Pre-bent shape design of full free-form curved beams using isogeometric method and semi-analytical sensitivity analysis

Seyed Farhad Hosseini, Behnam Moetakef-Imani, Saeid Hadidi-Moud, Behrooz Hassani

    Research output: Contribution to journalArticlepeer-review

    12 Citations (Scopus)
    116 Downloads (Pure)


    In this paper, isogeometric analysis (IGA) is employed to solve the problem of a curved beam with free-form geometry, arbitrary loading, and variable flexural/axial rigidity. The main objective of the study is to develop a unified approach for full free-from curved beam problems that can be integrated with a newly developed semi-analytical sensitivity analysis to solve pre-bent shape design problems. The required set of B-spline control points are calculated using an interpolation technique based on chord-length parameterization. The one-to-one correspondence is considered for parameters of the geometry, loading, and rigidity which is proven to have extreme importance. An IGA curved beam element is suggested based on the Euler-Bernoulli beam theory for the general curvilinear coordinate. The validity and effectiveness of the proposed formulation is confirmed by application to a variety of examples. Moreover, three shape optimization examples are taken into consideration. In the first two examples, the pre-bent shapes of spiral and Tschinhausen curved beams with free-form geometry under distributed loading are obtained. In the third example, the pre-bending problem of wind turbine blades is addressed as an industrial example.

    Original languageEnglish
    Pages (from-to)2621–2633
    Number of pages13
    JournalStructural and Multidisciplinary Optimization
    Issue number6
    Early online date30 Jun 2018
    Publication statusPublished - Dec 2018


    • Free-form curved beams
    • Isogeometric analysis
    • Pre-bending, Parameterization
    • Semi-analytical sensitivity analysis

    ASJC Scopus subject areas

    • Software
    • Control and Systems Engineering
    • Computer Science Applications
    • Computer Graphics and Computer-Aided Design
    • Control and Optimization


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