• Structural Engineering and Mechanics
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• v.5 no.5
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• pp.645-662
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• 1997

A nonlinear semi-three-dimensional layered finite element procedure is developed for cracking and failure analysis of reinforced concrete beams and the spandrel beam-column-slab connections of flat plates. The layered element approach takes the elasto-plastic failure behaviour and geometric nonlinearity into consideration. A strain-hardening plasticity concrete model and a smeared steel model are incorporated into the layered element formulation. Further, shear failure, transverse reinforcement, spandrel beams and columns are successfully modelled. The proposed method incorporating the nonlinear constitutive models for concrete and steel is implemented in a finite element program. Test specimens including a series of reinforced concrete beams and beam-column-slab connections of flat plates are analysed. Results confirm the effectiveness and accuracy of the layered procedure in predicting both flexural and shear cracking up to failure.

• Journal of the Korea Concrete Institute
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• v.11 no.5
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• pp.131-137
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• 1999

The use of higher strength materials with the strength methed of design has resulted in more slender member and shallower sections. For this reason, it is necessary to satisfy the requirements of serviceability even though the structural safety is the most important limit state. This paper is only concerned with the control of deflections in the serviceability. In this study, an analytical model is presented to predict the deflections of reinforced concrete beams to given loading and environmental conditions. This model is based on the finite element approach in which a finite element is generally divided into a number of stiffening effect due to cracking, creep and shrinkage. Comparisons are made with available measured deflections reported by others to assess the capability of the layered beam model. The calculated values of instantaneous and long-term deflection show good agreement with experimental results in the range of tension stiffening parameter $\beta$ between 2.5 and 3.0.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.21 no.1
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• pp.9-17
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• 2011

In this paper, the general equation of motion of damped sandwich beam with multi-viscoelastic material layer was derived based on the equation presented by Mead and Markus. The viscoelastic layer, which has characteristics of complex shear modulus, was assumed to be dominantly under shear deformation. The equation of motion of n-layered damped sandwich beam in bending could be represented by (n+3)th order ordinary differential equation. Finite element model for the n-layered damped sandwich beam was formulated and programmed using higher order shape functions. Several numerical examples were implemented to show the effects of damped material.

• Structural Engineering and Mechanics
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• v.75 no.6
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• pp.713-722
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• 2020

This article aims to illustrate the damped dynamic responses of layered functionally graded (FG) thick 2D beam under dynamic pulse sinusoidal load by using finite element method, for the first time. To investigate the response of thick beam accurately, two-dimensional plane stress problem is assumed to describe the constitutive behavior of thick beam structure. The material is distributed gradually through the thickness of each layer by generalized power law function. The Kelvin-Voigt viscoelastic constitutive model is exploited to include the material internal damping effect. The governing equations are obtained by using Lagrange's equations and solved by using finite element method with twelve -node 2D plane element. The dynamic equation of motion is solved numerically by Newmark implicit time integration procedure. Numerical studies are presented to illustrate stacking sequence and material gradation index on the displacement-time response of cantilever beam structure. It is found that, the number of waves increases by increasing the graduation distribution parameter. The presented mathematical model is useful in analysis and design of nuclear, marine, vehicle and aerospace structures those manufactured from functionally graded materials (FGM).

• Structural Engineering and Mechanics
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• v.22 no.3
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• pp.263-278
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• 2006

Starting with the geometrically non-linear formulation and the subsequent linearization, this paper presents a consistent formulation of the exact mechanical analysis of geometrically and materially linear three-layer continuous planar beams. Each layer of the beam is described by the geometrically linear beam theory. Constitutive laws of layer materials and relationships between interlayer slips and shear stresses at the interface are assumed to be linear elastic. The formulation is first applied in the analysis of a three-layer simply supported beam. The results are compared to those of Goodman and Popov (1968) and to those obtained from the formulation of the European code for timber structures, Eurocode 5 (1993). Comparisons show that the present and the Goodman and Popov (1968) results agree completely, while the Eurocode 5 (1993) results differ to a certain degree. Next, the analytical solution is used in formulating a general procedure for the analysis of layered continuous beams. The applications show the qualitative and quantitative effects of the layer and the interlayer slip stiffnesses on internal forces, stresses and deflections of composite continuous beams.

• KCI Concrete Journal
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• v.11 no.3
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• pp.115-126
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• 1999

An analytical method based on the nonlinear layered finite element method is developed to simulate an overall load-deflection behavior of strengthened beams. The developed model distinguishes itself by its capability to trace residual flexural behavior of a beam after the fracture of brittle strengthening materials at peak load. The model. which uses a rather advanced numerical technique for iterative convergence to equilibrium, can be regarded as superior to the two models based on load control and displacement control The model predictions were compared with the experimental results and it was observed that there was good agreement between them.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 1998.04a
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• pp.438-443
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• 1998

In this paper, the axial-bending coupled equations of motion for an elastic layered beam are derived. From this equation of motion, the spectral element is formulated for the vibration analysis by use of the spectral element method (SEM). The modal analysis methodology for the present coupled field equations of motion is then developed. As an illustrative example, a cantilevered beam is considered. The correctness of the equations of motion developed herein is verified by gradually reducing the thickness of upper elastic layer to converge to the single layered elastic beam solutions. Also, the accuracy of spectral element is confirmed by comparing its results with the result by modal analysis.

• Structural Engineering and Mechanics
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• v.62 no.6
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• pp.771-780
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• 2017

In this study, free vibration and damping behaviors of multilayered symmetric sandwich beams and single layered beams made of Functionally Graded Materials were investigated, experimentally and numerically. The beams were composed of Aluminum and Silicon Carbide powders and they were produced by powder metallurgy. Three beam models were used in the experiments. The first model was isotropic, homogeneous beams produced by using different mixing ratios. In the second model, the pure metal layers were taken in the middle of the beam and the weight fraction of the ceramic powder of each layer was increased towards to the surfaces of the beam in the thickness direction. In the third model, the pure metal layers were taken in the surfaces of the beam and the weight fraction of the ceramic powder of each layer was increased towards to middle of the beam. Then the vibration tests were performed. Consequently, the effects of stacking sequence and mixing ratio on the natural frequencies and damping responses of functionally graded beams were discussed from the results obtained. Furthermore, the results obtained from the tests were supported with a finite-element-based commercial program, and it was found to be in harmony.

• The Journal of the Acoustical Society of Korea
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• v.34 no.6
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• pp.470-478
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• 2015

A heuristic method treating a layered ocean bottom in a ray modeling is to use the plane wave reflection coefficient for multiple-layered structure, named an one-layer assumption in this paper. We examine the validity of one-layer assumption in the case of two-layered ocean bottom, and obtain a simple inequality condition depending on the sound speed ratio, the ratio of layer thickness to source-receiver range, and the grazing angle of first reflected ray. From this inequality condition, it is shown that an one-layer assumption can be applicable to ray propagation problems at mid frequencies. Finally, numerical experiments are performed in the ocean environment similar to the East Sea in Korea. Incoherent transmission loss is calculated by the geometrical beam model with the plane wave reflection coefficient for multiple-layered ocean bottom and compared with the result of SNUPE 2.0, which is a parabolic equation package developed in Seoul National University.

• Structural Engineering and Mechanics
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• v.14 no.3
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• pp.245-262
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• 2002

The free vibration analysis of stiffened laminated composite plates has been performed using the layered (zigzag) finite element method based on the first order shear deformation theory. The layers of the laminated plate is modeled using nine-node isoparametric degenerated flat shell element. The stiffeners are modeled as three-node isoparametric beam elements based on Timoshenko beam theory. Bilinear in-plane displacement constraints are used to maintain the inter-layer continuity. A special lumping technique is used in deriving the lumped mass matrices. The natural frequencies are extracted using the subspace iteration method. Numerical results are presented for unstiffened laminated plates, stiffened isotropic plates, stiffened symmetric angle-ply laminates, stiffened skew-symmetric angle-ply laminates and stiffened skew-symmetric cross-ply laminates. The effects of fiber orientations (ply angles), number of layers, stiffener depths and degrees of orthotropy are examined.