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Analytical solutions for two-bar structures under loads along uncertain direction

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Abstract

Two-bar structures under uncertain load are optimized analytically. The magnitudes of load are given and their directions are uncertain. The uncertain loads may be along any directions or in a certain range. The optimization problem of least weight structures with stress constraint and minimal compliance structures with prescribed material volume are studied. The most unfavorable directions of load are found. These examples may be used as benchmarks.

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References

  • Ben-Tal YA (1994) Non-probabilistic concept of reliability. Struct Saf 14(4):228–245

    Google Scholar 

  • Maute K (2014) Topology optimization under uncertainty. In: Rozvany GIN, Lewiński T (eds) Topology Optimization in Structural and Continuum Mechanics. Springer, Vienna, pp 457–471

    Chapter  Google Scholar 

  • Moore RE, Kearfott RB, Cloud MJ (2009) Introduction to interval analysis. SIAM, Philadelphia

    Book  MATH  Google Scholar 

  • Rozvany GIN, Gollub W (1990) Michell layouts for various combinations of line supports. Int J Mech Sci 32:1021–1043

    Article  MATH  Google Scholar 

  • Rozvany GIN, Maute K (2011) Analytical and numerical solutions for a reliability-based benchmark example. Struct Multidisc Optim 43(6):745–753

    Article  MATH  Google Scholar 

  • Rozvany GIN, Maute K (2013) Critical examination of recent assertions by Logo (2013) about a paper ‘Analytical and numerical solutions for a reliability based benchmark example’ (Rozvany and Maute 2011). Struct Multidisc Optim 48:1213–1220

    Article  Google Scholar 

  • Rozvany GIN, Pomezanski V (2014) Exact truss topology optimization for multiple and probabilistic loads. Review lecture at the CST2014 Conference (Naples), also in Comp Techn Rev 10:65–87

  • Rozvany GIN, Zhou M, Birker T (1993) Why multi-load topol designs based on orthogonal microstructures are in general non-optimal. Struct Optim 6:200–204

    Article  Google Scholar 

  • Rozvany GIN, Pomezanski V, Sokol T (2014a) Exact compliance based multi-load truss topology optimization revisited - also background material for an authors’ Reply to a Discussion by Logo. Struct Multidisc Optim 50:193–206

    Article  MathSciNet  Google Scholar 

  • Rozvany GIN, Sokol T, Pomezanski V, Pinter E (2014b) A preview of major progress in exact multi-load and probabilistic truss topology optimization - stress and displacement based elastic design. Struct Multidisc Optim, submitted

  • Shin YS, Grandhi RV (2001) A global structural optimization technique using an interval method. Struct Multidisc Optim 22:351–363

    Article  Google Scholar 

  • Valdebenito MA, Schueller GI (2010) A survey on approaches for reliability-based optimization. Struct Multidisc Optim 42:645–663

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgments

This work is financially supported by the National Natural Science Foundation of China (No. 11172106).

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Authors and Affiliations

  1. College of Civil Engineering, Huaqiao University, Xiamen, 361021, China

    Kemin Zhou

  2. School of Traffic & Transportation Engineering, Central South University, Changsha, 410075, China

    Yutong Zhou

Authors
  1. Kemin Zhou
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  2. Yutong Zhou
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Correspondence to Kemin Zhou.

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Zhou, K., Zhou, Y. Analytical solutions for two-bar structures under loads along uncertain direction. Struct Multidisc Optim 53, 1179–1183 (2016). https://doi.org/10.1007/s00158-014-1158-z

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  • DOI: https://doi.org/10.1007/s00158-014-1158-z

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