A Combined Approximation Based MATLAB Code for Dynamic Re-Analysis of Aerospace Structures

Achieving a high strength-to-weight ratio is one of the most important goals in the design of aerospace structures. Designers are continuously striving to find the optimum solutions that will make aerospace vehicles simultaneously strong and light. During the design process, the structure experiences several changes to reach this goal. Any change to the geometry and/or material property directly influences the global stiffness of the structure. Modification of the applied loading or stiffness impacts the solution of displacements. Each design change requires the implicit analysis equation to be resolved. In large scale models with thousands of degrees of freedom, the cost and time of repeated reanalysis, even for a small change, is significant. A combined approximation approach (CA) was previously developed to provide an efficient and accurate reanalysis of large structures, even with great changes in the design. High quality results have also been obtained through utilizing the CA method for dynamic reanalysis. This approach involves the combination of local and global approximation methods including series expansion, reduced basis vector, matrix factorization, and Gram-Schmidt orthonormalization. In this study, a combined approximation based MATLAB code for dynamic reanalysis has been developed. Changes in both baseline design properties and excitation frequency range have been introduced. The response of the modified system is calculated as a function of these changes, directly via inversion of the dynamic stiffness matrix and approximately via combined approximation method. A reanalysis example of a simplified aircraft wing spar model using this code is presented. Both methods are compared for solution accuracy.