Geometrical nonlinear analysis based on optimization technique

Rezaiee‐Pajand, Mohammad; Naserian, Rahele

doi:10.1016/j.apm.2017.08.003

Cited by 15 publications

(4 citation statements)

References 32 publications

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“…This example is also well-established in the literature in the context of nonlinear analysis of in-plane beams [51,24,52]. The frame consists of two rigidly connected beams and the displacement components at the point of force application are observed, Fig.…”

Section: Lee's Framementioning

confidence: 60%

Geometrically exact static isogeometric analysis of arbitrarily curved plane Bernoulli-Euler beam

Borković,

Marussig,

Radenković

2021

Preprint

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We present a geometrically exact nonlinear analysis of elastic in-plane beams in the context of finite but small strain theory. The formulation utilizes the full beam metric and obtains the complete analytic elastic constitutive model by employing the exact relation between the reference and equidistant strains. Thus, we account for the nonlinear strain distribution over the thickness of a beam. In addition to the full analytical constitutive model, four simplified ones are presented. Their comparison provides a thorough examination of the influence of a beam's metric on the structural response. We show that the appropriate formulation depends on the curviness of a beam at all configurations. Furthermore, the nonlinear distribution of strain along the thickness of strongly curved beams must be considered to obtain a complete and accurate response.

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Section: Lee's Framementioning

confidence: 60%

Geometrically exact static isogeometric analysis of arbitrarily curved plane Bernoulli-Euler beam

Borković,

Marussig,

Radenković

2021

Preprint

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“…Figures 2-7 below illustrate the 2D Planar view of a single truss member and 3D holistic isometric views of the modeled stadiums within Strand7 [36][37][38].…”

Section: Modelsmentioning

confidence: 99%

Designing Lightweight Stadium Roofing Structures Based on Advanced Analysis Methods

et al. 2023

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The current structural engineering practical standards are unable to offer an universal structural design standard for long-spanning lightweight stadium roofing structures. As such, the design procedure of a particular stadium roof is not replicable to another. This research aims to present a novel design procedure for lightweight stadium roofing structures considering the Lakhwiya stadium the Optus Stadium and the CommBank Stadium as experimental cases. Using the finite element analysis (FEA) software Strand7, the cases will be modelled and analysed. Varying load cases and combinations such as ultimate strength (ULS) and serviceability limit states (SLS) based on the Australian Standard AS1170.0:2002 will be calculated and subsequently applied. Linear static analysis will then be undertaken where critical members will be identified within the model. Based on this, preliminary member sizing and design feasibility checks will be conducted in order to ensure structural stability and compliance to the Australian Steel Structure code AS4100:2020. A linear buckling analysis is also conducted based on the selected sizes from the initial stage to determine critical loads. Advanced analysis including non-linear buckling computation is comprehensively managed. Some of the crucial parameters such as maximum displacement, maximum/minimum principal stresses, critical buckling loads, as well as load factors are examined. The main novelty of this study is to determine a clear road map to design stadium roofing systems subjected to a combination of different types of the loading.

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“…Especially, MIP Newton method can be well applied to high slenderness structures. Because of the importance of nonlinear solvers with respect to computational mechanics and their wide application, many solvers have been proposed to reduce number of iterations per load step and computation as the following: optimization-based iterative technique 6 and residual areas-based iterative technique, 7 dynamic relaxation techniques, [8][9][10] multipoint methods-based path following techniques, 11 a novel method to transform the discretized governing equations, 12 a data-driven nonlinear solver (DDNS), 13 an improved predictor-corrector method, 14 Koiter-Newton method with a superior performance for nonlinear analyses of structures, 15,16 etc. It is observed that employing time series prediction to reduce number of iterations of nonlinear solvers is very rare except the DDNS.…”

Section: Introductionmentioning

confidence: 99%

Deep learned one‐iteration nonlinear solver for solid mechanics

Nguyen

Lee

Dinh‐Tien

et al. 2022

Numerical Meth Engineering

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Nowadays, there are a lot of iterative algorithms which have been proposed for nonlinear problems of solid mechanics. The existing biggest drawback of iterative algorithms is the requirement of numerous iterations and computation to solve these problems. This can be found clearly when the large or complex problems with thousands or millions of degrees of freedom are solved. To overcome completely this difficulty, the novel one‐iteration nonlinear solver (OINS) using time series prediction and the modified Riks method (M‐R) is proposed in this paper. OINS is established upon the core idea as follows: (1) Firstly, we predict the load factor increment and the displacement vector increment and the convergent solution of the considering load step via the predictive networks which are trained by using the load factor and the displacement vector increments of the previous convergence steps and group method of data handling (GMDH); (2) Thanks to the predicted convergence solution of the load step is very close to or identical with the real one, the prediction phase used in any existing nonlinear solvers is eliminated completely in OINS. Next, the correction phase of the M‐R is adopted and the OINS iteration is started at the predicted convergence point to reach the convergent solution. The training process and the applying process of GMDH are continuously conducted and repeated during the nonlinear analysis in order to predict the convergence point at the beginning of each load step. Through numerical investigations, we prove that OINS is powerful, highly accurate and only needs about one iteration per load step. Thus, OINS significantly saves number of iterations and a huge amount of computation compared with the conventional methods. Especially, OINS not only can detect limit, inflection, and other special points but also can predict exactly various types of instabilities of structures.

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Geometrical nonlinear analysis based on optimization technique

Cited by 15 publications

References 32 publications

Geometrically exact static isogeometric analysis of arbitrarily curved plane Bernoulli-Euler beam

Geometrically exact static isogeometric analysis of arbitrarily curved plane Bernoulli-Euler beam

Designing Lightweight Stadium Roofing Structures Based on Advanced Analysis Methods

Deep learned one‐iteration nonlinear solver for solid mechanics

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