Optimization of load uniformity for triangular tube using non-linear programming

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The paper focuses on two topics, optimizing the proposed triangular tube for crashworthiness and solving a non-linear programming problem by a "mapping" technique, which the condition of Lagrange Multiplier Theorem is violated within the feasible region. The purpose of studying optimized triangular tubes is to prepare them for redesigning vehicle bumpers. The dimension optimization of triangular tube is carried out for its thickness and lateral length, based on the accomplished shape optimization under an impact. The load uniformity is taken as the objective function, which is defined as the ratio of maximum peak force and means crushing force. Meanwhile the mean crushing force and absorbed energy are treated as constraints. Based on FEA analysis, the regression functions for load uniformity, mean crushing force, and absorbed energy are formulated by RSM. The result has shown that triangular tube possesses an optimization region, under which the better-integrated property can be achieved to supply a more safety environment for vehicular occupants.

Original languageEnglish
Pages (from-to)121-140
Number of pages20
JournalMultidiscipline Modeling in Materials and Structures
Issue number1
StatePublished - Jan 1 2007


  • Load uniformity
  • Mapping
  • Non-linear programming
  • Optimization
  • Triangular tube


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