Numerical Method of Increasing the Critical Buckling Load for Straight Beam-Type Elements with Variable Cross-Sections

Abstract

Structural expressionism resembles the use of slender structural elements, in particular beam-type elements. To satisfy structural, functional, and also architectural requirements a comprehensive structural analysis must be performed. The main issue of this study is the buckling analysis of beam-type elements, concerning Cavalieri’s principle. The present study is divided into two separate sections. The first part is a theoretical study, in which a variable cross-section beam-type element is modeled. The stability analysis is performed by an indirect variational method and the stiffness of the support connections is also introduced. The numerical simulation highlights 6 cases defined by the restraints of the support connections. The case study follows the modification of the critical buckling load of the variable cross-section beam-type element. Prior to the case study, a novel verification method is proposed to achieve a realistic cross-section for the beam-type element. The study revealed that with ideal characteristics of the stiffness coefficients of the restrains significant increase of the critical buckling load is obtained, and further if an actual situation is considered with finite values of the stiffness of the restrains, the variable cross-section for the beam-type element is a recommended and rational choice to make, to eliminate stability issues.