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Approximate cutting pattern optimization of frame-supported and pneumatic membrane structures

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Abstract

A simple iterative method is presented for cutting pattern optimization of frame-supported and pneumatic membrane structures for minimizing the variation of stresses from the target values. The plane cutting sheet is generated by minimizing the error from the shape obtained by reducing the target stress from the desired curved shape of surface. The equilibrium shape is obtained using an energy approach to minimize of total strain energy under forced deformation at the boundary nodes. The external work done by the pressure is also incorporated for analysis of pneumatic membrane structures. An approximate method is also proposed to derive a discretized form for analysis of an ethylene tetrafluoroethylene (ETFE) film, where elasto-plastic behavior under monotonic loading condition is modeled as a nonlinear elastic material under monotonic loading condition. The proposed method is applied to examples of a frame-supported polyvinyl chloride membrane structure and an air pressured square ETFE film.

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References

  • Adriaenssens, S., Block, P., Veenendaal, D., Williams, C. (eds.): Shell Structures in Architecture. Routledge, Abingdon-on-Thames (2014)

    Google Scholar 

  • Azariadis, P.N., Aspragathos, N.A.: Geodesic curvature preservation in surface flattening through constrained global optimization. Comput. Aided Des. 33, 581–591 (2001)

    Article  Google Scholar 

  • Barnes, M.R.: Form-finding and analysis of prestressed nets and membranes. Comput. Struct. 30(3), 685–695 (1988)

    Article  Google Scholar 

  • Bathe, K.-J.: Finite Element Procedures. Prentice-Hall, Upper Saddle River (1996)

    MATH  Google Scholar 

  • Bletzinger, K.-U., Wünchmer, R., Daoud, F., Camprubi, N.: Computational methods for form finding and optimization of shells and membranes. Comput. Methods Appl. Mech. Eng. 194, 3438–3452 (2005)

    Article  MathSciNet  Google Scholar 

  • Bouzidi, R., Le Van, A.: Numerical solution of hyperelastic membranes by energy minimization. Comput. Struct. 82, 1961–1969 (2004)

    Article  Google Scholar 

  • Bown, A., Wakefield, D.: Inflatable membrane structures in architecture and aerospace: some recent projects. J. Int. Assoc. Shell Spat. Struct. 56(1), 5–16 (2015)

    Google Scholar 

  • Choi, K.K., Kim, N.-H.: Structural Sensitivity Analysis and Optimization 1: Linear Systems. Springer, New York (2005)

    Google Scholar 

  • Coelho, M., Roehl, D., Bletzinger, K.U.: Numerical simulation of burst-test of an ETFE membrane. In: Proceedings of IASS Symposium, Brasilia, International Association Shell and Spatial Structures, Paper No. 293 (2014a)

  • Coelho, M., Roehl, D., Bletzinger, K.-U.: Numerical and analytical solutions with finite strain for circular inflated membranes considering pressure-volume coupling. Int. J. Mech. Sci. 82, 122–130 (2014b)

    Article  Google Scholar 

  • Cui, J., Ohsaki, M.: An optimization method for generating self-equilibrium shape of curved surface from developable surface. In: Proceedings of the IASS Symposium 2017, Hamburg, Germany, International Association Shell and Spatial Structures, Paper No. 9576 (2017)

  • Cui, J., Ohsaki, M.: Shape design of curved surface of membrane structure using developable surface. J. Int. Assoc. Shell Spat. Struct. 59(3), 199–214 (2018)

    Google Scholar 

  • Daxini, S.D., Prajapati, J.M.: Structural shape optimization with meshless method and swarm-intelligence based optimization. Int. J. Mech. Mater. Des. 16, 167–190 (2020)

    Article  Google Scholar 

  • Dinh, T.D., Rezael, A., Puystiens, S., van Craenenbroeck, M., Carbonez, K., de Laet, L., Mollaert, M., van Hemelrick, D., van Paepegem, W.: A study of tension fabric membrane structures under in-plane loading: nonlinear finite element analysis and validation. Compos. Struct. 128, 10–20 (2015)

    Article  Google Scholar 

  • Dinh, T.D., Razaei, A., Punurai, W., de Laet, L., Molleart, M., van Hemelrijck, D., van Paepegem, W.: A shape optimization approach to integrated design and nonlinear analysis of tensioned fabric membrane structures with boundary cables. Int. J. Solids Struct. 83, 114–125 (2016)

    Article  Google Scholar 

  • Fischer, D.: Configuration dependent pressure potentials. J. Elast. 19, 77–84 (1998)

    Article  MathSciNet  Google Scholar 

  • Gill, P.E., Murray, W., Saunders, M.A.: SNOPT: an SQP algorithm for large-scale constrained optimization. SIAM J. Opt. 12, 979–1006 (2002)

    Article  MathSciNet  Google Scholar 

  • Gosling, P.D., Lewis, W.J.: Optimal structural membranes: I. Formulation of a curved quadrilateral element for surface definition. Comput. Struct. 61(5), 871–883 (1996)

    Article  Google Scholar 

  • Hu, J., Gao, C., He, S., Chen, W., Li, Y., Zhao, B., Shi, T., Yang, D.: Effects of on-axis and off-axis tension on uniaxial mechanical properties of plain woven fabrics for inflated structures. Compos. Struct. 171, 92–99 (2017)

    Article  Google Scholar 

  • Kim, J.-Y., Lee, J.-B.: A new technique for optimum cutting patterns generation of membrane structures. Eng. Struct. 24, 745–756 (2002)

    Article  Google Scholar 

  • Long, K., Wang, X., Du, Y.: Robust topology optimization formulation including local failure and load uncertainty using sequential quadratic programming. Int. J. Mech. Mater. Des. 15, 317–332 (2019)

    Article  Google Scholar 

  • Luo, Y., Xing, J., Niu, Y., Li, M., Kang, Z.: Wrinkle-free design of thin membrane structures using stress-based topology optimization. J. Mech. Phys. Solids 102, 277–293 (2017)

    Article  MathSciNet  Google Scholar 

  • Membrane Structures Association of Japan.: Testing Method for In-plane Shear Properties of Membrane Materials. MSAJ/M-01-1993. (1993) (in Japanese)

  • Membrane Structures Association of Japan.: Testing Method for Elastic Constants of Membrane Materials. MSAJ/M-02-1995 (1995) (in Japanese)

  • Morozov, E.V., Lopatin, A.V.: Analysis and design of the flexible composite membrane stretched on the spacecraft solar frame. Compos. Struct. 94, 3106–3114 (2012)

    Article  Google Scholar 

  • Mosler, J.: A novel variational algorithmic formulation for wrinkling at finite strains based on energy minimization: application to mesh adaptation. Comput. Methods Appl. Mech. Eng. 197, 1131–1146 (2008)

    Article  Google Scholar 

  • Ohsaki, M., Fujiwara, J.: Developability conditions for prestress optimization of a curved surface. Comput. Methods Appl. Mech. Eng. 192, 77–94 (2003)

    Article  Google Scholar 

  • Ohsaki, M., Saburi, S., Takeda, F.: Approximate method for cutting pattern optimization of membrane structures. In: Proceedings of IASS Symposium 2017, Hamburg, Germany, International Association of Shell and Spatial Structures, Paper No. 9503 (2017)

  • Ohsaki, M., Uetani, K.: Shape-stress trade-off design of membrane structures for specified sequence of boundary shapes. Comput. Methods Appl. Mech. Eng. 182, 73–88 (2000)

    Article  Google Scholar 

  • Pargana, J.B., Lloyd-Smith, D., Izzuddin, B.A.: Advanced material model for coated fabric used in tensioned fabric structures. Eng. Struct. 29, 1323–1336 (2007)

    Article  Google Scholar 

  • Philipp, B., Dieringer, F., Wüchner, R., Bletzinger, K.-U.: Form-finding and structural analysis for the design of hybrid structures. J. Int. Assoc. Shell Spat. Struct. 56(1), 17–25 (2015)

    Google Scholar 

  • Punurai, W., Tongpool, W., Morales, J.H.: Implementation of genetic algorithm for optimum cutting pattern generation of wrinkle free finishing membrane structures. Finite Elem. Anal. Des. 58, 84–90 (2012)

    Article  Google Scholar 

  • SciPy.: https://docs.scipy.org/doc/scipy/reference/spatial.html. Accessed 11 June 2019

  • Uetani, K., Mitsuda, E., Ohsaki, M.: Cutting pattern optimization of frame-supported membranes considering boundary shape and stress ratio as design parameters. J. Struct. Constr. Eng. Arch. Inst. Jpn. 66(540), 73–78 (2001). (in Japanese)

    Article  Google Scholar 

  • Wang, B.P., Babu, D., Nambiar, R.V., Lawrence, K.L.: Shape sensitivity analysis using closed-form stiffness matrix for hierarchic triangular elements. Comput. Struct. 43(1), 69–75 (1992)

    Article  Google Scholar 

  • Wang, C.C.L., Smith, S.S.-F., Yuen, M.M.F.: Surface flattening based on energy model. Comput. Aided Des. 34, 823–833 (2002)

    Article  Google Scholar 

  • Wang, Q., Pejhan, K., Telichev, I., Wu, C.Q.: Extensions of the U* theory for applications on orthotropic composites and nonlinear elastic materials. Int. J. Mech. Mater. Des. 13, 469–480 (2017)

    Article  Google Scholar 

  • Xing, J., Luo, Y., Zhan, J., Kang, Z.: Global shape optimization of fixtures to suppress wrinkles in large-displacement membrane structures. Int. J. Solids Struct. 144–145, 301–312 (2018)

    Article  Google Scholar 

  • Yoshino, T., Kato, S.: Viscous characteristics of ETFE film sheet under equal biaxial tensions. Proc. Eng. 155, 442–451 (2016)

    Article  Google Scholar 

  • Zhao, T., Ramos Jr., A.S., Paulino, G.H.: Material nonlinear topology optimization considering the von Mises criterion through an asymptotic approach: max strain energy and max load factor formulations. Int. J. Numer. Methods Eng. 118(13), 804–828 (2019)

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Architecture and Architectural Engineering, Kyoto University, Kyoto-Daigaku Katsura, Nishikyo, Kyoto, 615-8540, Japan

    Makoto Ohsaki

  2. National Research Institute for Earth Science and Disaster Resilience, Miki, Japan

    Jun Fujiwara

  3. Taiyo Kogyo Corporation, Osaka, Japan

    Fumiyoshi Takeda

Authors
  1. Makoto Ohsaki
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  2. Jun Fujiwara
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  3. Fumiyoshi Takeda
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Correspondence to Makoto Ohsaki.

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Ohsaki, M., Fujiwara, J. & Takeda, F. Approximate cutting pattern optimization of frame-supported and pneumatic membrane structures. Int J Mech Mater Des 16, 883–896 (2020). https://doi.org/10.1007/s10999-020-09492-z

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  • DOI: https://doi.org/10.1007/s10999-020-09492-z

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