Torsional Post-Buckling of a Simply Supported Thin-Walled Open-Section Beam Resting on a Two-Parameter Foundation

2018 ◽  
Vol 59 (1) ◽  
pp. 176-184 ◽  
Author(s):  
Ch. K. Rao ◽  
L. B. Rao
Keyword(s):  
Simply Supported ◽  
Open Section ◽  
Post Buckling ◽  
Thin Walled ◽  
Two Parameter

The Torsional Vibration of Uniform Thin-Walled Beams of Open Section

1969 ◽  
Vol 73 (704) ◽  
pp. 672-674 ◽  
Author(s):  
J. B. Carr
Keyword(s):  
Torsional Vibration ◽  
Characteristic Functions ◽  
Shear Stresses ◽  
Simply Supported ◽  
Open Section ◽  
Torsional Resistance ◽  
Approximate Frequency ◽  
Thin Walled ◽  
Image Position ◽  
Fixed End

The pure torsional vibration of uniform thin-walled beams of open section, which is governed by the differential equation has been extensively analysed by Gere He derived the exact frequency equations for beams with a variety of end conditions. However, these equations are, in most cases, highly transcendental. This note uses an energy approach to obtain approximate frequency equations for the fixed-fixed and the fixed-simply-supported beams. A fixed end is one which allows no twist and no warping and a simply-supported end allows no twist but permits warping to take place freely. The approximating functions used are those corresponding to the exact solution of the problem if the torsional resistance caused by the St Venant system of shear stresses is zero. These functions are similar to the characteristic functions of simple beams in flexure.

scholarly journals Three-dimensional beam element for pre- and post-buckling analysis of thin-walled beams in multibody systems

2021 ◽  
Author(s):  
J. B. Jonker
Keyword(s):  
Stability Analysis ◽  
Cross Section ◽  
Multibody Systems ◽  
Three Dimensional ◽  
Beam Element ◽  
Second Order ◽  
Open Section ◽  
Post Buckling ◽  
Thin Walled ◽  
Deformation Modes

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.

A New Concept of the Effective Shear Modulus for a Plate Buckled in Shear

1995 ◽  
Vol 39 (01) ◽  
pp. 70-75
Author(s):  
Jeom Kee Paik
Keyword(s):  
Shear Modulus ◽  
Theoretical Background ◽  
Effective Width ◽  
Ultimate Shear Strength ◽  
Effective Shear Modulus ◽  
Simply Supported ◽  
Buckling Behavior ◽  
Post Buckling ◽  
Thin Walled ◽  
Strength Formula

A new concept of the effective shear modulus is suggested for describing stiffness and strength of a plate in edge shear. This concept has quite similar advantages to the effective width, which has been recognized as an efficient approach for analysis of the post-buckling behavior of thin-walled members in compression. The theoretical background of the new idea is described, and based on results of the series analysis an empirical formula of the effective shear modulus for a simply supported rectangular plate is derived taking into account initial deflection effects. Using this formula, an ultimate shear strength formula of a plate is also suggested. The validity of the proposed formula is checked by comparison with the numerical results. It is concluded that the proposed idea will be quite useful if an effective shear modulus formula is successfully developed.

Dynamic Response of Thin-Walled Structures to Thermal Loadings and Random Acoustic Excitations

2014 ◽  
Vol 889-890 ◽  
pp. 1398-1405
Author(s):  
Feng Tong Zhao ◽  
Yun Dong Sha ◽  
Xiao Chi Luan ◽  
Lin Zhu
Keyword(s):  
Finite Element ◽  
Temperature Gradient ◽  
Equilibrium Position ◽  
Thermal Buckling ◽  
Vibration Characteristics ◽  
Aerodynamic Heating ◽  
Simply Supported ◽  
Thin Walled Structures ◽  
Post Buckling ◽  
Thin Walled

Hypersonic aircrafts are facing increasingly severe aerodynamic heating, noise and so on, which will lead to nonlinear vibration characteristics for thin-walled structures of hypersonic aircrafts. Considering the influence of thermo-acoustic loadings, finite element formulation of simply supported plate under combined thermo-acoustic loadings are founded, and vibration characteristics of simply supported plate under thermal loadings with temperature gradient and random acoustic loadings are investigated. According to finite element numerical method, modal frequencies, critical thermal buckling temperature difference, dynamic stress response of simply supported plates with temperature gradient under combined thermo-acoustic loadings were calculated before and after thermal buckling. The results show that three types of motion: random vibrations around initial equilibrium position in pre-buckling region, snap-through oscillations between two post-buckling equilibrium positions, nonlinear vibrations around one of the two post-buckling equilibrium position, and The RMS of nodes for different locations of the simply plate are obtained in pre-buckling post-buckling region, and it is shown that different interaction of tensile bend stress, compressive stress and compressive thermal stress lead to different RMS trends.

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

2002 ◽  
Vol 40 (12) ◽  
pp. 1013-1036 ◽  
Author(s):  
F. Mohri ◽  
L. Azrar ◽  
M. Potier-Ferry
Keyword(s):  
Buckling Analysis ◽  
Open Section ◽  
Post Buckling ◽  
Thin Walled

Nonlinear Torsional Vibrations of Thin-Walled Beams of Open Section

1975 ◽  
Vol 42 (1) ◽  
pp. 240-242 ◽  
Author(s):  
C. Kameswara Rao
Keyword(s):  
Differential Equation ◽  
Large Amplitude ◽  
Torsional Vibrations ◽  
Simply Supported ◽  
Open Section ◽  
Governing Differential Equation ◽  
Thin Walled

An attempt has been made to derive and solve the governing differential equation of large amplitude torsional vibrations of simply supported doubly symmetric thin-walled beams of open section. Graphs indicating the influence of large amplitudes on nonlinear period of torsional vibrations for various nondimensional beam constants are presented.

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