• 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.

• Steel and Composite Structures
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• 제27권6호
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• pp.789-801
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• 2018

A weak-form formulation of finite annular prism methods (FAPM) based on Reissner's mixed variational theorem (RMVT), is developed for the quasi three-dimensional (3D) static analysis of two-directional functionally graded (FG) circular plates with various boundary conditions and under mechanical loads. The material properties of the circular plate are assumed to obey either a two-directional power-law distribution of the volume fractions of the constituents through the radial-thickness surface or an exponential function distribution varying doubly exponentially through it. These FAPM solutions of the loaded FG circular plates with both simply-supported and clamped edges are in excellent agreement with the solutions obtained using the 3D analytical approach and two-dimensional advanced plate theories available in the literature.

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

• Steel and Composite Structures
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• 제11권5호
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• pp.359-374
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• 2011

In this paper, the influence of fibre orientation and aspect ratio on stability analysis of simply supported skew plates subjected to in plane loading is studied by using a four noded hybrid plate finite element. The formulation of the element is based on Hellinger-Reissner variational principle. The element is developed by combining a hybrid plane stress element and a hybrid plate element. Some numerical problems are solved and the effects of skew angle, aspect ratio, fibre orientation and loading type on the critical buckling loads are highlighted.

• 전산구조공학
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• 제3권3호
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• pp.101-111
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• 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.

• 한국공간구조학회논문집
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• 제7권5호
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• pp.67-74
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• 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.

• Structural Engineering and Mechanics
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• 제40권1호
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• pp.121-148
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• 2011

Closed form solutions for equilibrium and flexibility matrices of the Mindlin-Reissner theory based eight-node rectangular plate bending element (MRP8) using Integrated Force Method (IFM) are presented in this paper. Though these closed form solutions of equilibrium and flexibility matrices are applicable to plate bending problems with square/rectangular boundaries, they reduce the computational time significantly and give more exact solutions. Presented closed form solutions are validated by solving large number of standard square/rectangular plate bending benchmark problems for deflections and moments and the results are compared with those of similar displacement-based eight-node quadrilateral plate bending elements available in the literature. The results are also compared with the exact solutions.

• 한국공간구조학회논문집
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• 제14권2호
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• pp.59-68
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• 2014

A study on the vibration and buckling analyses of laminated composite plates is described in this paper. In order to carry out the analyses of laminated composite plates, a NURBS-based isogeometric general plate element based on Reissner-Mindlin (RM) theory is developed. The non-uniform rational B-spline (NURBS) is used to represent the geometry of plate and the unknown displacement field and therefore, all terms required in this element formulation are consistently derived by using NURBS basis function. Numerical examples are conducted to investigate the accuracy and reliability of the present plate element. From numerical results, the present plate element can produce the isogeometric solutions with sufficient accuracy. Finally, the present isogeometric solutions are provided as future reference solutions.

• Advances in materials Research
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• 제12권2호
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• pp.83-100
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• 2023

In this paper, sandwich plate, constructed with orthotropic and isotropic composite materials, is analyzed to obtain the static and harmonic behavior. The analysis is done by using ANSYS APDL FEM tool. A solid-shell 190 and an 8-node solid 185 elements are employed for face and core material respectively to analyze the plate. Results was attained by using Reissner-Mindlin theory. Effect of increasing thickness ratio of face sheet to depth of the plate is presented on static, vibration and harmonic response on the sheet and the results are discussed briefly. Published work in open domain was used to validate the results and observed excellent agreement. It can be stated that proposed model presents results with remarkable accuracy. Results are obtained to reduce the weight of the plate and minimizing the vibration amplitudes.

• Smart Structures and Systems
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• 제13권1호
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• pp.111-135
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• 2014

Based on the Reissner mixed variational theorem (RMVT), finite rectangular layer methods (FRLMs) are developed for the three-dimensional (3D) linear buckling analysis of simply-supported, fiber-reinforced composite material (FRCM) and functionally graded material (FGM) sandwich plates subjected to bi-axial compressive loads. In this work, the material properties of the FGM layers are assumed to obey the power-law distributions of the volume fractions of the constituents through the thickness, and the plate is divided into a number of finite rectangular layers, in which the trigonometric functions and Lagrange polynomials are used to interpolate the in- and out-of-plane variations of the field variables of each individual layer, respectively, and an h-refinement process is adopted to yield the convergent solutions. The accuracy and convergence of the RMVT-based FRLMs with various orders used for expansions of each field variables through the thickness are assessed by comparing their solutions with the exact 3D and accurate two-dimensional ones available in the literature.