Complex Variable Semianalytical Method for Sensitivity Evaluation in Nonlinear Path Dependent Problems: Applications to Periodic Truss Materials

  • Geovane A. Haveroth
  • Pablo A. Muñoz-RojasEmail author
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 49)


The evaluation of structural response derivatives with respect to design parameters, usually known as sensitivity analysis, is an issue of paramount importance in gradient-based optimization and reliability analyses in engineering. In the last 20 years, much research has been devoted to develop efficient strategies for the accurate evaluation of sensitivity information. A relatively new and promising procedure combines the semianalytical (SA) approach with the use of complex variables (CVSA). This method allows the use of diminutive perturbations, circumventing the weakness that the traditional SA approach shows when applied to shape design variables. In spite of the great potential of the CVSA, its formulation and application has been restricted to path independent problems. In this chapter we aim to extend the method to handle path dependent problems, emphasizing the treatment of internal variables, such as accumulated plastic strain and damage. In order to make the concept easy to understand, we use the method to evaluate the sensitivity of particular homogenized properties of a 2D periodic truss material (PTM). Optimization of PTMs has encountered great potential in tissue engineering, as well as in automotive and aeronautical applications. Generally PTMs are designed to operate in the linear geometrical and constitutive range. However, using sensitivity analysis we can obtain an insight about how these designed homogenized properties behave when geometrical and/or material nonlinearities are considered.


Design Variable Bulk Modulus Representative Volume Element Internal Variable Virtual Work 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The authors wish to express their gratitude to CNPq and CAPES (Brazilian research supporting agencies), and to UDESC for the concession of Master’s scholarships associated to this work.


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© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Department of Mechanical Engineering, Center for Technological SciencesSanta Catarina State University - UDESCJoinvilleBrazil

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