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A Modal Derivatives Enhanced Kron's substructuring method to Calculate Structural Responses and Response Sensitivities of Geometrically Nonlinear Systems

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INTERNATIONAL JOURNAL OF STRUCTURAL STABILITY AND DYNAMICS 2024年第1期24卷 2450005-2450005页

作者： Tian, Wei Weng, Shun Xia, Yong Hong Kong Polytech Univ Dept Civil & Environm Engn Hung Hom Kowloon Hong Kong Peoples R China Huazhong Univ Sci & Technol Sch Civil & Hydraul Engn Wuhan Hubei Peoples R China

This paper develops a modal derivative enhanced Kron's substructuring method to calculate the structural responses and response sensitivities of geometrically nonlinear systems. The proposed method divides the global structure into substructures, which are then assembled in a dual form. The substructural displacements are approximated around the initial linear equilibrium position by using a quadratic modal manifold governed by a few master modes only. A time-variant reduction basis augmented by the master modal derivatives is derived from the quadratic modal manifold, enabling the geometric nonlinearities to be accurately captured. With the reduction basis, the global system is transformed into a reduced one containing the master modes only. Subsequently, the master modal responses and response sensitivities are solved efficiently from the reduced system. The global structural responses and response sensitivities are finally recovered from the master modal solutions based on the quadratic modal manifold. The effectiveness of the proposed method is demonstrated through its application to a thin plate structure. The reduced system enjoys the merit of Kron's substructuring method that does not contain the interface degrees of freedom. Besides, the proposed reduced system is formed from the quadratic modal manifold directly. Its size is equal to the number of master modes of the substructures and smaller than that of the conventional method, where its size grows quadratically with the number of master modes.

关键词： Geometrically nonlinear system substructuring method modal derivative model order reduction quadratic manifold approximation

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Calculation of eigenvalue and eigenvector derivatives with the improved Kron's substructuring method

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STRUCTURAL ENGINEERING AND MECHANICS 2010年第1期36卷 37-55页

作者： Xia, Yong Weng, Shun Xu, You-Lin Zhu, Hong-Ping Hong Kong Polytech Univ Dept Civil & Struct Engn Kowloon Hong Kong Peoples R China Huazhong Univ Sci & Technol Sch Civil Engn & Mech Wuhan 430074 Hubei Peoples R China

For large-scale structures, the calculation of the eigensolution and the eigensensitivity is usually very time-consuming. This paper develops the Kron's substructuring method to compute the first-order derivatives of the eigenvalues and eigenvectors with respect to the structural parameters. The global structure is divided into several substructures. The eigensensitivity of the substructures are calculated via the conventional manner, and then assembled into the eigensensitivity of the global structure by performing some constraints on the derivative matrices of the substructures. With the proposed substructuring method, the eigenvalue and eigenvector derivatives with respect to an elemental parameter are computed within the substructure solely which contains the element, while the derivative matrices of all other substructures with respect to the parameter are zero. Consequently this can reduce the computation cost significantly. The proposed substructuring method is applied to the GARTEUR AG-11 frame and a highway bridge, which is proved to be computationally efficient and accurate for calculation of the eigensensitivity. The influence of the master modes and the division formations are also discussed.

关键词： substructuring method eigensolution eigensensitivity model updating

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Kron?s substructuring method to the calculation of structural responses and response sensitivities of nonlinear systems

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JOURNAL OF SOUND AND VIBRATION 2021年 502卷 116101-116101页

作者： Tian, Wei Weng, Shun Xia, Yong Hong Kong Polytech Univ Dept Civil & Environm Engn Kowloon Hung Hom Hong Kong Peoples R China Huazhong Univ Sci & Technol Sch Civil & Hydraul Engn Wuhan Hubei Peoples R China

Numerous civil engineering structures exhibit nonlinearities. Even though the nonlinear-ities constitute only a small part of the structure, the entire structure behaves nonlin-early, and the analysis of the whole structure is consequently computationally expensive. This paper develops Kron?s substructuring method for fast computation of structural re-sponses and response sensitivities of nonlinear systems. The nonlinearity is detected and located using the ordinary coherence function. The global structure is then divided into linear and nonlinear substructures. The local nonlinearities are thus restricted in a few nonlinear substructures. The linear substructural responses are interpreted as the combi-nation of a few master modal responses based on the mode superposition. The discarded slave modal responses of the linear substructures are compensated by the corresponding master modal responses, nonlinear substructural responses and external excitation on the linear substructures. A reduced vibration equation of a much smaller size is then derived with the transformation matrices. The structural responses and response sensitivities are calculated from the reduced vibration equation. The precision and efficiency of the pro-posed method are verified by a nonlinear spring-mass system and a relatively large-scale nonlinear frame. ? 2021 Elsevier Ltd. All rights reserved.

关键词： substructuring method Nonlinear systems Sensitivity analysis Kron?s method

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Efficient calculation of higher order time history response derivatives by substructuring method

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ADVANCES IN STRUCTURAL ENGINEERING 2024年第5期27卷 758-774页

作者： Li, Jiajing Wu, Qiaoyun Weng, Shun Wuhan Inst Technol Sch Civil Engn & Architecture Wuhan Peoples R China Huazhong Univ Sci & Technol Sch Civil & Hydraul Engn Wuhan Peoples R China

Time history response derivatives with respect to the design variables are frequently used in optimization design, damage detection, structural control, etc. This paper proposes a substructuring method for efficient calculation of higher order time history response derivatives of large-scale structures. First, the global structure is disassembled into several small substructures and the substructural displacement is projected onto the range space of a few substructural master eigenvectors. Afterwards, the derivative of substructural master eigenvectors of a few substructures containing the design variables are assembled to form the reduced first, second, and higher order sensitivity equations with a size of the number of master eigenvectors. The equivalent eigenvector which relates the slave and master eigenvectors is derived to compensate for the inertial effect of discarded slave eigenvectors. Finally, the first, second, and higher order time history response derivatives of global large-scale structure are efficiently solved from the reduced sensitivity equations by using Newmark-beta method. A numerical one-bay plane frame and a numerical highway bridge are applied to verify the accuracy and efficiency of proposed substructuring method.

关键词： large-scale structure substructuring method time history response derivative master eigenvector derivative reduced sensitivity equation

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Application of substructuring method to three-dimensional optical lithography simulation

Application of substructuring method to three-dimensional op...

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Optical Microlithography XI Conference

作者： Lee, SG Seo, CK Lee, DH Lee, JU Cho, MH Inha Univ Dept Elect Mat & Devices Engn Inchon South Korea

ISBN: (纸本)0819427799

The three-dimensional optical lithography simulator on the basis of finite element method is newly introduced. Contrary to the conventional direct finite element method, the problem of huge memory requirement can be resolved by applying the substructuring method to finite element method. In our scheme, the global domain, which consists of photoresist, interlayers, and the substrate, is divided into several subdomains. After each subdomain is treated locally, the calculation results are integrated altogether. Since the consuming memory is tremendously reduced by the substructuring method, the three-dimensional case can be successfully simulated at the engineering workstation. We have compared our scheme with the conventional direct finite element, and investigated the reduction of computational memory by the substructuring method.

关键词： optical lithography lithography simulation finite element method FEM substructuring method

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A substructuring method for Model Updating and Damage Identification

A Substructuring Method for Model Updating and Damage Identi...

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12th East Asia-Pacific Conference on Structural Engineering and Construction (EASEC)

作者： Xia, Yong Weng, Shun Xu, You-Lin Hong Kong Polytech Univ Dept Civil & Struct Engn Hong Kong Hong Kong Peoples R China

Model updating of large-scale structures is time-consuming as the global system matrices need to be assembled continuously and the global eigensolutions and eigensensitivities are required in each iteration, even only a few elemental parameters need updating. In this paper, a substructuring approach is proposed to extract the substructural dynamic flexibility matrices from the measured modal properties of the global structure under the constraints of force compatibility and displacement compatibility. Thereafter the focused substructure is treated as an independent structure and updated directly using the traditional model updating method. It not only reduces the size of the analytical model involved in model updating but also decreases the uncertain parameters that need updating, thus resulting in a rapid convergence of the optimization process. Moreover, if a particular substructure needs updating, the measurement can be focused on the local area of the interested substructure only and the requirement of measurement on the entire structure is avoided. A laboratory tested frame structure is employed to illustrate the effectiveness and accuracy of the proposed method.

关键词： substructuring method model updating damage identification modal flexibility large-scale structures

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IMPROVED substructuring method FOR CALCULATION OF EIGENSENSITIVITY

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12th International Symposium on Structural Engineering (ISSE-12)

作者： Weng, Shun Jiang, Tuoyu Zhu, Hongping Mao, Ling Xia, Yong Huazhong Univ Sci & Technol Sch Civil Engn & Mech Wuhan 430074 Peoples R China Hong Kong Polytech Univ Dept Civil & Struct Engn Kowloon Hong Kong Peoples R China

ISBN: (纸本)9787030357878

Calculation of eigensensitivity is usually time-consuming for a large-scale structure. This paper develops a substructuring method for computing the first-, second- and high-order eigensensitivity. The local area of a structure is treated as an independent substructure to be analyzed. The eigensensitivity of global structure with respect to a design parameter are calculated from the eigensensitivity of a particular substructure that contains the design parameter, thus allowing a significant reduction in computational cost. The accuracy and efficiency of the substructuring method is proved by a frame structure and a highway bridge.

关键词： Eigensensitivity eigensolution derivative substructuring method residual flexibility

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Ritz vector-based substructuring method using interface eigenmode-shape pseudo-forces

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FINITE ELEMENTS IN ANALYSIS AND DESIGN 2023年第1期227卷

作者： Koh, Hyeong Seok Yoon, Gil Ho Hanyang Univ Mech Engn Seoul South Korea Hanyang Univ Sch Mech Engn Seoul South Korea

We propose a new Ritz vector-based dynamic substructuring method which substitutes the unit pseudo-forces applied at the adjacent degrees of freedom (DOFs) using distributed forces. One of the main problems of the Ritz vector and unit pseudo-force-based dynamic substructuring method is the strong dependence of the number of reduction bases on the interface DOF, which is not reduced by substructuring. This type of dependency causes the number of reduction bases obtained by the unit pseudo-forces to be always exceed or at least equal to the number of interface DOFs. The number of Ritz vector bases required at adjacent interface DOFs is efficiently reduced by approximating the unit pseudo-force as a type of distributed force using an energy transfer approach. The distributed forces, called eigenmode-shape pseudo-forces, comprise low modes computed through the eigenvalue problem of substructures corresponding to adjacent DOFs, and a set of distributed forces is a subspace of the vector space spanned by the unit force vectors. The efficiency of the substructuring method may be increased by reducing the number of reduction bases. This approach was demonstrated through several numerical examples.

关键词： Interfacial pseudo-force substructuring method Krylov subspace Ritz vector method Quasi-static ritz vector method

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Model updating of nonlinear structures using substructuring method

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JOURNAL OF SOUND AND VIBRATION 2022年 521卷 116719-116719页

This paper develops the Kron's substructuring method for updating large-scale nonlinear structures. The global structure is divided into linear and nonlinear substructures. By using a transform basis, the global vibration equation is reduced to the master modal responses of linear substructures and responses of nonlinear substructures only. The sensitivity-based nonlinear model updating is then conducted on the reduced vibration equation. The element parameters in the linear and nonlinear substructures can be adjusted simultaneously so that the predicted responses match the measurement ones in an optimal manner. Only the concerned substructures and the reduced equation are re-analyzed in the optimization process, thus reducing the computational load compared with the traditional model updating methods on the global structure. Application to a nine-story frame with nonlinear base isolations demonstrates that the proposed method is very accurate and efficient in updating the linear and nonlinear parameters simultaneously with a few measured responses. The effects of measurement noise and the number of measurement points on the updating results are also investigated.

关键词： Nonlinear model updating substructuring method Structural response Response sensitivity Nonlinear base isolation

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Calculation of Structural Response and Response Sensitivity with Improved substructuring method

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JOURNAL OF AEROSPACE ENGINEERING 2019年第3期32卷

作者： Zhu, Hongping Li, Jiajing Weng, Shun Gao, Fei Chen, Zhidan Huazhong Univ Sci & Technol Sch Civil Engn & Mech Wuhan 430074 Hubei Peoples R China

Structural responses and response sensitivities are frequently required in structural health monitoring, whereas the computation of structural responses and response sensitivities of a large-size model is time consuming. This paper proposes a substructuring method for the fast computation of structural responses and response sensitivities. Structural responses are projected onto the range space of a few master substructural eigenvectors to construct a simplified vibration equation. The contribution of slave eigenvectors is compensated by a residue space to achieve high accuracy. Due to this compensation of the residue, a few master eigenvectors are needed to ensure the fast computation of structural responses and response sensitivities with high accuracy, avoiding the inclusion of numerous substructural eigenvectors. In addition, response sensitivities with respect to a parameter are calculated from master eigenvector derivatives of one substructure only, whereas derivatives of other substructures are zeroes. As simplified vibration equations are quite small, the proposed substructuring method can very quickly calculate structural responses and response sensitivities. The proposed method is verified by a frame structure and a bridge structure. (c) 2019 American Society of Civil Engineers.

关键词： substructuring method Structural response Response sensitivity Residue Master eigenvector

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