• Journal of the Korea Academia-Industrial cooperation Society
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• v.4 no.2
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• pp.76-80
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• 2003

In this study, it is presented analysis results of bending problems in the orthotropic thick plates and the orthotropic thin plates. Finite element method in this analysis was used. Both Kirchoffs assumptions and Mindlin assumptions are used as the basic governing equations of bending problems in the orthotropic plates. The analysis results are compared between the orthotropic thick plates and the orthotropic thin plates for the variations of thickness-width ratios.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.11 no.6
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• pp.2284-2291
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• 2010

In this paper, we investigate the vibration analysis of plates, using an 8-node shell element that accounts for the transverse shear strains and rotary inertia. The forced vibration analysis of plates subjected to arbitrary loading is investigated. In order to overcome membrane and shear locking phenomena, the assumed natural strain method is used. To improve an 8-node shell element for forced vibration analysis, the new combination of sampling points for assumed natural strain method was applied. The refined first-order shear deformation theory based on Reissner-Mindlin theory which allows the shear deformation without shear correction factor and rotary inertia effect to be considered is adopted for development of 8-node assumed strain shell element. In order to validate the finite element numerical solutions, the reference solutions of plates are presented. Results of the present theory show good agreement with the reference solution. In addition the effect of damping is investigated on the forced vibration analysis of plates.

• Transactions of the Korean Society of Mechanical Engineers
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• v.14 no.6
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• pp.1365-1381
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• 1990

A $C^{0}$ continuous displacement finite element method based on a higher-order shear deformation theory is employed in the prediction of the transient response of laminated composite plates subjected to low-velocity impact. A modified contact law was applied to calculate the contact force during impact. The discrete element chosen is a nine-noded quadrilateral with 5 degree-of-freedom per node. The Wilson-.theta. time integration algorithm is used for solving the time dependent equations of the impactor and the central difference method was adopted to perform time integration of the plate. Numerical results, including the contact force history, deflection, and velocity history, are presented. Comparisons of numerical results using a higher order theory and a first-order theory show that using a higher order theory provides more accurate results. Effects of boundary condition, impact velocity, and mass of the impactors are also discussed.d.

• Journal of Korean Association for Spatial Structures
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• v.7 no.5
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• pp.67-74
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• 2007

The unsymmetrically layered artificial material model is consistently introduced to find the optimum topologies of the plate structures. Reissner-Mindlin (RM) plate theory is adopted to formulate the present 9-node plate element considering the first-order shear deformation of the plates. In the topology optimization process, the strain energy to be minimized is employed as the objective function and the initial volume of structures is adopted as the constraint function. In addition, the resizing algorithm based on the optimality criteria is used to update the hole size introduced in the proposed artificial material model. Several numerical examples are rallied out to investigate the performance of the proposed technique. From numerical results, the proposed topology optimization techniques are found to be very effective to produce the optimum topology of plate structures. In particular, the proposed unsymmetric stiffening layer model make it possible to produce more realistic stiffener design of the plate structures.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2008.11a
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• pp.71-81
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• 2008

This paper proposes a spectral element which can represent dynamic responses in high frequency domain such as Lamb waves on a thin plate. A two layer beam model under 2-D plane strain condition is introduced to simulate high-frequency dynamic responses induced by piezoelectric layer (PZT layer) bonded on a base plate. In the two layer beam model, a PZT layer is assumed to be rigidly bonded on a base beam. Mindlin-Herrmann and Timoshenko beam theories are employed to represent the first symmetric and anti-symmetric Lamb wave modes on a base plate, respectively. The Bernoulli beam theory and 1-D linear piezoelectricity are used to model the electro-mechanical behavior of a PZT layer. The equations of motions of a two layer beam model are derived through Hamilton's principle. The necessary boundary conditions associated with electro mechanical properties of a PZT layer are formulated in the context of dual functions of a PZT layer as an actuator and a sensor. General spectral shape functions of response field and the associated boundary conditions are formulated through equations of motions converted into frequency domain. A detailed spectrum element formulation for composing the dynamic stiffness matrix of a two layer beam model is presented as well. The validity of the proposed spectral element is demonstrated through comparison results with the conventional 2-D FEM and the previously developed spectral elements.

• 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.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.18 no.11
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• pp.1157-1169
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• 2008

This paper presents spectral element formulation which approximates Lamb wave propagation by PZT transducers bonded on a thin plate. A two layer beam model under 2-D plane strain condition is introduced to simulate high-frequency dynamic responses induced by a piezoelectric (PZT) layer rigidly bonded on a base plate. Mindlin-Herrmann and Timoshenko beam theories are employed to represent the first symmetric and anti-symmetric Lamb wave modes on a base plate, respectively. The Euler-Bernoulli beam theory and 1-D linear piezoelectricity are used to model the electro-mechanical behavior of a PZT layer. The equations of motions of a two layer beam model are derived through Hamilton's principle. The necessary boundary conditions associated with the electro-mechanical properties of a PZT layer are formulated in the context of dual functions of a PZT layer as an actuator and a sensor. General spectral shape functions of response field and the associated boundary conditions are obtained through equations of motions converted into frequency domain. Detailed spectrum element formulation for composing the dynamic stiffness matrix of a two layer beam model is presented as well. The validity of the proposed spectral element is demonstrated through numerical examples.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.27 no.2
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• pp.63-70
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• 2014

Design sensitivity analysis and topology design optimization for a piezoelectric crystal resonator are developed. The piezoelectric crystal resonator is deformed mechanically when subjected to electric charge on the electrodes, or vice versa. The Mindlin plate theory with higher-order interpolations along thickness direction is employed for analyzing the thickness-shear vibrations of the crystal resonator. Thin electrode plates are masked on the top and bottom layers of the crystal plate in order to enforce to vibrate it or detect electric signals. Although the electrode is very thin, its weight and shape could change the performance of the resonators. Thus, the design variables are the bulk material densities corresponding to the mass of masking electrode plates. An optimization problem is formulated to find the optimal topology of electrodes, maximizing the thickness-shear contribution of strain energy at the desired motion and restricting the allowable volume and area of masking plates. The necessary design gradients for the thickness-shear frequency(eigenvalue) and the corresponding mode shape(eigenvector) are computed very efficiently and accurately using the analytical design sensitivity analysis method using the eigenvector expansion concept. Through some demonstrative numerical examples, the design sensitivity analysis method is verified to be very efficient and accurate by comparing with the finite difference method. It is also observed that the optimal electrode design yields an improved mode shape and thickness-shear energy.

• Journal of the Society of Naval Architects of Korea
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• v.36 no.3
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• pp.83-92
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• 1999

In this paper, the fluid-structure interaction of large floating structures has been rigorously analyzed and the shear effect on the structural deformation has been investigated in oblique waves. A constant panel method(CPM) based on the Green function method is implemented for computing the hydrodynamic pressure, while a finite element method(FEM) is applied for the structural response based on the Mindlin plate theory with including shear deformation. In order to validate the method, we compared numerical results with experimental ones of Mega Float carried out by Yago & Endo in head waves. General behavior shows good agreement but the local displacement at the ends is slightly different. The numerical results show that the radiation pressure due to the fluid-structure interaction is locally larger than that of wave excitation and mooring devices greatly reduce the response. It is observed that the shear effects among the total deformation constitutes about 4% in the case of Mega Float in oblique waves.