Non-linear Timoshenko Beam - Column Structure Model And Dynamic Behavior Analysis

The beam, being one of the basic components of thecomposition of various structures, have wide applications in hydraulicengineering, mechanical engineering, seismology. As a beam, thebeam element is analyzed and calculated based on the Kirchhoff-Loveassumption in elementary mechanics. The Kirchhoff-Love assumptionclaims that the bending is the main deformation and the sheardeformation is secondary, shear deformation effect is negligible. Forsolid web beam,height of which is much smaller than the span, thegeneral is not easy to cause significant errors. However, it is lessaccurate for high cross-ratio is not small fasting beam. Therefore,considering the shear deformation is necessary. Timoshenko beam, onecan consider the shear deformation of the beam. The displacement ofthe beam is the interpolation function independently regardingcross-section corner of the beam, rather than obtained by thedisplacement derivative. In this case, it is necessary to consider theshear deformation and rotational inertia effects of the beam.In this paper, using the Generalized Hamilton variationalprinciple, based on the Kirchhoff-Love assumptions of the beam,establish a general mathematical model for Timoshenko beam-column structure of the nonlinear mechanical properties. Themathematical model is highly nonlinear and coupled, thesemathematical models is widely used as a model of degradation andpromotion can be many other mathematical models, they can besuitable for the needs of the different engineering and technical fields.For the application of the model, taking into account thenonlinear static-dynamics problems of the uniform-cross-section beam.Assuming the structural distribution of power is time-related with theladder loading or cyclic loading, the equation established in the space domain by using the differential quadrature method, in time domainusing the finite difference method for discrete nonlinear Timoshenkobeam-column structure statics-dynamics. In this process, we take intoaccount the effect of dynamics characteristics by the rotationparameters of inertia, geometric and material nonlinear structural.As another application of the model, accounting to thecontinuity conditions and the conditions of intermittent beam structureof the appropriate connection conditions and intermittent conditions,we use and develop the differential quadrature element method,discrete space equation, while using the The finite difference method,discrete time equation. Finally, we use the Newton iterative method tosolving the discrete equation obtained to study the nonlinearTimoshenko beam-column structure statics-dynamics problem. Andconsider the influence of various parameters.This paper conducted a comprehensive study of the numericalsimulation of the DQM, DQEM, differential-algebraic methods,analyzing the static and dynamic characteristics of the beam-columnstructure. And give some conclusions. These conclusions hasimplications in engineering utilize.