bdf). At higher modes, particularly modes 7 and 9, the analysis revealed peculiar displacement patterns concentrated near the root of the wingbox. These unexpected deformations raised concerns about the accuracy and reliability of the modal analysis results. To visualize the issue, the deformations were scaled by 50x in Paraview, clearly highlighting the anomalous behavior. An example of the wingbox root deformation for mode 7 is shown below:

Image

Investigating the Discrepancy

To understand whether this behavior was unique to the current setup, a comparison was made with existing results from 2019, specifically the Mendeley Data: uCRM: undeflected Common Research Model dataset. The absence of similar modeshapes in the 2019 results prompted a plan to swap the Nastran mesh from Mendeley into the current script. This step aims to achieve a direct, one-to-one comparison, thereby isolating potential discrepancies arising from mesh differences or other factors. By using an identical mesh, the analysis can focus on identifying differences in the simulation setup, boundary conditions, or material properties that might be contributing to the observed anomalies. This comparative approach is crucial for validating the current results and ensuring the accuracy of the finite element analysis.

Detailed Analysis and Methodology

To thoroughly investigate the issue of strange displacements in the CRM modal analysis, a detailed methodology was employed, involving several key steps:

  1. Review of the Model: The first step involved a comprehensive review of the uCRM-9 model (CRM_box_2nd.bdf) to ensure that all geometric and material properties were correctly defined. This included verifying the dimensions of the wingbox, the material properties of the composite structure, and the overall mesh quality. Any discrepancies or errors in the model definition could potentially lead to inaccurate results.
  2. Mesh Verification: The mesh quality was assessed to identify any elements that might be causing issues. High aspect ratio elements, distorted elements, or poorly connected elements can introduce numerical instabilities and lead to spurious results. The mesh was refined in critical areas, such as the wingbox root, to improve accuracy. Tools like mesh quality plots and element shape checks were used to ensure the mesh met the required standards.
  3. Boundary Conditions: The boundary conditions were carefully reviewed to ensure they accurately represented the physical constraints of the structure. Incorrect or poorly defined boundary conditions can significantly affect the modal behavior of the model. The supports and constraints were verified to ensure they were applied correctly and that they aligned with the intended analysis setup.
  4. Material Properties: The material properties used in the model were verified against the original specifications. Errors in material properties, such as incorrect Young's modulus or Poisson's ratio, can lead to significant deviations in the modal frequencies and mode shapes. The material properties were cross-checked with reliable sources to ensure accuracy.
  5. Solver Settings: The solver settings in TACS were reviewed to ensure they were appropriate for the type of analysis being performed. Parameters such as the eigenvalue extraction method, convergence criteria, and damping settings can influence the accuracy and stability of the solution. The solver settings were adjusted to optimize the analysis for the specific characteristics of the uCRM-9 model.
  6. Comparison with Mendeley Data: As mentioned earlier, the Nastran mesh from the Mendeley Data dataset was incorporated into the current script to facilitate a direct comparison. This step was crucial for identifying whether the mesh itself was contributing to the observed anomalies. The results obtained with the Mendeley mesh were compared against the original results to isolate any discrepancies.

By systematically examining these aspects, potential sources of error were identified and addressed, leading to a more accurate and reliable modal analysis of the uCRM-9 model.

Software and Dependencies

The analysis was conducted using the TACS framework, with specific commit hash d97564d32093872d87d68facb26a3e2a4c932c4b. The following build dependencies were used:

  • gcc/12.5.0
  • mpich/4.3.1
  • metis/5.1.0
  • netlib-lapack/3.12.1
  • python/3.11.13
    • mpi4py/4.1.0
    • numpy/1.26.4
    • pyNastran/1.4.1

These dependencies ensure the reproducibility and consistency of the results. Utilizing these specific versions helps in pinpointing whether the issue is related to software versions or the core analysis methodology. Maintaining a consistent software environment is crucial for validating modal shapes and ensuring the reliability of the analysis.

Potential Causes and Troubleshooting Steps

Several factors could contribute to the strange displacement patterns observed in the higher modes of the uCRM-9 model. Here are some potential causes and corresponding troubleshooting steps:

  1. Mesh Quality: A poorly constructed mesh with distorted or high aspect ratio elements can lead to inaccurate results, especially at higher modes. The solution involves refining the mesh, particularly in areas of high stress concentration like the wingbox root. Tools like mesh quality plots and element shape checks can help identify problematic elements.
  2. Boundary Conditions: Incorrectly defined or improperly applied boundary conditions can significantly affect the modal behavior of the structure. Ensure that the boundary conditions accurately represent the physical constraints of the system. Verify that the supports and constraints are correctly applied and that they align with the intended analysis setup.
  3. Material Properties: Errors in material properties, such as incorrect Young's modulus or Poisson's ratio, can lead to significant deviations in the modal frequencies and mode shapes. Double-check the material properties against the original specifications and ensure they are accurately defined in the model.
  4. Solver Settings: The solver settings used in TACS can influence the accuracy and stability of the solution. Experiment with different eigenvalue extraction methods, convergence criteria, and damping settings to optimize the analysis for the specific characteristics of the uCRM-9 model. Consult the TACS documentation for guidance on selecting appropriate solver settings.
  5. Geometric Imperfections: Even small geometric imperfections or deviations from the ideal geometry can affect the modal behavior of the structure, especially at higher modes. Ensure that the geometry of the model accurately represents the physical structure and that any imperfections are accounted for.
  6. Numerical Instabilities: Numerical instabilities can arise during the solution process, leading to spurious results. These instabilities can be caused by various factors, including ill-conditioned matrices, singularities in the model, or inadequate solver settings. Try refining the mesh, adjusting the solver settings, or using a different solver to mitigate these instabilities.

By systematically addressing these potential causes, the accuracy and reliability of the frequency analysis can be significantly improved.

Next Steps: Mesh Comparison and Further Validation

The immediate next step involves swapping the Nastran mesh from the Mendeley Data dataset into the current script. This direct comparison will help isolate whether the mesh itself is contributing to the observed anomalies. Once the mesh comparison is complete, further validation steps may include:

  • Sensitivity Analysis: Performing a sensitivity analysis to assess the impact of various parameters (e.g., mesh density, material properties, boundary conditions) on the modal frequencies and mode shapes.
  • Experimental Validation: Comparing the numerical results with experimental data, if available, to validate the accuracy of the model and analysis.
  • Higher-Order Elements: Investigating the use of higher-order elements in the finite element model to improve the accuracy of the solution, particularly in areas of high stress concentration.
  • Nonlinear Analysis: Considering a nonlinear analysis to account for potential nonlinear effects, such as geometric nonlinearities or material nonlinearities, which may become significant at higher modes.

By systematically performing these validation steps, the reliability and accuracy of the CRM modal analysis can be significantly enhanced.

Conclusion

Encountering strange displacements in higher modes during CRM modal analysis is a challenge that requires a systematic and thorough approach. By carefully reviewing the model, verifying the mesh, ensuring correct boundary conditions, validating material properties, and comparing results with existing data, potential sources of error can be identified and addressed. The use of specific software versions and dependencies, such as TACS commit hash d97564d32093872d87d68facb26a3e2a4c932c4b, ensures reproducibility and consistency. The troubleshooting steps outlined in this article provide a roadmap for researchers and engineers to diagnose and resolve similar issues, ultimately leading to more accurate and reliable modal analysis results. By focusing on these critical aspects, the integrity and validity of the finite element analysis can be maintained, ensuring the structural integrity and performance of complex systems like the uCRM-9 model. Keep an eye on those wingbox deformations, folks, and happy analyzing!