On the use of Hermit-type WLS approximation in a high order continuation method for buckling and wrinkling analysis of von-Kàrmàn plates. (1st March 2023)

• Record Type: Journal Article
• Authors: Rammane, Mohammed; Elmhaia, Oussama; Mesmoudi, Said; Askour, Omar; Braikat, Bouazza; Tri, Abdeljalil; Damil, Noureddine
• Is Part Of: Engineering structures. Volume 278(2023)
• Publication Date: 2023-03-01
• Subjects: Weight Least Square (WLS) -- Hermite-type -- High Order Continuation Method (HOCM) -- Buckling -- Wrinkling -- Föppl–von Kàrmàn; Structural engineering -- Periodicals; Structural analysis (Engineering) -- Periodicals; Construction, Technique de la -- Périodiques; Génie parasismique -- Périodiques; Pression du vent -- Périodiques; Earthquake engineering; Structural engineering; Wind-pressure; Periodicals; 624.105
• DOI: 10.1016/j.engstruct.2022.115498
• Languages: English
• ISSNs: 0141-0296

Abstract

Abstract: The aim of this work is to develop an efficient numerical model for bifurcation analysis within the Föppl–von-Kàrmàn plate theory. This model consists in adapting the High Order Continuation Method (HOCM) with a Hermit-type Weighted Least Square (WLS) method. The collocated Hermit-type technique allows to approximate the binding unknowns and their derivatives. Furthermore, a new implementation of boundary conditions is developed by using the normal boundary derivatives of the main field unknowns to overcome the edge vertex's nodes normal issues related to the strong formulation boundary value problem. The HOCM has an adaptative step length which is very efficient and performed especially for bifurcation problems. By this way, we are able to detect precisely the critical buckling and wrinkling loads for very thin membranes with fewer degrees of freedom and less CPU time. A comparison between the proposed approach with analytical solution, Finite Element Method (FEM), and Element-Free Galerkin (EFG) method is illustrated in some numerical results that demonstrate the accuracy and robustness of the proposed approach. Highlights: Development of a Hermit mesh-free model to solve boundary value problems in the strong formulation of von-Kàrmàn plates. Coupling the Hermit model with a high order continuation method to evaluate the buckling and wrinkling critical loads. Overcoming the normal edge vertex's nodes boundary condition issues encountered in the use of strong formulation. Reducing the huge number of degrees of freedom and CPU time performed by the reference methods as the finite element. Analyzing the influence of the tensile effort and the plate geometry on the wrinkling modes and critical load.