A Novel Boundary Averaging Operator with an Application for Beam Structures

EasyChair Preprint 12992

Abstract

The paper presents a new boundary averaging operator (BAO) in which the particular role of boundary values is considered in a more suitable way than the conventional approach. A remarkable feature of BAO is that this operator contains a parameter of boundary regulation p and depends on a local value h of the integration domain. By varying these two parameters one can regulate the obtained approximate solutions in order to get more accurate ones. Therefore, BAO can serve as a sophisticated tool for approximate analysis in various fields of mathematics and mechanics. One of the effective applications of BAO is integrating this operator with the Galerkin method to determine the limit loads for the buckling problem of beams with constant and variable thicknesses. The balance equation of the beam is established from the third-order shear deformation theory. The critical buckling load of the beam is determined by applying BAO to three different cases. The calculation results show that the critical buckling load depends on the boundary conditions and the values of the parameters h and p. It is shown that BAO can give more accurate approximate solutions than the ones obtained by the convential averaging operator

Keyphrases: Buckling, Galerkin method, Varying cross section, beam, boundary averaging operator (BAO)

@booklet{EasyChair:12992,
  author    = {Nguyen Dong Anh and Phung Van Minh and Tran Van Ke and Van Thom Do},
  title     = {A Novel Boundary Averaging Operator with an Application for Beam Structures},
  howpublished = {EasyChair Preprint 12992},
  year      = {EasyChair, 2024}}