Timoshenko beam theory

About: Timoshenko beam theory is a research topic. Over the lifetime, 9426 publications have been published within this topic receiving 200570 citations.

Nonlinear Vibration Analysis of Timoshenko Beams Using the Differential Quadrature Method

Abstract: This paper addresses the large-amplitude free vibration of simplysupported Timoshenko beams with immovable ends. Various nonlineareffects are taken into account in the present formulation and thegoverning differential equations are established based on theHamilton Principle. The differential quadrature method (DQM) isemployed to solve the nonlinear differential equations. Theeffects of nonlinear terms on the frequency of the Timoshenkobeams are discussed in detail. Comparison is made with otheravailable results of the Bernoulli–Euler beams and Timoshenkobeams. It is concluded that the nonlinear term of the axial forceis the dominant factor in the nonlinear vibration of Timoshenkobeams and the nonlinear shear deformation term cannot be neglectedfor short beams, especially for large-amplitude vibrations.

Imperfection sensitivity of postbuckling behaviour of functionally graded carbon nanotube-reinforced composite beams

Abstract: The imperfection sensitivity of the postbuckling behaviour of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) beams subjected to axial compression is investigated based on the first-order shear deformation beam theory with a von Karman geometric nonlinearity. The material properties of FG-CNTRC are assumed to vary in the beam thickness direction and are estimated according to the extended rule of mixture. The differential quadrature method is employed to discretize the governing differential equations and the modified Newton-Raphson iterative technique is used to obtain the postbuckling equilibrium paths of FG-CNTRC beams with various imperfections. Parametric studies are carried out to examine the effects of imperfection modes, half-wave number, location, and amplitude on the postbuckling response of beams. The influences of CNT distribution pattern and volume fraction, boundary conditions, and slenderness ratio are also discussed. Numerical results in graphical form show that the postbuckling behaviour is highly sensitive to the imperfection amplitude. The imperfection mode and its half-wave number also moderately affect the imperfection sensitivity of the postbuckling response, whereas the effects of other parameters are much less pronounced.

Brittle and ductile failure of rocks: Embedded discontinuity approach for representing mode I and mode II failure mechanisms

Abstract: In this work we present a discrete beam lattice model with embedded discontinuities capable of simulating rock failure as a result of propagating cracks through rock mass. The developed model is a 2D (plane strain) micro- scale representation of rocks as a two-phase heterogeneous material. Phase I is chosen for intact rock part, while phase II stands for pre- existing micro-cracks and other defects. The proposed model relies on Timoshenko beam elements enhanced with additional kinematics to describe localized failure mechanisms. The model can properly take into account the fracture process zone with pre-existing microcracks coalescence, along with localized failure modes, mode I of tensile opening and mode II of shear sliding. Furthermore, we give the very detailed presentation for two different approaches to capturing the evolution of mode I and mode II, and their interaction and combination. The first approach is to deal with mode I and mode II separately, where mode II can be activated but compression force may still be transferred through rock mass which is not yet completely damaged. The second approach is to represent both modes I and II being activated simultaneously at a point where complete failure is reached. A novel numerical procedure for dealing with two modes failure within framework of method of incompatible modes is presented in detail and validated by a set of numerical examples.