• Coupled systems mechanics
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• v.3 no.3
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• pp.247-265
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• 2014

This article discusses the dynamic response of Bernoulli-Euler straight beam with angular elastic supports subjected to moving load with variable velocity. A new engineering approach for determination of the dynamic effect from the moving load on the stressed and strained state of the beam has been developed. A dynamic coefficient, a ratio of the dynamic to the static deflection of the beam, has been defined on the base of an infinite geometrical absolutely summable series. Generalization of the R. Willis' equation has been carried out: generalized boundary conditions have been introduced; the generalized elastic curve's equation on the base of infinite trigonometric series method has been obtained; the forces of inertia from normal and Coriolis accelerations and reduced beam mass have been taken into account. The influence of the boundary conditions and kinematic characteristics of the moving load on the dynamic coefficient has been investigated. As a result, the dynamic stressed and strained state has been obtained as a multiplication of the static one with the dynamic coefficient. The developed approach has been compared with a finite element one for a concrete engineering case and thus its authenticity has been proved.

• Structural Engineering and Mechanics
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• v.76 no.3
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• pp.395-412
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• 2020

In this article, the values of internal force and deformation of a curved beam under any action with the firm or elastic supports are determined by using structural matrices. The article presents the general differential formulation of a curved beam in global coordinates, which is solved in an orderly manner using simple integrals, thus obtaining the transfer matrix expression. The matrix expression of rigidity is obtained through reordering operations on the transfer notation. The support conditions, firm or elastic, provide twelve equations. The objective of this article is the construction of the algebraic system of order twenty-four, twelve transfer equations and twelve support equations, which relates the values of internal force and deformation associated with the two ends of the directrix of the curved beam. This final algebraic system, expressed in matrix form, is divided into two subsystems: twelve algebraic equations of internal force and twelve algebraic equations of deformation. The internal force and deformation values for any point in the curved beam directrix are determined from these values in the initial position. The five examples presented show how to apply the matrix procedures developed in this article, whether they are curved beams with the firm or elastic support.

• Composites Research
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• v.20 no.6
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• pp.15-20
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• 2007

In this work, the structural response of thin-walled, composite beams with built-in twist angles is analyzed using a mixed beam approach. The analytical model includes the effects of elastic couplings, shell wall thickness, and torsion warping. Reissner's semi-complimentary energy functional is used to describe the beam theory and also to deal with the mixed-nature in the beam kinematics. The bending and torsion related warpings introduced by the non-zero pretwist angles are derived in closed-form through the proposed beam formulation. The theory is validated with available literature and detailed finite element analysis results for rectangular solid section beams with elastic couplings. Very good correlation has been obtained for the cases considered.

• Structural Engineering and Mechanics
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• v.27 no.5
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• pp.555-574
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• 2007

Static response of an elastic beam on a two-parameter tensionless foundation is investigated by assuming that the beam is symmetrically subjected to a uniformly distributed load and concentrated edge loads. Governing equations of the problem are obtained and solved by pointing out that a concentrated edge foundation reaction in addition to a continuous foundation reaction along the beam axis in the case of complete contact and a discontinuity in the foundation reactions in the case of partial contact come into being as a direct result of the two-parameter foundation model. The numerical solution of the complete contact problem is straightforward. However, it is shown that the problem displays a highly non-linear character when the beam lifts off from the foundation. Numerical treatment of the governing equations is accomplished by adopting an iterative process to establish the contact length. Results are presented in figures to demonstrate the linear and non-linear behavior of the beam-foundation system for various values of the parameters of the problem comparatively.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 1997.10a
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• pp.28-31
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• 1997

Buckling analysis of thin compressed beam has been carried out. Pre-buckling and post-buckling are simulated by finite element method incorporating with the incremental nonlinear theory and the Newton-Raphson solution technique. In order to find the bifurcation point, the determinent of the stiffness matrix is calculated at every iteration procedure. For post-buckling analysis, a small perturbed initial guess is given along the eigenvector direction at the bifurcation point. Nonlinear elastic buckling and elastic-plastic buckling of cantilever beam are analyzed. The buckling load and buckled shape of the two models are compared.

• Structural Engineering and Mechanics
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• v.55 no.4
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• pp.743-763
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• 2015

This work presents a new nonlocal hyperbolic shear deformation beam theory for the static, buckling and vibration of nanoscale-beams embedded in an elastic medium. The present model is able to capture both the nonlocal parameter and the shear deformation effect without employing shear correction factor. The nonlocal parameter accounts for the small size effects when dealing with nanosize structures such as nanobeams. Based on the nonlocal differential constitutive relations of Eringen, the equations of motion of the nanoscale-beam are obtained using Hamilton's principle. The effect of the surrounding elastic medium on the deflections, critical buckling loads and frequencies of the nanobeam is investigated. Both Winkler-type and Pasternak-type foundation models are used to simulate the interaction of the nanobeam with the surrounding elastic medium. Analytical solutions are presented for a simply supported nanoscale-beam, and the obtained results compare well with those predicted by the other nonlocal theories available in literature.

• Geomechanics and Engineering
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• v.36 no.2
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• pp.183-204
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• 2024

In current investigation, a novel beam finite element model is formulated to analyze the buckling and free vibration responses of functionally graded porous beams resting on Winkler-Pasternak elastic foundations. The novelty lies in the formulation of a simplified finite element model with only three degrees of freedom per node, integrating both C⁰ and C¹ continuity requirements according to Lagrange and Hermite interpolations, respectively, in isoparametric coordinate while emphasizing the impact of z-coordinate-dependent porosity on vibration and buckling responses. The proposed model has been validated and demonstrating high accuracy when compared to previously published solutions. A detailed parametric examination is performed, highlighting the influence of porosity distribution, foundation parameters, slenderness ratio, and boundary conditions. Unlike existing numerical techniques, the proposed element achieves a high rate of convergence with reduced computational complexity. Additionally, the model's adaptability to various mechanical problems and structural geometries is showcased through the numerical evaluation of elastic foundations, with results in strong agreement with the theoretical formulation. In light of the findings, porosity significantly affects the mechanical integrity of FGP beams on elastic foundations, with the advanced beam element offering a stable, efficient model for future research and this in-depth investigation enriches porous structure simulations in a field with limited current research, necessitating additional exploration and investigation.

• Journal of the Korean Society for Precision Engineering
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• v.20 no.4
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• pp.49-58
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• 2003

In this study, the equation of motion of impacting elastic structures was derived through the theory, and the shape control of impact force using correlations of the dynamic characteristics and impact force history between two elastic structures was accomplished. Through numerical analysis and experiments, the classical contact mechanisms were verified, and the effects of the relative motion between impactor and elastic structure on the impact force shape were studied, and then the shape change of impact force depending on the impact position and mode shape of cantilever beam were analyzed. The 2-DOF impactor was designed and used. Reconstruction characteristics of impact force in cantilever beam were reviewed .

• Journal of KSNVE
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• v.10 no.6
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• pp.1022-1028
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• 2000

This paper presents a modeling method for the vibration analysis of rotating cantilever beams considering the elastic foundation effect. Mass and stiffness matrices are derided explicitly by considering coupling effect between stretching and bonding motion. Numerical results show that the bending direction elastic foundation stiffness influences the vibration characteristics significantly in practical range of beam configuration. The ranges of elastic foundation stiffness to avoid the dynamic buckling are also presented. The method presented in this paper can be used to predict the variations of natural frequencies of rotating cantilever beams with elastically restrained root.

• Transactions of Materials Processing
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• v.11 no.7
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• pp.575-580
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• 2002

To evaluate elastic and micro-failure properties of MEMS materials, the electro-statically operated test devices were designed and fabricated by micro machining technology. The test structures consist or comb drives for loading and suspending beams in testing. From the analysis of beam displacement based on elastic beam theory, elastic modulus and yield strength of Al film were measured. And, by introducing the micro notch and cyclic loading, the micro-failure was Induced and the micro-fracture toughness of Si film was evaluated. Moreover, the cycles to failure were estimated from the degradation of resonant frequency. Finally, the effects of notch on micro failure were discussed.