• Journal of the Korea institute for structural maintenance and inspection
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• v.8 no.4
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• pp.107-114
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• 2004

In this paper, a simple improved 8-node finite element for the finite element analysis of fibrous composite plates is presented by using the direct modification. We drive explicit expressions of shape functions for the 8-node element with bilinear element geometry, which is modified so that it can represent any quadratic fields in Cartesian coordinates. The refined first-order shear deformation theory is proposed, which results in parabolic through-thickness distribution of the transverse shear strains and stresses from the formulation based on the third-order shear deformation theory. It eliminates the need for shear correction factors in the first-order theory. This finite element is further improved by combined use of assumed strain, modified shape function, and refined first-order theory. To show the effectiveness of our simple modification on the 8-node finite elements, numerical studies are carried out the static, buckling and free vibration analysis of fibrous composite plates.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.25 no.6
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• pp.505-512
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• 2012

In this paper, an efficient yet accurate method for the thermal stress analysis using a first order shear deformation theory(FSDT) is presented. The main objective herein is to systematically modify transverse shear strain energy through the mixed variational theorem(MVT). In the mixed formulation, independent transverse shear stresses are taken from the efficient higher-order zigzag plate theory, and the in-plane displacements are assumed to be those of the FSDT. Moreover, a smooth parabolic distribution through the thickness is assumed in the transverse normal displacement field in order to consider a transverse normal deformation. The resulting strain energy expression is referred to as an enhanced first order shear deformation theory, which is obtained via the mixed variational theorem with transverse normal deformation effect(EFSDTM_TN). The EFSDTM_TN has the same computational advantage as the FSDT_TN(FSDT with transverse normal deformation effect) does, which allows us to improve the through-the-thickness distributions of displacements and stresses via the recovery procedure. The thermal stresses obtained by the present theory are compared with those of the FSDT_TN and three-dimensional elasticity.

• Journal of Korean Society of Steel Construction
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• v.9 no.3 s.32
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• pp.333-340
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• 1997

This paper will expand the third-order shear deformation theory by the double-Fourier series and reduce to the solution of a system of ordinary differential equations in time, which are integrated numerically using Newmark's direct integration method and clarify the undamped dynamic responses for the cross-ply and antisymmetric angle-ply laminated composite plates and shells with simply supported boundary condition. Numerical results for deflections are presented showing the effect of side-to-thickness ratio, aspect ratio, material anisotropy, and lamination scheme.

• Journal of Korean Society of Steel Construction
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• v.10 no.2 s.35
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• pp.317-326
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• 1998

This paper describes a reduced finite element formulation for nonlinear transient heat transfer analysis based on Lanczos Algorithm. In the proposed reduced formulation all material nonlinearities of irradiation boundary element are included using the pseudo force method and numerical time integration of the reduced formulation is conducted by Galerkin method. The results of numerical examples demonstrate the applicability and the accuracy of the proposed method for the nonlinear transient heat transfer analysis.

• 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 Computational Structural Engineering Institute of Korea
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• v.17 no.1
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• pp.21-30
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• 2004

This study deals with free vibrations of laminated composite structures with a channel section using finite element method. In this paper, the mixed finite element method using Lagrangian and Hermite interpolation functions is adopted and a high-order plate theory is used to analyze laminated composite non-prismatic folded plates with a channel section more accurately for free vibration. The theory accounts for parabolic distribution of the transverse shear stress and requires no shear correction factors supposed in the first-order plate theory. An 32×32 matrix is assembled to transform the system element matrices from the local to global coordinates using a coordinate transformation matrix, in which an eighth drilling degree of freedom (DOF) per node is appended to the existing 7-DOF system. The results in this study are compared with those of available literatures for the conventional and first-order plate theory. Sample studies are carried out for various layup configurations and length-thickness ratio, and geometric shapes of plates. The significance of the high-order plate theory in analyzing complex composite structures with a channel section is enunciated in this paper.

• Journal of KSNVE
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• v.8 no.1
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• pp.132-138
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• 1998

The dynamic response of symmetric cross-ply and angle-ply composite laminated plates under impact loads is investigated using a higher order shear deformation theory. A modified Hertz law is used to predict the impact loads and a four node finite element is used to model the plate. By using a higer order shear deformation theory, the out-of-plane shear stresses, which can be a crucial factor in the failure of composite plates, are determined with significant accuracy. This is accomplished by using a stress recovery technique using the in-plane stresses. The results compared with previous investigations showed good agreement. It can be seen that this method of analyzing impact problems is more efficient than current three dimensional methods in terms of time and expense.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.1
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• pp.65-76
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• 1994

A higher-oder laminated plate theory including the effect of transverse shear deformation is developed to calculate the gross response and the detailed stress distribution. The theory satisfies the continuity condition of transverse shear stress, and accounts for parabolic variation of the transverse shear stresses through the thickness of each layer. Exact closed-ply laminates are obtained and the results are compared with three-dimensional elasticity solutions and a simple higher-order theory solutions. The results of the present work exhibit acceptable accuracy when compared to the three-dimensional elasticity solutions.

• Journal of the Earthquake Engineering Society of Korea
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• v.10 no.5 s.51
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• pp.35-48
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• 2006

The object of this study is to propose the efficient method for analyzing the building floors subjected to the loading with high frequency contents. For this purpose, the method for mesh division and the selection of master DOF for FE model of building floors with these loadings are studied. Also, it is verified that the availability of thin plate element that is used by structural engineers for the modelling of the building floor of which the span-thickness ratio is usually ten times and over. And the possibility and limit of the equivalent plate which is already studied by other researcher for the multi-layer plate are investigated. At last, proposed modelling method is examined by the example structure.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.20 no.1
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• pp.29-37
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• 2007

This study deals with displacement analysis of anisotropic folded structures with triangular elements and quadrilateral elements. When folded plates are analyzed, triangular elements as well as quadrilateral elements are needed for conveniences of modelling. However, using triangular elements is not a simple problem. A simple formulation is presented which allows a quadrilateral element to degenerate into a triangular element. Therefore it can easily be used for computational simplicity and avoided complexities on mixed use of triangular element and quadrilateral element. In this paper, a high-order shear deformation theory using only Lagrangian interpolation functions and drilling degrees of freedom for folded plates are utilized for more accurate analysis. Especially, various results of anisotropic laminated and folded composite structures with triangular element and quadrilateral element show the structural behavior characteristics of them.