With the rapid development of computer technology, computational mechanics plays an increasingly important role in engineering design, scientific research, and product development. However, any numerical simulation results must undergo strict verification to ensure their credibility and practicality. The verification of computational mechanics results is an important link to ensure that the simulation results are consistent with actual physical phenomena, and mainly includes the following aspects.



1. Theoretical Analysis and Comparison with Analytical Solutions



In computational mechanics, the numerical simulation results can first be compared with known analytical solutions. For some simple geometric structures and boundary conditions, such as beam bending and stress distribution of elastic bodies, there exist analytical solutions or classical formulas. By comparing the numerical solution with the analytical solution, the accuracy of the computational model can be judged. If the error is within an acceptable range, it indicates that the model settings are reasonable; if the error is large, it is necessary to check whether the mesh generation, boundary conditions, or material parameters are set correctly.



2. Mesh Convergence Analysis

　　Mesh generation is an important factor affecting the accuracy of computational results. The 'mesh refinement' method is usually used to judge whether the results have converged. That is, the mesh is gradually densified, and the trend of changes in key output variables (such as displacement, stress, strain, etc.) is observed. When the mesh is refined to a certain extent, if the results change slightly, it can be considered that the results have converged, indicating that the mesh density is sufficiently accurate.



3. Comparison with Experimental Results

　　Experimental validation is the most direct and effective method to test the results of numerical simulation. By designing physical experiments, obtaining actual measurement data, and comparing it with simulation results, the reliability of the model can be effectively evaluated. For example, in the field of structural mechanics, the deformation or vibration frequency of components can be measured experimentally and compared with the finite element simulation results. If both are well matched, it indicates that the simulation results are credible; if there are significant deviations, it is necessary to re-evaluate the assumptions of the model, material model, or boundary treatment.



4. Multi-method Cross-validation

　　In some complex problems, different numerical methods (such as finite element method, boundary element method, meshless method) can be used for cross-validation. If the results obtained from multiple methods tend to be consistent, it indicates that the results have a high degree of credibility. In addition, different commercial software can also be used to model the same problem to verify the consistency of the results.



5. Engineering Experience and Rationality Judgment



In addition to the aforementioned quantitative analysis methods, engineers' experience and understanding of physical phenomena also play an important role. By making intuitive judgments of simulation results, such as whether the stress distribution is reasonable and whether the deformation trend conforms to expectations, the reliability of the results can be辅助判断.



Conclusion



In summary, the verification of computational mechanics results is a systematic and rigorous process, involving theoretical analysis, numerical computation, experimental validation, and engineering experience in many aspects. Only simulation results that have been fully verified can be used in practical engineering applications, thereby improving design efficiency, reducing development costs, and ensuring the safety and reliability of structures. With the development of artificial intelligence and big data technology, future verification methods will also become more intelligent and automated, providing stronger support for engineering simulation.