• Journal of Korean Society of Steel Construction
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• v.16 no.3 s.70
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• pp.295-303
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• 2004

In this paper, an improved four-node Reissner-Mindlin plate-bending element with enhanced assumed strain field is presented for the analysis of isotropic and laminated composite plates. To avoid the shear locking and spurious zero energy modes, the transverse shear behavior is improved by the addition of a new enhanced shear strain based on the incompatible displacement mode approach and bubble function. The "standard" enhanced strain fields (Andelfinger and Ramm, 1993) are also employed to improve the in-plane behaviors of the plate elements. The four-node quadrilateral element derived using the first-order shear deformation theory is designated as "14EASP". Several applications are investigated to assess the features and the performances of the proposed element. The results are compared with other finite element solutions and analytical solutions. Numerical examples show that the element is stable, invariant, passes the patch test, and yields good results especially in highly distorted regimes.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2007.04a
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• pp.663-668
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• 2007

An enhanced first shear deformation theory for composite plate is developed. The detailed process is as follows. Firstly, the theory is formulated by modifying higher order zigzag theory. That is, the higher order theory is separated into the warping function representing the higher order terms and lower order terms. Secondly, the relationships between higher order zig-zag field and averaged first shear deformation field based on the Reissner-Mindlin's plate theory are derived. Lastly, the effective shear modulus is calculated by minimizing error between higher order energy and first order energy. Then the governing equation of FSDT is solved by substituting shear modulus into effective shear modulus. The recovery processing with the nodal unknown obtained from governing equation is performed. The accuracy of the present proposed theory is demonstrated through numerical examples. The proposed method will serve as a powerful tool in the prediction of laminated composite plate.

• The Journal of the Acoustical Society of Korea
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• v.6 no.3
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• pp.5-16
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• 1987

In this paper, the sound radiation from a clamped circular plate with a viscoelastic layer excited by impact force is studied both analytically and experimentally. The composite plate vibrations are obtained by using the normal mode analysis and the eigenvalues are obtained by a Mindlin plate theory including the rotary inertia and shear deformation, The contact force developed between the ball and the plate with attached layers is obtained by Hertz contact theory. The radiated sound pressure is calculated by the Rayleigh integral. Prediction of the waveforms of sound radiating from the plate with attached layers and a method for reducing noise generation from the plate by impact force are also shown in this paper.

• Structural Engineering and Mechanics
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• v.50 no.2
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• pp.181-199
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• 2014

Locking phenomenon is a mesh problem and can be staved off with mesh refinement. If the studier is not preferred going to the solution with increasing mesh size or the computer memory can stack over flow than using higher order plate finite element or using integration techniques is a solution for this problem. The purpose of this paper is to show the shear locking phenomenon can be avoided by increase low order finite element mesh size of the plates and to study shear locking-free analysis of thick plates using Mindlin's theory by using higher order displacement shape function and to determine the effects of various parameters such as the thickness/span ratio, mesh size on the linear responses of thick plates subjected to uniformly distributed loads. A computer program using finite element method is coded in C++ to analyze the plates clamped or simply supported along all four edges. In the analysis, 4-, 8- and 17-noded quadrilateral finite elements are used. It is concluded that 17-noded finite element converges to exact results much faster than 8-noded finite element, and that it is better to use 17-noded finite element for shear-locking free analysis of plates.

• Smart Structures and Systems
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• v.3 no.4
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• pp.439-454
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• 2007

In this paper a damage imaging technique using pre-stack migration is developed using Lamb (guided) wave propagation in composite structures for imaging multi damages by both numerical simulations and experimental studies. In particular, the paper focuses on the experimental study using a finite number of sensors for future practical applications. A composite laminate with a surface-mounted linear piezoelectric ceramic (PZT) disk array is illustrated as an example. Two types of damages, one straight-crack damage and two simulated circular-shaped delamination damage, have been studied. First, Mindlin plate theory is used to model Lamb waves propagating in laminates. The group velocities of flexural waves in the composite laminate are also derived from dispersion relations and validated by experiments. Then the pre-stack migration technique is performed by using a two-dimensional explicit finite difference algorithm to back-propagate the scattered energy to the damages and damages are imaged together with the excitation-time imaging conditions. Stacking these images together deduces the resulting image of damages. Both simulations and experimental results show that the pre-stack migration method is a promising method for damage identification in composite structures.

• Structural Engineering and Mechanics
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• v.67 no.1
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• pp.21-31
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• 2018

In this work, the dynamic stability of carbon nanotubes (CNTs) reinforced composite pipes conveying pulsating fluid flow is investigated. The pipe is surrounded by viscoelastic medium containing spring, shear and damper coefficients. Due to the existence of CNTs, the pipe is subjected to a 2D magnetic field. The radial induced force by pulsating fluid is obtained by the Navier-Stokes equation. The equivalent characteristics of the nanocomposite structure are calculated using Mori-Tanaka model. Based on first order shear deformation theory (FSDT) or Mindlin theory, energy method and Hamilton's principle, the motion equations are derived. Using harmonic differential quadrature method (HDQM) in conjunction with the Bolotin's method, the dynamic instability region (DIR) of the system is calculated. The effects of different parameters such as volume fraction of CNTs, magnetic field, boundary conditions, fluid velocity and geometrical parameters of pipe are shown on the DIR of the structure. Results show that with increasing volume fraction of CNTs, the DIR shifts to the higher frequency. In addition, the DIR of the structure will be happened at lower excitation frequencies with increasing the fluid velocity.

• Earthquakes and Structures
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• v.16 no.3
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• pp.359-368
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• 2019

This paper focuses on the study of dynamic analysis of thick plates resting on Winkler foundation. The governing equation is derived from Mindlin's theory. This study is a parametric analysis of the reflections of the thickness / span ratio, the aspect ratio and the boundary conditions on the earthquake excitations are studied. In the analysis, finite element method is used for spatial integration and the Newmark-${\beta}$ method is used for the time integration. While using finite element method, a new element is used. This element is 17-noded and it's formulation is derived from using higher order displacement shape functions. C++ program is used for the analyses. Graphs are presented to help engineers in the design of thick plates subjected to earthquake excitations. It is concluded that the 17-noded finite element is used in the earthquake analysis of thick plates. It is shown that the changes in the aspect ratio are more effective than the changes in the aspect ratio. The center displacements of the reinforced concrete thick clamped plates for b/a=1, and t/a=0.2, and for b/a=2, and t/a=0.2, reached their absolute maximum values of 0.00244 mm at 3.48 s, and of 0.00444 mm at 3.48 s, respectively.

• Journal of the Society of Naval Architects of Korea
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• v.29 no.1
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• pp.158-172
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• 1992

In ships and offshore structures, there are many local structures formed of thick plates and/or having the form of double wall panels. For the vibration analysis of such a kind of structures, Mindlin plate theory which includes the effects of shear deformation and rotary inertia is usually adopted. In this paper, the vibration and dynamic sensitivity analysis of Mindlin plates having the boundary conditions elastically restrained against rotation have been accomplished using the Rayleigh-Ritz method. Polynomials having the property of the Timoshenko beam functions are introduced and used as trial functions in the spatial representation of the deflection and rotations of cross sections in two directions of the plates. The results obtained by the introduced polynomials gave nearly the same numerical results as those by the Timoshenko beam functions with the remarkable reduction of computational efforts especially in the dynamic sensitivity analysis.

• Structural Engineering and Mechanics
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• v.14 no.5
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• pp.575-593
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• 2002

Based on the Mindlin plate theory, a refined discrete 15-DOF triangular laminated composite plate finite element RDTMLC with the re-constitution of the shear strain is proposed. For constituting the element displacement function, the exact displacement function of the Timoshenko's laminated composite beam as the displacement on the element boundary is used to derive the element displacements. The proposed element can be used for the analysis of both moderately thick and thin laminated composite plate, and the convergence for the very thin situation can be ensured theoretically. Numerical examples presented show that the present model indeed possesses the properties of higher accuracy for anisotropic laminated composite plates and is free of locking even for extremely thin laminated plates.

• Structural Engineering and Mechanics
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• v.6 no.6
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• pp.643-658
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• 1998

A thermal postbuckling analysis is presented for a moderately thick rectangular plate subjected to uniform or nonuniform tent-like temperature loading and resting on an elastic foundation. The plate is assumed to be simply supported on its two opposite edges and the two side edges remain free. The initial geometrical imperfection of the plate is taken into account. The formulation are based on the Reissner-Mindlin plate theory considering the first order shear deformation effect, and including plate-foundation interaction and thermal effects. The analysis uses a mixed Galerkin-perturbation technique to determine the thermal buckling loads and postbuckling equilibrium paths. Numerical examples are presented that relate to the performances of perfect and imperfect, moderately thick plates resting on Pasternak-type or softening nonlinear elastic foundations from which results for Winker elastic foundations follow as a limiting case. Typical results are presented in dimensionless graphical form.