Torsional post-buckling of thin-walled open section beams resting on a continuous elastic foundation

AbstractThis paper presents a three-dimensional beam element for stability analysis of elastic thin-walled open-section beams in multibody systems. The beam model is based on the generalized strain beam formulation. In this formulation, a set of independent deformation modes is defined which are related to dual stress resultants in a co-rotational frame. The deformation modes are characterized by generalized strains or deformations, expressed as analytical functions of the nodal coordinates referred to the global coordinate system. A nonlinear theory of non-uniform torsion of open-section beams is adopted for the derivation of the elastic and geometric stiffness matrices. Both torsional-related warping and Wagner’s stiffening torques are taken into account. Second order approximations for the axial elongation and bending curvatures are included by additional second order terms in the expressions for the deformations. The model allows to study the buckling and post-buckling behaviour of asymmetric thin-walled beams with open cross-section that can undergo moderately large twist rotations. The inertia properties of the beam are described using both consistent and lumped mass formulations. The latter is used to model rotary and warping inertias of the beam cross-section. Some validation examples illustrate the accuracy and computational efficiency of the new beam element in the analysis of the buckling and post-buckling behaviour of thin-walled beams under various loads and (quasi)static boundary conditions. Finally, applications to multibody problems are presented, including the stability analysis of an elementary two-flexure cross-hinge mechanism.

Download Full-text

Lateral post-buckling analysis of thin-walled open section beams

Thin-Walled Structures ◽

10.1016/s0263-8231(02)00043-5 ◽

2002 ◽

Vol 40 (12) ◽

pp. 1013-1036 ◽

Cited By ~ 43

Author(s):

F. Mohri ◽

L. Azrar ◽

M. Potier-Ferry

Keyword(s):

Buckling Analysis ◽

Open Section ◽

Post Buckling ◽

Thin Walled

Download Full-text

Buckling Behavior of Tire Breaker Structure

Tire Science and Technology ◽

10.2346/1.2150978 ◽

1983 ◽

Vol 11 (1) ◽

pp. 3-19

Author(s):

T. Akasaka ◽

S. Yamazaki ◽

K. Asano

Keyword(s):

Elastic Foundation ◽

Elastic Moduli ◽

Wave Length ◽

Bending Moment ◽

Experimental Results ◽

Automobile Tire ◽

Buckling Behavior ◽

Post Buckling ◽

Steel Cord ◽

Interlaminar Shear

Abstract The buckled wave length and the critical in-plane bending moment of laminated long composite strips of cord-reinforced rubber sheets on an elastic foundation is analyzed by Galerkin's method, with consideration of interlaminar shear deformation. An approximate formula for the wave length is given in terms of cord angle, elastic moduli of the constituent rubber and steel cord, and several structural dimensions. The calculated wave length for a 165SR13 automobile tire with steel breakers (belts) was very close to experimental results. An additional study was then conducted on the post-buckling behavior of a laminated biased composite beam on an elastic foundation. This beam is subjected to axial compression. The calculated relationship between the buckled wave rise and the compressive membrane force also agreed well with experimental results.

Download Full-text

Post-buckling inelastic analysis of thin-walled metal members using the Generalised Beam Theory

10.31224/osf.io/5xndm ◽

2019 ◽

Author(s):

Miguel Abambres ◽

Dinar Camotim ◽

Miguel Abambres

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Beam Theory ◽

Flow Theory ◽

Promising Alternative ◽

Inelastic Analysis ◽

Post Buckling ◽

Thin Walled ◽

Shell Finite Element ◽

Generalised Beam Theory

A 2nd order inelastic Generalised Beam Theory (GBT) formulation based on the J2 flow theory is proposed, being a promising alternative to the shell finite element method. Its application is illustrated for an I-section beam and a lipped-C column. GBT results were validated against ABAQUS, namely concerning equilibrium paths, deformed configurations, and displacement profiles. It was concluded that the GBT modal nature allows (i) precise results with only 22% of the number of dof required in ABAQUS, as well as (ii) the understanding (by means of modal participation diagrams) of the behavioral mechanics in any elastoplastic stage of member deformation .

Download Full-text