Skip to main content
SpringerLink
Log in

Efficient stochastic finite element analysis of irregular wall structures with inelastic random field properties over manifold

  • Original Paper
  • Published:
Computational Mechanics Aims and scope Submit manuscript

Abstract

In the stochastic finite element analysis of irregular wall structures considering material uncertainties, the random fields simulation and deterministic finite element analysis (FEA) are the two focuses. In this paper, we present an efficient stochastic finite element analysis procedure for irregular wall structures with inelastic random field properties. In the procedure, the geometry domains of irregular wall structures are deemed as two-dimensional (2D) manifolds. Then Isometric feature mapping (Isomap) is used to map the manifold to a 2D Euclidean domain, over which the well-developed stochastic harmonic function representation is applied to simulate the random field. Meanwhile, to accurately reflect the nonlinear behaviors of the irregular wall structures, we adopt an enhanced deterministic FEA method, which combines the multi-layered shell element, the softened damage-plasticity concrete model and the quasi-Newton solution with a two-level secant stiffness in a framework. Finally, the proposed approach is applied to the stochastic analysis of a U-shaped reinforced concrete shear wall to illustrate its feasibility and applicability. The results demonstrate that the proposed approach can effectively simulate the random fields over irregular geometry domains and can reproduce the representative stochastic inelastic behaviors of irregular wall structures. The approach can be further used in reliability or safety evaluation of structures.

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

Similar content being viewed by others

References

  1. Nicolae I, Reynouard JM (2005) Behaviour of u-shaped walls subjected to uniaxial and biaxial cyclic lateral loading. J Earthq Eng 9(1):67–94

    Article  Google Scholar 

  2. Katrin B, Alessandro D, Priestley MJN (2008) Quasi-static cyclic tests of two u-shaped reinforced concrete walls. J Earthq Eng 12(7):1023–1053

    Article  Google Scholar 

  3. Susumu K, Kohei S, Masanobu S (2011) Simulation of seismic load resistance of core-walls for tall buildings. Appl Mech Mater 82:386–391

    Article  Google Scholar 

  4. Raluca C, Katrin B (2016) Behaviour of U-shaped RC walls under quasi-static cyclic diagonal loading. Eng Struct 106:36–52

    Article  Google Scholar 

  5. George S (2009) The stochastic finite element method: past, present and future. Comput Methods Appl Mech Eng 198(9–12):1031–1051

    MATH  Google Scholar 

  6. Rauter N (2021) A computational modeling approach based on random fields for short fiber-reinforced composites with experimental verification by nanoindentation and tensile tests. Comput Mech 67:1–24

    Article  MathSciNet  MATH  Google Scholar 

  7. Hasini G, Sergio Z, Pedro D, Verhoosel Clemens V, van Brummelen EH (2020) A proper generalized decomposition (PGD) approach to crack propagation in brittle materials: with application to random field material properties. Comput Mech 65(2):451–473

    Article  MathSciNet  MATH  Google Scholar 

  8. Kiureghian A, Ke J (1988) The stochastic finite element method in structural reliability. Probab Eng Mech 3:83–91

    Article  Google Scholar 

  9. Matthies H, Brenner C, Bucher C, Soares C (1997) Uncertainties in probabilistic numerical analysis of structures and solids-stochastic finite elements. Struct Saf 19:283–336

    Article  Google Scholar 

  10. Kam LW, Belytschko T, Mani A (1986) Random field finite elements. Int J Numer Methods Eng 23:1831–1845

    Article  MathSciNet  MATH  Google Scholar 

  11. Masanobu S, George D (1991) Simulation of stochastic processes by spectral representation. Appl Mech Rev 44(4):191

    Article  MathSciNet  Google Scholar 

  12. Huang SP, Quek ST, Phoon KK (2001) Convergence study of the truncated Karhunen-Loeve expansion for simulation of stochastic processes. Int J Numer Methods Eng 52(9):1029–1043

    Article  MATH  Google Scholar 

  13. Jianbing C, Jie L (2011) Stochastic harmonic function and spectral representations. Chin J Theor Appl Mech 43(3):505–513

    MathSciNet  Google Scholar 

  14. Jianbing C, Weiling S, Jie L, Jun X (2013) Stochastic harmonic function representation of stochastic processes. J Appl Mech 80(1):1001

    Google Scholar 

  15. Schenk CA, Schuëller GI (2003) Buckling analysis of cylindrical shells with random geometric imperfections. Int J Non-Linear Mech 38(7):1119–1132

    Article  MATH  Google Scholar 

  16. Schenk CA, Schuëller GI (2007) Buckling analysis of cylindrical shells with cutouts including random boundary and geometric imperfections. Comput Methods Appl Mech Eng 196(35–36):3424–3434

    Article  MATH  Google Scholar 

  17. Vissarion P, Manolis P (2005) The effect of material and thickness variability on the buckling load of shells with random initial imperfections. Comput Methods Appl Mech Eng 194(12–16):1405–1426

    MATH  Google Scholar 

  18. Betz W, Papaioannou I, Straub D (2014) Numerical methods for the discretization of random fields by means of the Karhunen–Loève expansion. Comput Methods Appl Mech Eng 271:109–129

    Article  MATH  Google Scholar 

  19. Scarth C, Adhikari S, Cabral PH, Silva GH, do Prado AP (2019) Random field simulation over curved surfaces: applications to computational structural mechanics. Comput Methods Appl Mech Eng 345:283–301

    Article  MathSciNet  MATH  Google Scholar 

  20. Samih Z, Adissa L, David D (2019) Simulation of a Gaussian random field over a 3d surface for the uncertainty quantification in the composite structures. Comput Mech 63(6):1083–1090

    Article  MathSciNet  Google Scholar 

  21. Polak M, Vecchio F (1993) Nonlinear analysis of reinforced-concrete shells. J Struct Eng 119:3439–3462

    Article  Google Scholar 

  22. Vecchio F, Collins M (1986) The modified compression-field theory for reinforced concrete elements subjected to shear. ACI J 83(2):219–231

    Google Scholar 

  23. Hsu T, Zhu RH (2002) Softened membrane model for reinforced concrete elements in shear. Struct J 99:460–469

    Google Scholar 

  24. Lubliner J, Oliver J, Oller S, Oñate E (1989) A plastic-damage model for concrete. Int J Solids Struct 25:299–326

    Article  Google Scholar 

  25. JianYing W, Jie L, Rui F (2006) An energy release rate-based plastic-damage model for concrete. Int J Solids Struct 43(3–4):583–612

    MATH  Google Scholar 

  26. Tesser L, Filippou F, Talledo D, Scotta R, Vitaliani R (2011) Nonlinear analysis of RC panels by a two parameter concrete damage model

  27. Ju J (1989) On energy-based coupled elastoplastic damage theories: constitutive modeling and computational aspects. Int J Solids Struct 25:803–833

    Article  MATH  Google Scholar 

  28. De-Cheng F, Xiaodan R, Jie L (2018) Cyclic behavior modeling of reinforced concrete shear walls based on softened damage-plasticity model. Eng Struct 166:363–375

    Article  Google Scholar 

  29. Matthies H, Strang G (1979) The solution of nonlinear finite element equations. Int J Numer Methods Eng 14:1613–1626

    Article  MathSciNet  MATH  Google Scholar 

  30. Dennis J, Schnabel B (1983) Numerical methods for unconstrained optimization and nonlinear equations. In: Prentice Hall series in computational mathematics

  31. Masanobu S, George D (1996) Simulation of multi-dimensional Gaussian stochastic fields by spectral representation. Appl Mech Rev 49(1):29–53

    Article  Google Scholar 

  32. Jianbing C, Jingran H, Xiaodan R, Jie L (2018) Stochastic harmonic function representation of random fields for material properties of structures. J Eng Mech 144(7):04018049

    Google Scholar 

  33. Shixue L, Weiling S, Jie L (2012) Simulation of multi-dimensional random fields by stochastic harmonic functions. J Tongji Univ Nat Sci 40(7):965–970

    Google Scholar 

  34. Tenenbaum JB, De Silva V, Langford JC (2000) A global geometric framework for nonlinear dimensionality reduction. Science 290(5500):2319–2323

    Article  Google Scholar 

  35. Cox TF, Cox MAA (2001) Multidimensional scaling. J R Stat Soc 46(2):1050–1057

    MathSciNet  MATH  Google Scholar 

  36. Niroomandi A, Pampanin S, Dhakal R, Ashtiani MS (2016) Finite element analysis of rectangular reinforced concrete walls under bi-directional loading

  37. Xinzheng L, Linlin X, Hong G, Yuli H, Xiao L (2015) A shear wall element for nonlinear seismic analysis of super-tall buildings using OpenSees. Finite Elem Anal Des 98:14–25

    Article  Google Scholar 

  38. Nakamura N, Naohiko T, Nakano T, Tachibana E (2009) Analytical study on energy consumption and damage to cylindrical and I-shaped reinforced concrete shear walls subjected to cyclic loading. Eng Struct 31:999-1009

    Article  Google Scholar 

  39. Xiaodan R, Shajie Z, Jie L (2015) A rate-dependent stochastic damage-plasticity model for quasi-brittle materials. Comput Mech 55(2):267–285

    Article  MathSciNet  MATH  Google Scholar 

  40. De-Cheng F, Xiaodan R, Jie L (2018) Softened damage-plasticity model for analysis of cracked reinforced concrete structures. J Struct Eng 144(6):04018044

    Article  Google Scholar 

  41. JianYing W, Jie L (2007) Unified plastic-damage model for concrete and its applications to dynamic nonlinear analysis of structures. Struct Eng Mech 25(5):519–540

    Article  Google Scholar 

  42. JianYing W, Miguel C (2018) A novel positive/negative projection in energy norm for the damage modeling of quasi-brittle solids. Int J Solids Struct 139:250–269

    Google Scholar 

  43. Jie L, Xiaodan R (2009) Stochastic damage model for concrete based on energy equivalent strain. Int J Solids Struct 46(11–12):2407–2419

    MATH  Google Scholar 

  44. Hsu Thomas TC (1988) Softened truss model theory for shear and torsion. ACI Struct J 85(6):624–635

    Google Scholar 

  45. Rui F, Oliver J, Cervera M (1998) A strain-based plastic viscous-damage model for massive concrete structures. Int J Solids Struct 35(14):1533–1558

    Article  MATH  Google Scholar 

  46. Wu JY (2004) Damage energy release rate-based elastoplastic damage constitutive model for concrete and its application to nonlinear analysis of structures. Ph.D. thesis

  47. Xiaodan R, Jie L (2018) Two-level consistent secant operators for cyclic loading of structures. J Eng Mech 144(8):04018065

    Google Scholar 

  48. Jian-Ying W, Yuli H, Phu NV (2020) On the BFGS monolithic algorithm for the unified phase field damage theory. Comput Methods Appl Mech Eng 360:112704

    Article  MathSciNet  MATH  Google Scholar 

  49. Dennis JE (1996) Numerical methods for unconstrained optimization and nonlinear equations. SIAM Classics in Applied Mathematics

  50. Code of China (2010) Code for design of concrete structures.GB 50010-2010. China Architecture & Building Press, Beijing

Download references

Acknowledgements

Financial supports from the National Natural Science Foundation of China (Grant Nos. 52078119, 52078361) and the Fundamental Research Funds for the Central Universities are greatly appreciated.

Author information

Authors and Affiliations

  1. School of Civil Engineering, Tongji University, 1239 Siping Road, Shanghai, 200092, China

    Yan-Ping Liang & Xiaodan Ren

  2. Key Laboratory of Concrete and Prestressed Concrete Structures of the Ministry of Education, Southeast University, Nanjing, 211189, China

    De-Cheng Feng

Authors
  1. Yan-Ping Liang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xiaodan Ren
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. De-Cheng Feng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to De-Cheng Feng.

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

Liang, YP., Ren, X. & Feng, DC. Efficient stochastic finite element analysis of irregular wall structures with inelastic random field properties over manifold. Comput Mech 69, 95–111 (2022). https://doi.org/10.1007/s00466-021-02084-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00466-021-02084-4

Keywords

Search

Navigation