Research On High-fidelity Model Order Reduction Methods For Dynamics Optimization And Model Updating Of Complex Thin-walled Structures

Due to the light weight and high load bearing,thin-walled structures have been widely used in aeronautics and space structures,such as fuel tanks and nozzles,et al.Rich structural details lead to a sharp increase in size of the finite element model(FEM)of thsese thin-walled structures,resulting in a huge time-consuming in dynamics analyses and optimization.Although many existing model order reduction methods saved many computational time effectively,it still cannot meet these requirements of capturing global modes and shell lobetype modes acccurately,predicting frequency response precisely and matching numerical modes exacltly with incomplete experimental modes in the process of dynamics optimization and FEM updating for complex thin-walled structures.Therfore,a research on high-fidelity model order reduction method was performed for dynamics optimization and FEM updating of complex thin-walled structures in this paper.Firstly,a model order reduction method based on the polynomial function and shape function was proposed.The global modes and shell lobetype modes of thin-walled structures can be captured accurately by this high-fidelity reducedorder model(ROM).Secondly,an adaptive ROM based on the SOAR algorithm was studied and a novel adaptive model order reduction strategy was proposed to improve the efficiency of harmonic analysis and optimization.The frequency response function can be predicted accurately by this adaptive ROM with less computational cost.Finally,a novel framework consisting of an off-line phase and on-line phase for FEM updating was established in this paper.In the off-line phase,a global reduced order basis was constructed by the static displacement field using a POD technique,and the FEM updating was performed on the ROM with less computational cost in the on-line phase.This framework solves the problem of mode matching caused by incomplete experimental modes in FEM updating.The main content of this thesis is as follows:(1)A physical model order reduction method based on the polynomial and shape function of beam was proposed to improve the efficiency of dynamics analyses and optimization of thinwalled structures.For thin-walled structures with regular sections,nodal displacements of fullorder models were condensed into the centroid of the section by the polynomial.Furthermore,the beam element shape function was introduced to improve the polynomial-based model order reduction method,which circumvented the deficiency of the polynomial-based model order reduction method,such as the size of reduce order basis was too large for complex structures with numerous cross sections.In order to assess the accuracy of the ROM in this paper,an improved modal accurance criterion was proposed to evaluate the modal similarity between the ROM and the full-order model.Numerical examples demonstrated that the ROM can efficiently and accurately capture the global modes and shell lobe-type modes of thin-walled structures.(2)A model order reduction method based on a SOAR algorithm was studied to improve the efficiency of harmonic analysis and optimization for complex thin-walled structures.Firstly,an adaptive method based on the bisection and cross-validation strategy was proposed to determine the number of frequency points and orders of orthonormal basis.Then,on the basis of this adaptive ROM,a framework for harmonic response oprimizaiton was developed for complex thin-walled structures.Finally,some numerical examples demonstrated that these adaptive ROMs could save more computational time than corresponding full-order models.(3)With respect to the difficulty of mode identification in the FEM updating for periodic thin-walled structures,a model order reduction method based on the POD technique was studied.Firstly,a reduced order basis was constructed by the static displacement field using a POD technique,and an effective update strategy based on the sequential sampling technology was developed to update the POD basis.Then,a novel FEM updating framework consisting of an off-line phase and on-line phase was established to perform FEM updating of periodic thinwalled structures with incompleted measured modes.Illustrative numerical and experimental examples were carried out to verify the effectiveness of the proposed framework.In comparison to the corresponding full order models,this framework showed more high prediction accuracy and efficiency in the FEM updating of periodic thin-walled structures.