A meshfree Hermite point interpolation method for buckling and post-buckling analysis of thin plates

Hilali, Youssef; Bourihane, Oussama

doi:10.1007/s00366-021-01457-w

Cited by 11 publications

(7 citation statements)

References 33 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The aim of this work is to introduce the spectral method in the HOCM. Latterly, the HOCM with meshless methods such as MLS, WLS, or RPIM has been applied successfully for the resolution of nonlinear problems written under a strong form 19,20,24,25 or a weak form 14,15 . In this investigation, we propose to couple the spectral Chebyshev method as a discretization technique with the HOCM.…”

Section: Description Of Spectral Chebyshev Methodsmentioning

confidence: 99%

“…Latterly, the HOCM with meshless methods such as MLS, WLS, or RPIM has been applied successfully for the resolution of nonlinear problems written under a strong form 19,20,24,25 or a weak form. 14,15 In this investigation, we propose to couple the spectral Chebyshev method as a discretization technique with the HOCM. The introduction of this method allows us to avoid the difficulties lied to the implementation of boundary conditions.…”

Section: Description Of Spectral Chebyshev Methodsmentioning

confidence: 99%

“…In addition, the use of beam model, which takes into account the nonlinear term neglected in several works of the literature, permits us to analyze buckling and bending problems by using the classical Timoshenko model and to handle the boundary conditions that several works could not to take into account. The HOCM has been coupled with meshless methods successfully in several works such as the moving least squares (MLS), 14,15 the method of fundamental solutions (MFS), [16][17][18] and the radial point interpolation method (RPIM). 19,20 The SCDQM has been also used in several works and showed its ability and efficiency in the computation of FG porous plates reinforced by graphene platelets.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Spectral Chebyshev method coupled with a high order continuation for nonlinear bending and buckling analysis of functionally graded sandwich beams

Mesmoudi

Askour

Rammane

et al. 2022

Numerical Meth Engineering

View full text Add to dashboard Cite

The main objective of the present work is to couple the spectral Chebyshev differential quadrature method (SCDQM) to the high order continuation method (HOCM) which was proposed in previous works with several discretization techniques. This new approach (SCDQM-HOCM) is proposed to analyze the nonlinear bending and buckling analysis of functionally graded sandwich beams.The originality of this work consists also to use a beam model which taken into account the nonlinear term neglected in several works of the literature. This term makes it possible to have the buckling and bending problems by using the classical Timoshenko model and to handle the boundary conditions that several works could not to take into account. A strong form of nonlinear equations is established based on the first order shear deformation theory of beams with the von-Kármán kinematic hypothesis. Regarding functionally graded materials (FGM), two typical types are investigated: sandwich beam with FGM faces and ceramic core (Type-A), and sandwich beam with FGM core and uniform faces (Type-B). The accuracy and efficiency of the SCDQM-HOCM compared with finite element method coupled with high order continuation method (FEM-HOCM) are illustrated on numerical examples of the FGM beams and then the FG sandwich beams. Furthermore, a parametric study is led to carry out the influence of different skin-core-skin thickness ratios, span-to-height ratio, and volume fraction on the bending and buckling behavior of FG sandwich beams subjected to different loadings and various boundary conditions. K E Y W O R D Sfirst order shear deformation theory, geometrically nonlinear Timoshenko FGM beam, high order continuation method, sandwich Timoshenko FGM beam, spectral Chebyshev differential quadrature method

show abstract

Section: Description Of Spectral Chebyshev Methodsmentioning

confidence: 99%

Section: Description Of Spectral Chebyshev Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Spectral Chebyshev method coupled with a high order continuation for nonlinear bending and buckling analysis of functionally graded sandwich beams

Mesmoudi

Askour

Rammane

et al. 2022

Numerical Meth Engineering

View full text Add to dashboard Cite

show abstract

“…This could mean, for example, a transition from a stable equilibrium to an unstable one, or the emergence of new oscillatory behavior. 20,22,23,29,[31][32][33][34][35][36][37][38][39][40] Bifurcation analysis has applications in many areas of science and engineering. For example, in physics, bifurcation analysis can be used to understand the behavior of complex systems such as fluid flows.…”

Section: Buckling Phenomon: Effect Of Boundary Conditionsmentioning

confidence: 99%

“…In particular, bifurcation analysis is concerned with identifying critical parameter values at which the behavior of the system undergoes a qualitative change. This could mean, for example, a transition from a stable equilibrium to an unstable one, or the emergence of new oscillatory behavior 20,22,23,29,31–40 . Bifurcation analysis has applications in many areas of science and engineering.…”

Section: Buckling Phenomon: Effect Of Boundary Conditionsmentioning

confidence: 99%

Radial point interpolation‐Chebychev method with asymptotic numerical method for nonlinear buckling analysis of graphene oxide powder‐reinforced composite beams

Askour,

Rammane,

Mesmoudi

et al. 2024

Numerical Meth Engineering

Self Cite

View full text Add to dashboard Cite

SummaryThis study aims to analyze the buckling and post‐buckling behaviors of multilayer nanocomposite beams reinforced with graphene oxide powders (GOPs) at low concentrations. The GOPs are randomly oriented and evenly distributed throughout the composite layers, with their weight fraction varying in the thickness direction. The Halpin‐Tsai model is employed to estimate each layer's effective material properties. The nonlinear governing equations for the FG‐GOPRC beam are derived based on the first‐order shear deformation beam theory, and a nonlinear algebraic system is formulated using the principle of potential energy. In this research, a comprehensive parametric analysis is conducted to examine the influence of various factors on the buckling and post‐buckling behaviors of the composite beams. These factors include the distribution pattern and weight fraction of graphene platelets (GPLs) nanofillers, as well as the geometry, size, slenderness ratio, and boundary conditions of the beams. Through the analysis, the study highlights the significant strengthening effect of these factors on the buckling and post‐buckling performance of the composite beams. The findings from this investigation contribute to a deeper understanding of the behavior of multilayer nanocomposite beams reinforced with GOPs. This knowledge can be valuable in designing and optimizing of composite structures for enhanced buckling resistance and post‐buckling performance.

show abstract

Impact of Polymeric Composites on Static and Dynamic Behaviors of Timoshenko Beams Using Spectral and Newmark-$$\beta $$ Methods

Omar,

Sitli,

Elmhaia

et al. 2024

J. Vib. Eng. Technol.

View full text Add to dashboard Cite

A meshfree Hermite point interpolation method for buckling and post-buckling analysis of thin plates

Cited by 11 publications

References 33 publications

Spectral Chebyshev method coupled with a high order continuation for nonlinear bending and buckling analysis of functionally graded sandwich beams

Spectral Chebyshev method coupled with a high order continuation for nonlinear bending and buckling analysis of functionally graded sandwich beams

Radial point interpolation‐Chebychev method with asymptotic numerical method for nonlinear buckling analysis of graphene oxide powder‐reinforced composite beams

Impact of Polymeric Composites on Static and Dynamic Behaviors of Timoshenko Beams Using Spectral and Newmark-$$\beta $$ Methods

Contact Info

Product

Resources

About