Skip to main content
SpringerLink
Log in

A Developed Transfer Matrix Method for Analysis of Elastic–Plastic Behavior of Structures

  • Published:
International Journal of Steel Structures Aims and scope Submit manuscript

Abstract

The ductility of structure or component is particularly important when it encounters earthquake or other sudden disasters. It can reduce the damage of structure to a certain extent. The ductility mechanism of structure is closely related to the analysis of elastic–plastic behavior of structure. Therefore, an improved transfer matrix method based on elastic–plastic transfer element is proposed to analyze the elastic–plastic behavior of structures. The elastic–plastic element consists of two parts, elastic region and plastic region. According to the section stress analysis, the ratio of elastic zone to plastic zone can be determined to reflect the elastic–plastic behavior. The analysis process is as follows: firstly, the elastic–plastic part of the structure is determined according to the mechanical behavior of the whole structure, then the elastic–plastic transfer unit is proposed according to the determined proportion of the elastic–plastic zone, and finally the mechanical behavior of the whole structure is analyzed. Through numerical examples, the correctness and effectiveness of the proposed method are verified by comparing the analytical model with the theoretical solution. The results show that this method provides a new way for the further study of engineering structure mutation process.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23

Similar content being viewed by others

References

  • Antoni, N. (2019). A novel rapid method of purely elastic solution correction to estimate multiaxial elastic-plastic behaviour. Journal of Computational Design and Engineering, 6(3), 269–283.

    Article  Google Scholar 

  • Arai, M., Kuroda, S., & Ito, K. (2021). Static Elastic-Plastic Analysis of a Pipe Structure by the Transfer Matrix Method. Journal of Pressure Vessel Technology-Transactions of the ASME, Doi, 10(1115/1), 4047680.

    Google Scholar 

  • Baggett, J. F., & Martin, J. B. (1983). Evaluation of the inelastic spectrum design method for two degree-of-freedom structures under earthquake loading. Engineering Structures, 5(4), 247–254.

    Article  Google Scholar 

  • Canh, V. L., Tran, T. D., & Pham, D. C. (2016). Rotating plasticity and nonshakedown collapse modes for elastic–plastic bodies under cyclic loads. International Journal of Mechanical Sciences, 111–112, 55–64.

    Google Scholar 

  • Chopra, A. K., & Chintanapakdee, C. (2004). Inelastic deformation ratios for design and evaluation of structures: Single-degree-of-freedom bilinear systems. Journal of Structural Engineering, 130(9), 1309–1319.

  • Dastjerdi, S., & Abbasi, M. (2019). A Vibration Analysis of a CrackedMicro-cantilever in an Atomic Force Microscope by Using TransferMatrix Method. Ultramicroscopy, 196, 33–39.

    Article  Google Scholar 

  • Dokainish, M. A. (1972). A New Approach for Plate Vibrations: Combination of Transfer Matrix and Finite-Element Technique. Journal of Engineering for Industry, 94(2), 526–530.

    Article  Google Scholar 

  • Duan, L., & Reno, M. (1999). Performance-Based Seismic Design Criteria For Bridges. CRC Press LLC.

    Google Scholar 

  • Firstov, S. A., Podrezov, Y. N., Shtyka, L. G., Zherdin, A. G., & Malyshenko, A. A. (1990). Modeling of the ductile-brittle transition in porous metallic materials under conditions of crack resistance tests. Powder Metallurgy and Metal Ceramics, 29(5), 411–416.

  • Geradin, M., & Chen, S. L. (1995). An exact model reduction technique for beam structures: Combination of transfer and dynamic stiffness matrices. Journal of Sound and Vibration, 185(3), 431–440.

  • Guarracino, F. (2019). Remarks on the stability analysis of some thin-walled structures in the elastic-plastic range. Thin-Walled Structures, 138, 208–214.

    Article  Google Scholar 

  • Shokrollahi, H., Fallah, F., Naghdabadi, R., & Kargarnovin, M. H. (2017). Elastic-plastic behavior of sandwich cylindrical shell panels with a flexible core. Proceedings of the Institution of Mechanical Engineers, 231(2), 223–241.

  • Hong, H. P., & Hong, P. (2007). Assessment of ductility demand and reliability of bilinear single-degree-of-freedom systems under earthquake loading. Canadian Journal of CivilEngineering, 34(12), 1606–1615.

    Article  Google Scholar 

  • Huang, Q., Choe, J., Yang, J., et al. (2019). An efficient approach for post-buckling analysis of sandwich structures with elastic-plastic material behavior. International Journal of Engineering Science, 142, 20–35.

    Article  MathSciNet  Google Scholar 

  • Jiang, Y., Ott, W., & Baum, C. (2009). Fatigue life predictions by integrating EVICD fatigue damage model and an advanced cyclic plasticity theory. International Journal of Plasticity, 25(5), 780–801.

    Article  Google Scholar 

  • Jiang, H., Lu, X., & Zhu, J. (2012). Performance-based seismic analysis and design of code-exceeding tall buildings in Mainland China. Structural Engineering and Mechanics, 43(4), 1–16.

    Article  Google Scholar 

  • Karavasilis, T. L., & Seo, C. Y. (2011). N Makris Dimensional Response Analysis of Bilinear Systems Subjected to Non-Pulse-like Earthquake Ground Motions. Journal of Structural Engineering, 137(5), 600–606.

    Article  Google Scholar 

  • Li, R., & Sieradzki, K. (1992). Ductile-brittle transition in random porous Au. Physical Review Letters, 68(8), 1168–1171.

  • Lignos, D. G., & Krawinkler, H. D. (2011). eterioration modeling of steel components in support of collapse prediction of steel moment frames under earthquake loading. Journal of Structural Enginee, 137(11), 1291–1302.

    Article  Google Scholar 

  • Lin, Y., Zhang, X., Xu, W., & Zhou, M. (2019). Importance Assessment of Structural Members Based on Elastic-Plastic Strain Energy. Advances in Materials Science and Engineering., 2019, 1–17.

    Article  Google Scholar 

  • Liu, Y., Zhang, X,, & Cen, Z. (2003). Lower bound limit analysis of three dimensional elastoplastic structures by boundary element method. Applied Mathematics and Mechanics, 24(12), 1301–1308.

  • Mahbod, M., Asgari, M., & Mittelstedt, C. (2020). Architected functionally graded porous lattice structures for optimized elastic-plastic behavior. Proceedings of the Institution of Mechanical Engineers Part l-Journal of Materials-Design and Applications, 234(8), 1099–1116.

    Article  Google Scholar 

  • Mavroeidis, G. P., & Dong, G. (2004). AS Papageorgiou Near-fault ground motions and the response of elastic and inelastic single-degree-of-freedom (SDOF) systems. Earthquake Engineering Structural Dynamics, 33(9), 1023–1049.

    Article  Google Scholar 

  • McClintock, F. A. (1968). A Criterion for Ductile Fracture by the Growth of Holes. Journal of Applied Mechanics, 35(2), 363–371.

    Article  Google Scholar 

  • Miranda, E. (1993). Evaluation of Site-Dependent Inelastic Seismic Design Spectra. ASCE Journal of Structure Engineering, 199(5), 1319–1338.

    Article  Google Scholar 

  • Nassar, A, A., &Krawinkler, H. (1991). Seismic for SDOF and MDOF System, Report No.95, The John A . Blume Earthquake Engineering Center, Stanford University, Stanford, California.

  • Newmark, N. M., & Hall, W. J. (1982). Earthquake spectra and design. Berkeley, California: EERI.

  • Park, R., & Paulay, T. (1975). Reinforced concrete structures. John Wiley & Sons.

    Book  Google Scholar 

  • Petruska, J., Kubik, P., Hulka, J., & Sebek, F. (2013). Ductile fracture criteria in prediction of chevron cracks. Advanced Materials Research, 716, 653–658.

  • Pineau, A. (2008). Modeling ductile to brittle fracture transition in steels-micromechanical and physical challenges. International Journal of Fracture, 150(1), 129–156.

    Article  Google Scholar 

  • Riddell, R. (1995). Inelastic Design Spectra Accounting for Soil Conditions. Earthquake Engineering & Structural Dynamics, 24(11), 1491–1510.

    Article  Google Scholar 

  • Rodigari, D., Franchi, A., & Genna, F. (2019). A linear complementarity approach to the time integration of dynamic elastic-plastic structural problems. Meccanica, 54(10), 1597–1609.

    Article  MathSciNet  Google Scholar 

  • Su, X., Kang, H., et al. (2020). Modeling and parametric analysis of in-plane free vibration of a floating cable-stayed bridge with transfer Matrix Method. International Journal of Structural Stability and Dynamics, 20(1), 2050004.

    Article  MathSciNet  Google Scholar 

  • Su, X., Kang, H., & Guo, T. (2019). Dynamic analysis of the in-plane free vibration of a multi-cable-stayed beam with transfer matrix method. Archive of Applied Mechanics, 89(12), 2431–2448.

    Article  Google Scholar 

  • Sun, J., Huang, W., Zhu, L., Liu, Y., & Yang, J. (2020). Investigation and finite element simulation analysis on collapse accident of Heyuan Dongjiang Bridge. Engineering Failure Analysis, 115, 104655.

    Google Scholar 

  • Wallach, J. C., & Gibson, L. J. (2001). Mechanical behaviorof a three-dimensional truss material. International Journal of Solids and Structures, 38(40–41), 7181–7196.

    Article  Google Scholar 

  • Wang, R., Tsai, K.-C., & Lin, B. (2011). Extremely large displacement dynamic analysis of elastic-plastic plane frames. Earthquake Engineering and Structural Dynamics, 40, 1515–1533.

    Article  Google Scholar 

  • Wu, J. Y., & Xu, S. L. (2011). An augmented multicrack elastoplastic damage model for tensile cracking. Int. Solids Struct, 48, 2511–2527.

    Article  Google Scholar 

  • Yao, D., Cai, L., & Chen, B. (2016). A new fracture criterion for ductile materials based on a finite element aided testing method. Materials Science & Engineering, 673, 633–647.

    Article  Google Scholar 

  • Yi, W. J., Zhang, H. Y., & Kunnath, S. K. (2007). Probabilistic Constant-Strength Ductility Demand Spectra. Journal of Structural Engineering, 133(4), 567–575.

    Article  Google Scholar 

  • Yu, J., & Tan, K. H. (2017). Structural behavior of reinforced concrete frames subjected to progressive collapsed. ACI Structural Journal, 114(1), 63–74.

    Article  Google Scholar 

  • Zhai, C., & Xie, L. (2005). Constant-ductility strength demand spectra for seismic design of structures. Earthquake Engineering and Engineering Vibration, 4(2), 243–250.

    Article  Google Scholar 

  • Zhan, L., Wang, S., Xi, H., & Xiao, H. (2020). High and low cycle fatigue failure effects of metals predicted automatically from innovative elastoplastic equations with high-efficiency algorithms. Continuum Mechanics and Thermodynamics., 33(4), 1041–1052.

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

The financial support of Xi’an Science and technology innovation talent service enterprise project (2020KJRC0047), Provincial Natural Science Foundation of Shaanxi (2020JM-475) and National Natural Science Foundation of China (Grant Nos. 51408453) are much appreciated.

Author information

Authors and Affiliations

  1. School of Civil Engineering, Xi’an University of Architecture and Technology, Xi’an, 710055, People’s Republic of China

    Jianpeng Sun, Kai Liu, Guangmeng Liu & Hui Li

Authors
  1. Jianpeng Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kai Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Guangmeng Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Hui Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jianpeng Sun.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sun, J., Liu, K., Liu, G. et al. A Developed Transfer Matrix Method for Analysis of Elastic–Plastic Behavior of Structures. Int J Steel Struct 21, 1620–1629 (2021). https://doi.org/10.1007/s13296-021-00524-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13296-021-00524-8

Keywords

Search

Navigation