• Structural Engineering and Mechanics
• /
• 제49권6호
• /
• pp.793-810
• /
• 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
• /
• 제30권4호
• /
• pp.387-402
• /
• 2008

The Integrated Force Method (IFM) has been developed in recent years for the analysis of civil, mechanical and aerospace engineering structures. In this method all independent or internal forces are treated as unknown variables which are calculated by simultaneously imposing equations of equilibrium and compatibility conditions. The solution by IFM needs the computation of element equilibrium and flexibility matrices from the assumed displacement, stress-resultant fields and material properties. This paper presents a general purpose code for the automatic generation of element equilibrium and flexibility matrices for plate bending elements using the Integrated Force Method. Kirchhoff and the Mindlin-Reissner plate theories have been employed in the code. Paper illustrates development of element equilibrium and flexibility matrices for the Mindlin-Reissner theory based four node quadrilateral plate bending element using the Integrated Force Method.

• 한국강구조학회 논문집
• /
• 제16권3호통권70호
• /
• pp.295-303
• /
• 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
• /
• 제9권5호
• /
• pp.433-448
• /
• 2000

In this paper we deal with the numerical solution of the Reissner-Mindlin plate problem with the use of high order finite elements. In previous papers we have solved the problem using approximation spaces of Serendipity type, in order to minimize the number of internal degrees of freedom. Since further numerical experiences have evidenced that the addition of bubble functions improved the quality of the results we have modified the previous family of hierarchic finite elements, adding internal degrees of freedom, to make a systematic analysis of their performance. Of course, more degrees of freedom are introduced. Nonetheless the numerical results indicate that the reduction of the error outnumbers the increase of degrees of freedom and therefore bubble plus elements are preferable.

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

• Steel and Composite Structures
• /
• 제48권5호
• /
• pp.583-597
• /
• 2023

This paper introduces a novel approach to multi-material topology optimization (MTO) targeting in-plane bi-directional functionally graded (IBFG) non-uniform thickness Reissner-Mindlin plates, employing an alternative active phase approach. The mathematical formulation integrates a first shear deformation theory (FSDT) to address compliance minimization as the objective function. Through an alternating active-phase algorithm in conjunction with the block Gauss-Seidel method, the study transforms a multi-phase topology optimization challenge with multi-volume fraction constraints into multiple binary phase sub-problems, each with a single volume fraction constraint. The investigation focuses on IBFG materials that incorporate adequate local bulk and shear moduli to enhance the precision of material interactions. Furthermore, the well-established mixed interpolation of tensorial components 4-node elements (MITC4) is harnessed to tackle shear-locking issues inherent in thin plate models. The study meticulously presents detailed mathematical formulations for IBFG plates in the MTO framework, underscored by numerous numerical examples demonstrating the method's efficiency and reliability.

• Structural Engineering and Mechanics
• /
• 제76권4호
• /
• pp.435-449
• /
• 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.

• 전산구조공학
• /
• 제3권3호
• /
• pp.101-111
• /
• 1990

p-version 유한요소법을 사용한 바닥 슬래브의 탄성해석은 어떤 종류의 요형모서리, 개구 그리고 손상단면을 갖는 점에서 응력특이성을 수반하게 된다. Reissner-Mindlin의 평판이론에 근거한 C.deg.- 평판 계층요소를 사용한 결과가 이론치 및 참고문헌에 발표된 수치해석값과 비교되었다. h-, p-와 hp-version의 수렴속도는 전체적 차원에서의 자유도 증가에 따른 에너지 노름값을 사용하여 예측할 수 있다. 만약에 자유도의 항으로 나타내지는 정확도를 여러 해석방법을 비교하는 기준으로 삼으면 본 연구에서 새로 제안되는 p-version 유한요소해석법의 근사해는 종래의 h-version에 근거하여 현재 까지 발표된 어떤 것 보다 훨씬 효율적 접근방법이라 하겠다. 해석예로는 150.deg. 둔각을 갖는 마름모꼴평판과 손상단면을 갖는 정방형평판이 사용되었다.

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

• 한국공간구조학회논문집
• /
• 제7권5호
• /
• pp.67-74
• /
• 2007

본 연구에서는 판 구조물의 최적위상을 찾기 위한 비대칭 층을 가지는 인공재료모델을 이용한 위상최적화기법을 제시하였다. 구절점 판요소를 형성하기 위하여 판의 일차전단변형을 고려하는 Reissner-Mindlin 판이론이 도입되었다. 최소화하고자 하는 변형에너지를 목적함수로 하고 구조물의 초기부피를 제약함수로 채택하였다 인공재료모델에 존재하는 다공성물질의 구멍의 크기를 조절하기 위하여 최적정기준법을 바탕으로 하는 크기조절알고리듬을 도입하였다. 제시된 위상최적화 기법의 성능을 조사하기 위하여 수치예제를 수행하였다. 수치해석결과로부터 제시된 위상최적화기법은 판구조물의 최적위상을 도출하는데 매우 효과적인 것으로 나타났다. 특히 제시된 비대칭 층모델은 판구조물의 보강재를 보다 실제적으로 도출하는데 유용할 것으로 나타났다.