• Structural Engineering and Mechanics
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• 제36권5호
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• pp.625-642
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• 2010

The Integrated Force Method (IFM) is a novel matrix formulation developed for analyzing the civil, mechanical and aerospace engineering structures. In this method all independent/internal forces are treated as unknown variables which are calculated by simultaneously imposing equations of equilibrium and compatibility conditions. This paper presents a new 12-node serendipity quadrilateral plate bending element MQP12 for the analysis of thin and thick plate problems using IFM. The Mindlin-Reissner plate theory has been employed in the formulation which accounts the effect of shear deformation. The performance of this new element with respect to accuracy and convergence is studied by analyzing many standard benchmark plate bending problems. The results of the new element MQP12 are compared with those of displacement-based 12-node plate bending elements available in the literature. The results are also compared with exact solutions. The new element MQP12 is free from shear locking and performs excellent for both thin and moderately thick plate bending situations.

• 한국구조물진단유지관리공학회 논문집
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• 제8권2호
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• pp.147-158
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• 2004

많은 장점을 가진 복합재료를 사용한 보강판에 대하여 지금까지 많은 연구자들이 변위법에 근거한 등매개변수 평판 요소와 보요소를 결합한 유한요소법을 사용하여왔다. 이러한 유한요소법은 보요소를 평판 요소의 절점에 대한 강성으로 치환하기 때문에 보강재에 대한 국부적인 거동을 파악할 수 없으며 복합적층 구조인 경우 그 적용성이 제한적이다. 따라서, 본 연구에서는 복합재료 보강판의 해석에 있어 보강재 및 판에 대하여 3차원 쉘요소를 사용하여 거동을 분석하고자 한다. 본 연구에서는 Reissner-Mindlin의 1차 전단변형이론을 사용하였다. 그러나 Reissner-Mindlin이론에 의한 등매개변수 평판 휨 요소는 판의 두께가 얇아지는 경우 일반적으로 전단잠김현상과 가상의 제로에너지 모드가 발생하는데 이를 제거하기 위해 대체전단변형률장을 사용하였다. 폭-두께비, 형상비 뿐만아니라 경사판의 경사각 변화에 따른 임의방향 보강재를 갖는 단순지지된 복합적층 구형 및 경사판에 대한 처짐분포를 비교 분석하였다.

• Structural Engineering and Mechanics
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• 제49권6호
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• pp.793-810
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• 2014

This research work deals with the development of a new Triangular finite element for the linear analysis of plate bending with transverse shear effect. It is developed in perspective to building shell elements. The displacements field of the element has been developed by the use of the strain-based approach and it is based on the assumed independent functions for the various components of strain insofar as it is allowed by the compatibility equations. Its formulation uses also concepts related to the fourth fictitious node, the static condensation and analytic integration. It is based on the assumptions of tick plate.s theory (Reissner-Mindlin theory). The element possesses three essential external degrees of freedom at each of the four nodes and satisfies the exact representation of the rigid body modes of displacements. As a result of this approach, a new bending plate finite element (Pep43) which is competitive, robust and efficient.

• Structural Engineering and Mechanics
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• 제33권4호
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• pp.485-502
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• 2009

A new 8-node serendipity quadrilateral plate bending element (MQP8) based on the Mindlin-Reissner theory for the analysis of thin and moderately thick plate bending problems using Integrated Force Method is presented in this paper. The performance of this new element (MQP8) is studied for accuracy and convergence by analyzing many standard benchmark plate bending problems. This new element MQP8 performs excellent in both thin and moderately thick plate bending situations. And also this element is free from spurious/zero energy modes and free from shear locking problem.

• Structural Engineering and Mechanics
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• 제26권6호
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• pp.725-739
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• 2007

In recent years there are many plate bending elements that emerged for solving both thin and thick plates. The main features of these elements are that they are based on mix formulation interpolation with discrete collocation constraints. These elements passed the patch test for mix formulation and performed well for linear analysis of thin and thick plates. In this paper a member of this family of elements, namely, the Discrete Reissner-Mindlin (DRM) is further extended and developed to analyze both thin and thick plates with geometric nonlinearity. The Von K$\acute{a}$rm$\acute{a}$n's large displacement plate theory based on Lagrangian coordinate system is used. The Hu-Washizu variational principle is employed to formulate the stiffness matrix of the geometrically Nonlinear Discrete Reissner-Mindlin (NDRM). An iterative-incremental procedure is implemented to solve the nonlinear equations. The element is then tested for plates with simply supported and clamped edges under uniformly distributed transverse loads. The results obtained using the geometrically NDRM element is then compared with the results of available analytical solutions. It has been observed that the NDRM results agreed well with the analytical solutions results. Therefore, it is concluded that the NDRM element is both reliable and efficient in analyzing thin and thick plates with geometric non-linearity.

• Structural Engineering and Mechanics
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• 제76권4호
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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.

• 한국강구조학회 논문집
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• 제16권3호통권70호
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• pp.295-303
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• 2004

본 연구에서는 등방성 및 복합적층판 해석을 위해 추가변형률을 갖는 개선된 4절점 Reissner-Mindlin 평판휨요소를 제안하였다. 전단잠김현상과 가상적인 제로에너지모드를 제거하기 위해 비적합 변위모드와 Bubble 함수식에 근거한 새로운 형태의 전단변형률을 추가함으로써 횡방향 전단거동을 개선하였다. Andelfinger와 Ramm(1993)이 제시한 기본적인 추가변형률은 면내거동을 개선시키고자 그대로 적용하였다. 1차전단변형이론에 근거한 새로 개발된 4절점 평판요소를 '14EASP'라 명하였다. 14EASP 유한요소의 특징과 성능을 평가하고자 몇가지의 수치해석예제를 적용하였으며, 다른 유한요소 및 해석적인 해와 비교하였다. 그 결과 본 연구에서 제안한 14EASP는 보다 안정적이고, 수렴성이 빠르며, 특히 요소형상이 왜곡된 경우에도 정확한 결과를 도출하였다.

• Structural Engineering and Mechanics
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• 제6권6호
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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.

• Architectural research
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• 제18권2호
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• pp.65-74
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• 2016

Free vibration analysis of plates and shells is carried out by using isogeometric approach. For this purpose, an isogeometric shell element based on Reissner-Mindlin (RM) shell theory is developed. Non-uniform rational B-spline surface (NURBS) definition is introduced to represent the geometry of shell and it is also used to derive all terms required in the isogeometric element formulation. New anchor positions are proposed to calculate the shell normal vector. Gauss integration rule is used for the formation of stiffness and mass matrices. The proposed shell element is then used to examine vibrational behaviours of plate and shell structures. From numerical results, it is found to be that reliable natural frequencies and associated mode shapes can be predicted by the present isogeometric RM shell element.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제17권2호
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• pp.67-85
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• 2013

Reproducing Polynomial Particle Method (RPPM) is one of meshless methods that use meshes minimally or do not use meshes at all. In this paper, the RPPM is employed for free vibration analysis of shear-deformable plates of the first order shear deformation model (FSDT), called Reissner-Mindlin plate. For numerical implementation, we use flat-top partition of unity functions, introduced by Oh et al, and patchwise RPPM in which approximation functions have high order polynomial reproducing property and the Kronecker delta property. Also, we demonstrate that our method is highly effective than other existing results for various aspect ratios and boundary conditions.