Analysis of regular and chaotic dynamics of the Euler-Bernoulli beams using finite difference and finite element methods

Chaotic vibrations of flexible non-linear Euler-Bernoulli beams subjected to harmonic load and with various boundary conditions（symmetric and non-symmetric）are studied in this work.Reliability of the obtained results is verified by the finite difference method（FDM）and the finite element method（FEM）with the Bubnov-Galerkin approximation for various boundary conditions and various dynamic regimes（regular and non-regular）.The influence of boundary conditions on the Euler-Bernoulli beams dynamics is studied mainly,dynamic behavior vs.control parameters { ωp,q0 } is reported,and scenarios of the system transition into chaos are illustrated.

A new 3-D element formulation on displacement of steel-concrete composite box beam

Slip of a composite box beam may reduce its stiffness, enlarge its deformation and affect its performance. In this work, the governing differential equations and boundary conditions of composite box beams were established. Analytic solutions of combined differential equations were also established. Partial degree of freedom was adopted to establish a new FEA element of three-dimensional beam, taking into account the slip effect. Slip and its first-order derivative were introduced into the nodes of composite box beams as generalized degree of freedom. Stiffness matrix and load array of beam elements were established. A three-dimensional nonlinear calculation program was worked out. The results show that the element is reliable and easy to divide and is suitable for special nonlinear analysis of large-span composite box beams.

Light weight analysis of a skeleton vehicle frame using BS960 super-high-strength steel

Static strength finite element analysis was conducted to decrease the weight of a skeleton vehicle＇s frame. Results indicated that the maximum stress occurs on the front beam ＇s variable section area. Dynamic sensitivity analysis elucidated the relationship between the maximum stress and the thickness of a particular beam,e. g.,top,middle,and bottom beam. Displacement was analyzed by the key part that influenced the maximum stress. Finally,the new plan using BS960 super-high-strength beam steel and the preferred beam thickness was compared with the original plan. New combinations of beam thickness were introduced on the basis of different purposes; the maximum responding light w eight ratio was 21%.

Elastic-plastic seismic response of CRTS II slab ballastless track system on high-speed railway bridges

China railways track structure II (CRTS II) slab ballastless track on bridge is one kind of track structures unique to China. Its main bearing component of longitudinal force is the continuous base plate rather than rail. And the track-bridge interaction is weakened by the sliding layer installed between base plate and bridge deck. In order to study the dynamic response of CRTS II slab ballastless track on bridge under seismic action, a 3D nonlinear dynamic model for simply-supported bridges and CRTS II track was established, which considered structures such as steel rail, fasteners, track plate, mortar layer, base plate, sliding layer, bridge, consolidation, anchors, stoppers, etc. Then its force and deformation features under different intensities of seismic excitation were studied. As revealed, the seismic response of the system increases with the increase of seismic intensity. The peak stresses of rail, track plate and base plate all occur at the abutment or anchors. Both track plate and base plate are about to crack. Besides, the rapid relative displacement between base plate and bridge deck due to the small friction coefficient of sliding layer is beneficial to improve the seismic performance of the system. During the earthquake, a large vertical displacement appears in base plate which leads to frequent collisions between stoppers and base plate, as a result, stoppers may be damaged.