Keywords: lateral buckling, nonlinearity, shear deformations, variable cross sections, hyperelastic modeling, tensor notation, finite strain..

A nonlinear lateral buckling analysis is presented in this paper for Timoshenko-type beams with variable cross sections considering the shear deformations based on large displacements and rotations. The constitutive laws for stresses and finite strains are defined adopting the consistent hyperelastic constitutive material modeling with the application of tensor analysis to simplify the complex geometric presentation. The generalized equilibrium equations are developed for the variable cross-sectional beams. The energy criterion is adopted to assess the stability of the system. The positive definiteness of the second variation of the total potential implies stability and enables the application of finite element modeling. The shear rotation displacement is accounted for in the finite element formulation by introducing an extra node in the middle of the element. In the tapering beams where all section properties are not constant, the locations of the centroidal and shear center axes are precisely determined instead of using an approximate method. The numerical examples of doubly symmetric flange-tapered and web-tapered I-cantilevers under concentrated end load are investigated. The lateral buckling load predictions obtained are in good agreement with the published solutions, therefore the developed formulation is validated.

purchase the full-text of this paper (price £20)

go to the previous paper
go to the next paper
return to the table of contents
return to the book description
purchase this book (price £65 +P&P)