A high order mesh-free method for buckling and post-buckling analysis of shells

Fouaidi, Mustapha; Hamdaoui, Abdellah; Jamal, Mohammad; Braikat, Bouazza

doi:10.1016/j.enganabound.2018.11.014

Cited by 20 publications

(9 citation statements)

References 47 publications

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“…is a quadratic form, which represents the convection term; and F is a given force vector. In the following section, we present the description of the HO‐MFA to solve problem . We show that this HO‐MFA is a powerful continuation method, which can be applied without correction.…”

Section: Mathematical Formulationmentioning

confidence: 99%

“…In other works, the high‐order mesh‐free approach (HO‐MFA) is used for the computation of elasto‐plastic contact problems, the treatment of the frictional contact of two elastic deformable bodies in the static case, and buckling and postbuckling analysis of shells. In another hand, this algorithm is used for the simulation of material mixing observed in friction stir welding (FSW) process in dynamic case …”

Section: Introductionmentioning

confidence: 99%

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Solving the incompressible fluid flows by a high‐order mesh‐free approach

Rammane

Mesmoudi

Tri

et al. 2019

Numerical Methods in Fluids

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Summary In this paper, we propose for the first time to extend the application field of the high‐order mesh‐free approach to the stationary incompressible Navier‐Stokes equations. This approach is based on a high‐order algorithm, which combines a Taylor series expansion, a continuation technique, and a moving least squares (MLS) method. The Taylor series expansion permits to transform the nonlinear problem into a succession of continuous linear ones with the same tangent operator. The MLS method is used to transform the succession of continuous linear problems into discrete ones. The continuation technique allows to compute step‐by‐step the whole solution of the discrete problems. This mesh‐free approach is tested on three examples: a flow around a cylindrical obstacle, a flow in a sudden expansion, and the standard benchmark lid‐driven cavity flow. A comparison of the obtained results with those computed by the Newton‐Raphson method with MLS, the high‐order continuation with finite element method, and those of literature is presented.

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Section: Mathematical Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Solving the incompressible fluid flows by a high‐order mesh‐free approach

Rammane

Mesmoudi

Tri

et al. 2019

Numerical Methods in Fluids

Self Cite

View full text Add to dashboard Cite

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“…The meshless method is mainly suitable for solving deformation analysis of jointed rock mass (Hajiazizi and Graili, 2018), fluid-structure interactions (Hu et al, 2019), fracture analysis (Memari and Mohebalizadeh, 2019), diffusion problem (Tayefi et al, 2018) and large deformation problem (Lin et al, 2014), etc. This method has been widely used in multiple fields (Wang, 2012;Belytschko et al, 1995;Fouaidi et al, 2019;Li and Belytschko, 2001).…”

Section: Introductionmentioning

confidence: 99%

Meshless numerical method for the contact problems of joint surface

Wang

Shi

Cao

et al. 2022

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PurposeThe partition of unity of the standard meshless Galerkin method is used as basis in expressing the discontinuity of the contact surface displacement, particularly by adding discontinuous terms into the displacement mode, and constructing the discontinuous meshless displacement field function. In this study the contact surface equation is aimed to derive from the improved Coulomb friction contact model.Design/methodology/approachIn this paper based on the basic idea of meshless method, an improved moving least squares approximation function (expansion method based on out of unit division) is applied to the analysis of two-dimensional contact problems.FindingsOn the basis of this equation after discrete processing, it is combined with the discrete form of the virtual work equation with added contact conditions, and eventually transformed into a standard linear complementary problem. Moreover, it is solved by using the Lemke algorithm, and a corresponding example is provided in this research.Originality/valueThe proposed method can effectively control the mutual embedding of the contact surface, and the stress distribution that is the same as the actual situation can be obtained on the contact surface.

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“…e computational issues associated with strain-softening materials are briefly discussed by Barrera et al [8] from the material constitutive relation aspect and by Zienkiewicz and Taylor [9] from the numerical calculation aspect. For a specific class of proportional loading that loads can be expressed by a load multiplier (e.g., the pushover analysis), the softening branch in the global load-displacement curve can be simulated by a displacement-control approach, with the prescribed displacement in one degree [10,11] or the prescribed incremental displacement norm [12,13].…”

Section: Introductionmentioning

confidence: 99%

Kinematic and Static Solutions for Beam Column with Nonlinear Springs Using the Extended Linear Matching Method

Gao

2021

Shock and Vibration

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In this paper, the kinematic and static solutions for solving the static response of the beam column with nonlinear springs are presented by adopting the extended linear matching method (LMM). The extended LMM can be used to predict the displacement response of the beam-column system consisting of perfectly plastic and strain-softening materials. It is found that the kinematic solution generated by the extended LMM demonstrates a monotonic decrease for perfect plastic materials with certain restrictions on the yield surface. The potential energy of the system is proved to decrease with iterations for both perfect plastic and strain-softening materials if the loading multiplier remains constant. The extended LMM method is then applied to analyse the response of the pile system in a 3-leg offshore platform. An incremental procedure is recommended to determine the peak load for the soil exhibiting strain-softening. A displacement-control approach is used with the loading multiplier obtained from the variation of the potential energy. Good convergence of the method is obtained.

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A high order mesh-free method for buckling and post-buckling analysis of shells

Cited by 20 publications

References 47 publications

Solving the incompressible fluid flows by a high‐order mesh‐free approach

Solving the incompressible fluid flows by a high‐order mesh‐free approach

Meshless numerical method for the contact problems of joint surface

Kinematic and Static Solutions for Beam Column with Nonlinear Springs Using the Extended Linear Matching Method

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