• Journal of the Computational Structural Engineering Institute of Korea
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• v.26 no.4
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• pp.255-262
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• 2013

In this paper, a shape design sensitivity analysis(DSA) method is presented for Mindlin plates using an isogeometric approach. The isogeometric method possesses desirable advantages; the representation of exact geometry and the higher order inter-element continuity, which lead to the fast convergence of solution as well as accurate sensitivity results. Unlike the finite element methods using linear shape functions, the isogeometric method considers the exact normal vector and curvature of the CAD geometry, taking advantages of higher order NURBS basis functions. A selective reduced integration(SRI) technique is incorporated to overcome the difficulty of 'shear locking' phenomenon. This simple technique is surprisingly helpful for the accuracy of the isogeometric shape sensitivity without complicated formulation. Through the numerical examples of plate bending problems, the accuracy of the proposed isogeometric analysis method is compared with that of finite element one. Also, the isogeometric shape sensitivity turns out to be very accurate when compared with finite difference sensitivity.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.11 no.12
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• pp.5199-5206
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• 2010

In this paper, we investigate the buckling analysis of laminated composite plates, using a improved assumed natural strain shell element. In order to overcome membrane and shear locking phenomena, the assumed natural strain method is used. The eigenvalues of the laminated composite plates are calculated by varying the width-thickness ratio and angle of fiber. To improve an shell element for buckling analysis, the new combination of sampling points for assumed natural strain method was applied and the refined first-order shear deformation theory which allows the shear deformation without shear correction factor. In order to validate the present solutions, the reference solutions are used and discussed. The results of laminated composite plates under the in-plane shear loading may be the benchmark test for the buckling analysis.

• Structural Engineering and Mechanics
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• v.28 no.5
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• pp.603-633
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• 2008

A four-node plate finite element for the analysis of laminated composites which is developed using strain gradient notation is presented. The element is based on a first-order shear deformation theory and on the equivalent lamina assumption. Strains and stresses can be calculated at different points through the thickness of the plate. They are averaged values due to the equivalent lamina assumption. A shear correction factor is used as the transverse shear strain is taken to be constant over the plate thickness while its actual variation is parabolic. Strain gradient notation, which is physically interpretable, allows for the detailed a-priori analysis of the finite element model. The polynomial expansions are inspected and spurious terms responsible for modeling errors are identified in the shear strains polynomial expansions. The element is corrected by simply removing the spurious terms from the shear strains expansions. The element is implemented into a FORTRAN finite element code in two versions; namely, with and without spurious terms. Results are compared to show the effects of the spurious terms on the solutions. It is also shown that a refined mesh composed of corrected elements provides solutions which approximate very well the analytical solutions, validating the procedure.

• The Journal of the Korean bone and joint tumor society
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• v.16 no.2
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• pp.80-86
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• 2010

Purpose: The skeleton is commonly affected by metastatic cancer. The purpose of this study was to evaluate the results of treating metastatic pathologic fractures in lower extremities using locking plates. Materials and Methods: Between 2004 and 2010, we evaluated 12 patients (13 cases) of metastatic pathologic fractures in lower extremities, treated with the locking plate. Mean patient age was 62.2 years (range, 50-81 years), the locations of the fractures were; proximal femur in 2 cases, femoral mid-shaft in 3, distal femur in 3, proximal tibia in 4, and distal tibia in 1 case. The interval to wheelchair ambulation, pain relief and complications were evaluated. Additionally, we assessed operation time and postoperative blood loss. Results: Mean time from operation to wheelchair ambulation was 3.2 days (range, 1-6 days). Mean VAS scores improved from a preoperative score of 8.1 points (range, 7-9 points) to a score of 2.7 points (range, 2-4 points) at 1 week postoperatively. No early complications associated with surgery were encountered. Mean operation time was 88.4 minutes (range, 70-105 minutes), and mean postoperative blood loss was 246.5 ml (range, 130-320 ml). Conclusion: Internal fixation of metastatic pathologic fractures using a locking plate in the lower extremity can be an effective treatment option in the meta- or diaphyseal area of long bones with massive bony destruction or poor bone stock by offering early ambulation, pain relief and low postoperative complications.

• Journal of the Korean Society of Costume
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• v.61 no.10
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• pp.135-150
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• 2011

The ranking belts for Joseon dynasty officials that are based on references and relics are studied in this paper in terms of architecture, detailed names, and structural changes according to different time. Officials' uniforms consist of hats, clothes, belts, and shoes. Among these, the belt is an important sign that represents the wearer's ranking. The ranking belts of the Joseon dynasty which were brought from Ming at the late stage of the Koryo dynasty became classified as the following four classes : Seo-dai(a rhinoceros' horn, 犀帶), Gum-dai(gold, 金帶), Eun-dai(silver, 銀帶), and Heug-gag-dai(black horn, 黑角帶). A ranking belt consists of a basic belt body and a plaque that represents the wearer's rank. A plaque consists of 20 plates: three front-center plates that represent the Sam-tai(三台) constellation, six front-side plates that represent the Namduyug constellation(南斗六星), seven back plates that represent the Big Dipper(北斗七星), left side Bo(輔), right side Pil(弼), and a couple of Tamie at both ends. The architecture of the belt body; the basic frame for ranking belts, shows some differences between the former and the latter periods of the Joseon dynasty. In the former period, the belt had a pair of a buckle so that the wearers were able to adjust the belt size. But later, the belt didn't have the buckles to adjust the belt size and consequently it only performed a locking or unlocking function. Therefore, the belts in the latter period were longer than normal and one size fit all. In addition to the functional change of buckles, the shapes of the ranking belts show changes from the round shape to the square shape as time goes on.

• Steel and Composite Structures
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• v.21 no.2
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• pp.373-394
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• 2016

The postbuckling behavior of laminated composite plates and shells, subjected to various shear loadings, is presented, using a modified 8-ANS method. The finite element, based on a modified first-order shear deformation theory, is further improved by the combined use of assumed natural strain method. We analyze the influence of the shell element with the various location and number of enhanced membrane and shear interpolation. Using the assumed natural strain method with proper interpolation functions, the present shell element generates neither membrane nor shear locking behavior even when full integration is used in the formulation. The effects of various types of lay-ups, materials and number of layers on initial buckling and postbuckling response of the laminated composite plates and shells for various shear loading have been discussed. In addition, the effect of direction of shear load on the postbuckling behavior is studied. Numerical results and comparisons of the present results with those found in the literature for typical benchmark problems involving symmetric cross-ply laminated composites are found to be excellent and show the validity of the developed finite element model. The study is relevant to the simulation of barrels, pipes, wing surfaces, aircrafts, rockets and missile structures subjected to intense complex loading.

• Steel and Composite Structures
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• v.35 no.1
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• pp.129-145
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• 2020

In typical, structural topology optimization plays a significant role to both increase stiffness and save mass of structures in the resulting design. This study contributes to a new numerical approach of topologically optimal design of Mindlin-Reissner plates considering Winkler foundation and mathematical formulations of multi-directional variable thickness of the plate by using multi-materials. While achieving optimal multi-material topologies of the plate with multi-directional variable thickness, the weight information of structures in terms of effective utilization of the material at the appropriate thickness location may be provided for engineers and designers of structures. Besides, numerical techniques of the well-established mixed interpolation of tensorial components 4 element (MITC4) is utilized to overcome a well-known shear locking problem occurring to thin plate models. The well-founded mathematical formulation of topology optimization problem with variable thickness Mindlin-Reissner plate structures by using multiple materials is derived in detail as one of main achievements of this article. Numerical examples verify that variable thickness Mindlin-Reissner plates on Winkler foundation have a significant effect on topologically optimal multi-material design results.

• Structural Engineering and Mechanics
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• v.76 no.4
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• pp.435-449
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• 2020

This work presents the formulation of the isogeometric collocation method to solve the strong form equation of a unified and integrated approach of Reissner Mindlin plate theory (UI-RM). In this plate theory model, the total displacement is expressed in terms of bending and shear displacements. Rotations, curvatures, and shear strains are represented as the first, the second, and the third derivatives of the bending displacement, respectively. The proposed formulation is free from shear locking in the Kirchhoff limit and is equally applicable to thin and thick plates. The displacement field is approximated using the B-splines functions, and the strong form equation of the fourth-order is solved using the collocation approach. The convergence properties and accuracy are demonstrated with square plate problems of thin and thick plates with different boundary conditions. Two approaches are used for convergence tests, e.g., increasing the polynomial degree (NELT = 1×1 with p = 4, 5, 6, 7) and increasing the number of element (NELT = 1×1, 2×2, 3×3, 4×4 with p = 4) with the number of control variable (NCV) is used as a comparable equivalent variable. Compared with DKMQ element of a 64×64 mesh as the reference for all L/h, the problem analysis with isogeometric collocation on UI-RM plate theory exhibits satisfying results.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.17 no.3
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• pp.279-293
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• 2004

The analysis of linear static and free vibration problems of isotropic and laminated composite plates and shells is performed by the improved 9-node shell element with the new strain displacement relationship. In that relationship, the effect of new additional terms between the bending strain and displacement has been investigated in the warping problem. Natural co ordinate based strains, stresses and constitutive equations are used. The assumed natural strain method is used to alleviate both membrane and shear locking behavior from the element. The Lanczos method is employed in the calculation of the eigenvalues of laminated composite structures and the Gauss integration rule is adopted to evaluate the mass matrix. The numerical examples are compared with the analytical solutions to validate the current formulation and the results presented could be useful for the understanding of the behaviour of laminates under free vibration conditions.

• Structural Engineering and Mechanics
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• v.13 no.4
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• pp.387-410
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• 2002

Formulation of an 8 nodes assumed strain shell element is presented for the analysis of shells. The stiffness matrix based on the Mindlin-Reissner theory is analytically integrated through the thickness. The element is free of membrane and shear locking behavior by using the assumed strain method such that the element performs very well in modeling of thin shell structures. The material is assumed to be isotropic and laminated composite. The element has six degrees of freedom per node and can model the stiffened plates and shells. A great number of numerical testing carried out for the validation of present 8 node shell element are in good agreement with references.