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A Linear Approach for Sizing Optimization of Isostatic Trussed Structures Subjected to External and Self-Weight Loads

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Abstract

The implementation of a new linear method to optimum weight design of trussed structures subjected to external and self-weight loads is proposed. Design variables are the cross-section areas of the members. Inequality constraints are written based on the force-method for isostatic structures considering maximum and minimum axial stress criteria. The novelty of the proposed approach is the benefit created from the combination of a linear inequality-constrained formulation with interior-point methods to tunnel the solution rapidly and monotonically towards the minimum value through feasible space, also eliminating the need to directly explore the finite-element model. To evaluate the performance of the algorithm, trusses are subject to optimization processes based on different techniques: (i) the proposed method, called by “indirect-method”; (ii) a design problem with constraint evaluated directly from the finite-element model; (iii) optimization based on Genetic Algorithms. The three methods are compared using trusses with 10, 37 and 1240 bar-elements. The results showed that the indirect-method was able to provide great performance for complex topologies, returning weight designs up to 70 times lighter in 1% of the time required by a Genetic Algorithm.

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Authors and Affiliations

  1. CECS, UFABC, PO Box 09210-580, Santo Andre, SP, Brazil

    Flavio Avila Correia Martins, Juan Pablo Julca Avila & Marcelo Araujo da Silva

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  1. Flavio Avila Correia Martins
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  2. Juan Pablo Julca Avila
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  3. Marcelo Araujo da Silva
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Correspondence to Flavio Avila Correia Martins.

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Martins, F.A.C., Avila, J.P.J. & Silva, M.A.d. A Linear Approach for Sizing Optimization of Isostatic Trussed Structures Subjected to External and Self-Weight Loads. Int J Steel Struct 19, 1146–1157 (2019). https://doi.org/10.1007/s13296-018-0194-8

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