System and method of recovering Lagrange multipliers in modal dynamic analysis

A computer system for performing a modal analysis on simulating a modeled real-world object under dynamic excitation, the system comprising:

• a processor;
• and
• a memory with computer code instructions stored thereon, the memory operatively coupled to the processor such that, when executed by the processor, the computer code instructions cause the computer system to implement:
• a simulation module of a computer-aided design (CAD) system configured to:
• receive a finite element model (FEM), the FEM representing a real-world object;
• employ the FEM in a modal analysis for modeling stress and reaction forces of the FEM, the modal analysis modeling structural response of the FEM as a system of equations that includes constraints applied to the FEM, the constraints being represented using Lagrange multipliers;
• a correction module operatively coupled to the simulation module and configured to:
• calculate a correction term that comprises corrected values of the Lagrange multipliers of the system of equations modeling structural response of the FEM, the calculating includes minimizing the norm of residual of the system of equations modeling structural response of the FEM;
• and
• modify the modal analysis using the correction term to correct values of the Lagrange multipliers, the modified modal analysis providing accurate stress and reaction force results;
• and
• the simulation module of the CAD system further configured to use the stress and reaction force results to accurately simulate the real-world object under dynamic excitation.

A computer program product executed by a server in communication across a network with one or more clients, the computer program product comprising:

• a non-transitory computer readable medium, the computer readable medium comprising program instructions for simulating a modeled real-world object under dynamic excitation which, when executed by a processor causes:
• providing a finite element model (FEM) to a computer-aided design (CAD) system, the FEM representing a real-world object;
• employing, by the CAD system, the FEM in a modal analysis for modeling stress and reaction forces of the FEM, the modal analysis modeling structural response of the FEM as a system of equations that include constraints applied to the FEM, the constraints being represented using Lagrange multipliers;
• calculating a correction term that comprises corrected values of the Lagrange multipliers of the system of equations modeling structural response of the FEM, the calculating includes minimizing the norm of residual of the system of equations modeling structural response of the FEM;
• modifying the modal analysis using the correction term to correct values of the Lagrange multipliers, the modified modal analysis providing accurate stress and reaction force results;
• and
• using the stress and reaction force results by the CAD system to accurately simulate the real-world object under dynamic excitation.