• Coupled systems mechanics
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• v.7 no.1
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• pp.27-42
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• 2018

Behavior of soil is usually described with continuum type of failure models such as Mohr-Coulomb or Drucker-Prager model. The main advantage of these models is in a relatively simple and efficient way of predicting the main tendencies and overall behavior of soil in failure analysis of interest for engineering practice. However, the main shortcoming of these models is that they are not able to capture post-peak behavior of soil nor the corresponding failure modes under extreme loading. In this paper we will significantly improve on this state-of-the-art. In particular, we propose the use of a discrete beam lattice model to provide a sharp prediction of inelastic response and failure mechanisms in coupled soil-foundation systems. In the discrete beam lattice model used in this paper, soil is meshed with one-dimensional Timoshenko beam finite elements with embedded strong discontinuities in axial and transverse direction capable of representing crack propagation in mode I and mode II. Mode I relates to crack opening, and mode II relates to crack sliding. To take into account material heterogeneities, we determine fracture limits for each Timoshenko beam with Gaussian random distribution. We compare the results obtained using the discrete beam lattice model against those obtained using the modified three-surface elasto-plastic cap model.

• 제어로봇시스템학회:학술대회논문집
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• 1990.10a
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• pp.382-387
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• 1990

In this paper, the dynamic modeling and tip position of rotating Timoshenko beam analyzed by means of FEM (finite element method) and Hyperstability MRAC(model referenced adaptive control) technique of each other. The governing equations of the rotating beams are drived from Hamilton's principle. The dynamic model of this multi-link is drived by Lagrange approach. The shear deformation and rotary inertia are incorporated into a finite element model for determining the bending frequencies of the rotating beam. Simulation results for uniform cantilever beams by using the MRAC are compared with the available results. It will be shown that the proposed method offers an accurate and effective one to solve the free vibration problems of rotating beams' stability.

• Structural Engineering and Mechanics
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• v.66 no.6
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• pp.703-711
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• 2018

In this paper is studied the effect of considering the theory of Timoshenko in the vibration of AFG beams that support ground masses. As it is known, Timoshenko theory takes into account the shear deformation and the rotational inertia, provides more accurate results in the general study of beams and is mandatory in the case of high frequencies or non-slender beams. The Rayleigh-Ritz Method is employed to obtain approximated solutions of the problem. The accuracy of the procedure is verified through results available in the literature that can be represented by the model under study. The incidence of the Timoshenko theory is analyzed for different cases of beam slenderness, variation of its cross section and compositions of its constituent material, as well as different amounts and positions of the attached masses.

• Structural Engineering and Mechanics
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• v.53 no.3
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• pp.537-573
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• 2015

Multiple-step beams carrying intermediate lumped masses with/without rotary inertias are widely used in engineering applications, but in the literature for free vibration analysis of such structural systems; Bernoulli-Euler Beam Theory (BEBT) without axial force effect is used. The literature regarding the free vibration analysis of Bernoulli-Euler single-span beams carrying a number of spring-mass systems, Bernoulli-Euler multiple-step and multi-span beams carrying multiple spring-mass systems and multiple point masses are plenty, but that of Timoshenko multiple-step beams carrying intermediate lumped masses and/or rotary inertias with axial force effect is fewer. The purpose of this paper is to utilize Numerical Assembly Technique (NAT) and Differential Transform Method (DTM) to determine the exact natural frequencies and mode shapes of the axial-loaded Timoshenko multiple-step beam carrying a number of intermediate lumped masses and/or rotary inertias. The model allows analyzing the influence of the shear and axial force effects, intermediate lumped masses and rotary inertias on the free vibration analysis of the multiple-step beams by using Timoshenko Beam Theory (TBT). At first, the coefficient matrices for the intermediate lumped mass with rotary inertia, the step change in cross-section, left-end support and right-end support of the multiple-step Timoshenko beam are derived from the analytical solution. After the derivation of the coefficient matrices, NAT is used to establish the overall coefficient matrix for the whole vibrating system. Finally, equating the overall coefficient matrix to zero one determines the natural frequencies of the vibrating system and substituting the corresponding values of integration constants into the related eigenfunctions one determines the associated mode shapes. After the analytical solution, an efficient and easy mathematical technique called DTM is used to solve the differential equations of the motion. The calculated natural frequencies of Timoshenko multiple-step beam carrying intermediate lumped masses and/or rotary inertias for the different values of axial force are given in tables. The first five mode shapes are presented in graphs. The effects of axial force, intermediate lumped masses and rotary inertias on the free vibration analysis of Timoshenko multiple-step beam are investigated.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2004.04a
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• pp.17-24
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• 2004

This paper established the dynamic model of a flexible Timoshenko beam with geometrical nonlinearities subject to large overall motions by using the finite element method. The equations of motion are derived by using Hamilton principle based on expressing the kinetic and potential energies of the flexible beam in terms of generalized coordinates. The nonlinear constraint equations are adjoined to the system equations of motion by using Lagrange multipliers.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.3
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• pp.623-630
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• 1995

The impulse response functions (force-strain relations) for Euler-Bernoulli and Timoshenko beams are considered. The response of a beam to a transverse impact force is numerically obtained with the convolution approach using the impulse response function obtained by Laplace transform. Using this relation, the impact force history is determined in the time domain and results are compared with those from Hertz's contact law. The parameters of timpact force model are identified using the recovered force and compared with the Hertz's contact model. In order to verify the proposed algorithm, measurements were done using an impact hammer and a steel ball drop test and these results are also compared with the simulated values.

• Journal of KSNVE
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• v.8 no.4
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• pp.616-622
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• 1998

An analytical method has been developed to estimate the dynamic contact force between wheel and rail when trains are running on rail with vertical irregularities. In this method, the effect of Hertzian deformation at the contact point is considered as a linearized spring and the wheel is considered as an sprung mass. The rail is modelled as a discretely-supported Timoshenko beam, and the periodic structure theory was adopted to obtain the driving-point receptance. As an example, the dynamic contact force for a typical wheel/rail system was analysed by the method developed in this research and the dynamic characteristics of the system was also discussed. It is revealed that discretely-supported Timoshenko beam model should be used instead of the previously used continuously-supported model or discretelysupported Euler beam model, for the frequency range above several hundred hertz.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.11b
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• pp.1066-1071
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• 2002

The use of frequency-dependent spectral element matrix (or exact dynamic stiffness matrix) in structural dynamics is known to provide very accurate solutions, while reducing the number of degrees-of-freedom to resolve the computational and cost problems. Thus, in the present paper, the spectral element model is formulated for the axially moving Timoshenko beam under a uniform axial tension. The high accuracy of the present spectral element is then verified by comparing its solutions with the conventional finite element solutions and exact analytical solutions. The effects of the moving speed and axial tension on the vibration characteristics, the dispersion relation, and the stability of a moving Timoshenko beam are investigated, analytically and numerically.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.10
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• pp.1653-1660
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• 2003

The use of frequency-dependent spectral element matrix (or exact dynamic stiffness matrix) in structural dynamics is known to provide very accurate solutions, while reducing the number of degrees-of-freedom to resolve the computational and cost problems. Thus, in the present paper, the spectral element model is formulated for the axially moving Timoshenko beam under a uniform axial tension. The high accuracy of the present spectral element is then verified by comparing its solutions with the conventional finite element solutions and exact analytical solutions. The effects of the moving speed and axial tension on the vibration characteristics, the dispersion relation, and the stability of a moving Timoshenko beam are investigated, analytically and numerically.

• Coupled systems mechanics
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• v.9 no.2
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• pp.125-145
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• 2020

In this paper, we present a 3D thermo-hydro-mechanical coupled discrete beam lattice model of structure built of the nonisothermal saturated poro-plastic medium subjected to mechanical loads and nonstationary heat transfer conditions. The proposed model is based on Voronoi cell representation of the domain with cohesive links represented as inelastic Timoshenko beam finite elements enhanced with additional kinematics in terms of embedded strong discontinuities in axial and both transverse directions. The enhanced Timoshenko beam finite element is capable of modeling crack formation in mode I, mode II and mode III. Mode I relates to crack opening, mode II relates to in-plane crack sliding, and mode III relates to the out-of-plane shear sliding. The pore fluid flow and heat flow in the proposed model are governed by Darcy's law and Fourier's law for heat conduction, respectively. The pore pressure field and temperature field are approximated with linear tetrahedral finite elements. By exploiting nodal point quadrature rule for numerical integration on tetrahedral finite elements and duality property between Voronoi diagram and Delaunay tetrahedralization, the numerical implementation of the coupling results with additional pore pressure and temperature degrees of freedom placed at each node of a Timoshenko beam finite element. The results of several numerical simulations are presented and discussed.