Reanalysis of 2D and 3D truss structures considering simultaneous variations in topology, geometry and size
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ORIGINAL ARTICLE
Reanalysis of 2D and 3D truss structures considering simultaneous variations in topology, geometry and size Mohammad Rezaiee‑Pajand1 · Mehran Momenipour1,2 · Seyed Mojtaba Hozhabrossadati2 Received: 27 June 2020 / Accepted: 27 October 2020 © Springer-Verlag London Ltd., part of Springer Nature 2020
Abstract Approximate reanalysis methods provide effective processes to achieve structural approximate responses without solving the complete set of modified implicit analysis equations. This paper presents methods for carrying out approximate reanalysis of 2D and 3D trusses. Apparently, for the first time, the simultaneous modifications in topology, geometry and size of the structures are taken into account. Three numerical methods, namely, combined approximation, rational approximation and Sherman–Morrison–Woodbury approximation (SMWA), are analyzed and compared for this purpose. The flowchart corresponding to each scheme is presented. Design variables considered are nodal coordinates and cross sectional properties. Moreover, an arrival with bounds between zero and arbitrary amounts includes the variations of the variables. Unlike most works, large trusses with many members are analyzed as numerical examples. Based on obtained outcomes in the several instances, a comparison is conducted between the three schemes and benefits and drawbacks of each method are thoroughly discussed. Keywords Reanalysis · Truss structures · Combined approximation · Rational approximation · Sherman–Morrison– Woodbury formula · Displacement error
1 Introduction Repeated analysis of structures, which is called structural reanalysis, is an important topic in many branches of engineering such as civil, mechanical and aerospace engineering [1–9]. Structural optimization, structural nonlinear analysis, designing damage-proof structures and eigenvalue problems are among the current problems the solutions of which needs reanalysis. In such problems, it is likely to run repeated procedures due to changes in properties of structures. This fact leads to structural reanalysis of structures which entails huge computational efforts. Approximate reanalysis methods are suggested by many researchers to tackle this significant task. The most important point is to increase the efficiency and accuracy of methods while reducing the computational
* Seyed Mojtaba Hozhabrossadati [email protected] 1
Department of Civil Engineering, Ferdowsi University of Mashhad, Mashhad, Iran
Department of Civil Engineering, Toos Institute of Higher Education, Mashhad, Iran
2
costs. Therefore, several approaches are proposed to deal with structural reanalysis of structures. Kirsch [10–18] in a series of works, introduced and developed the most well-known reanalysis scheme called combined approximation method. In this approach, the basis vector for predicting the modified structure is constructed by complete analysis and binomial series. It is informative to point out that Sidi [19] suggested that the partial sum of Macluren series of a vecto
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