Large deflections of non-prismatic nonlinearly elastic cantilever beams subjected to non-uniform continuous load and a concentrated load at the free end

This work studies large deflections of slen- der, non-prismatic cantilever beams subjected to a combined loading which consists of a non-uniformly distributed con- tinuous load and a concentrated load at the free end of the beam. The material of the cantilever is assumed to be non- linearly elastic. Different nonlinear relations between stress and strain in tensile and compressive domain are considered. The accuracy of numerical solutions is evaluated by com- paring them with results from previous studies and with a laboratory experiment.

Codimension-two bifurcation of axial loaded beam bridge subjected to an infinite series of moving loads

A novel model is proposed which comprises of a beam bridge subjected to an axial load and an infinite series of moving loads. The moving loads, whose distance between the neighbouring ones is the length of the beam bridge, coupled with the axial force can lead the vibration of the beam bridge to codimension-two bifurcation. Of particular concern is a parameter regime where non-persistence set regions undergo a transition to persistence regions. The boundary of each stripe represents a bifurcation which can drive the system off a kind of dynamics and jump to another one, causing damage due to the resulting amplitude jumps. The Galerkin method, averaging method, invertible linear transformation, and near identity nonlinear transformations are used to obtain the universal unfolding for the codimension-two bifurcation of the mid-span deflection. The efficiency of the theoretical analysis obtained in this paper is verified via numerical simulations.

Shear deformable finite beam elements for composite box beams

The shear deformable thin-walled composite beams with closed cross-sections have been developed for coupled flexural, torsional, and buckling analyses. A theoretical model applicable to the thin-walled laminated composite box beams is presented by taking into account all the structural couplings coming from the material anisotropy and the shear deformation effects. The current composite beam includes the transverse shear and the restrained warping induced shear deformation by using the first-order shear deformation beam theory. Seven governing equations are derived for the coupled axial-flexural-torsional-shearing buckling based on the principle of minimum total potential energy. Based on the present analytical model, three different types of finite composite beam elements, namely, linear, quadratic and cubic elements are developed to analyze the flexural, torsional, and buckling problems. In order to demonstrate the accuracy and superiority of the beam theory and the finite beam elements developed by this study,numerical solutions are presented and compared with the results obtained by other researchers and the detailed threedimensional analysis results using the shell elements of ABAQUS. Especially, the influences of the modulus ratio and the simplified assumptions in stress-strain relations on the deflection, twisting angle, and critical buckling loads of composite box beams are investigated.

Application of semi-analytical finite element method to analyze asphalt pavement response under heavy traffic loads

Accurate assessment of the impact of heavy traffic loads on asphalt pavements requires a computational model which is able to calculate the response of the pavement fast and precisely. Currently the most finite element analysis programs based on traditional methods have various limitations. A specific program SAFEM was developed based on a semi-analytical finite element method to overcome the problems. It is a three-dimensional FE program that requires only a two-dimensional mesh by incorporating the semi- analytical method using Fourier series in the third dimension. The computational accuracy and efficiency of the program was verified by analytical verification previously. The experimental verification is carried out in this paper and the results show that the SAFEM is able to predict the mechanical responses of the asphalt pavement. Using the program SAFEM, the impact of heavy traffic loads was analyzed in terms of stress and strain dis- tribution, surface deflection and fatigue life. The results indicate that if the asphalt pave- ment is subjected to the heavy traffic load more, the thicknesses and stiffness of the pavement structural layers should be increased adequately in order to support the surface deflection, The compressive stress in asphalt binder course is relatively large and increases more significantly compared with that in the other asphalt layers when the axle load becomes larger. With comparison of the predicted fatigue life, the increase of the axle load will lead to the destruction of the asphalt pavement extremely easily.