• Proceedings of the KSME Conference
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• 대한기계학회 2001년도 춘계학술대회논문집A
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• pp.680-685
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• 2001

In this paper, RKPM is extended for solving moderately thick and thin structures. General Timoshenko beam and Mindlin plate theory are used far formulation. Shear locking is the main difficulty in analysis of these kinds of structures. Shear relaxation factor, which is formulated using the difference between bending and shear strain energy, is introduced to overcome shear locking. Analysis results obtained reveal that RKPM using introduced method is free of locking and very effectively applicable to deeply as well as shallowly beams and plates.

• 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.

• Structural Engineering and Mechanics
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• 제53권1호
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• pp.105-130
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• 2015

In this paper, the classical continuum mechanics is adopted and modified to be consistent with the unique behavior of micro/nano solids. At first, some kinematical principles are discussed to illustrate the effect of the discrete nature of the microstructure of micro/nano solids. The fundamental equations and relations of the modified couple stress theory are derived to illustrate the microstructural effects on nanostructures. Moreover, the effect of the material surface energy is incorporated into the modified continuum theory. Due to the reduced coordination of the surface atoms a residual stress field, namely surface pretension, is generated in the bulk structure of the continuum. The essential kinematical and kinetically relations of nano-continuums are derived and discussed. These essential relations are used to derive a size-dependent model for Mindlin functionally graded (FG) nano-plates. An analytical solution is derived to show the feasibility of the proposed size-dependent model. A parametric study is provided to express the effect of surface parameters and the effect of the microstructure couple stress on the bending behavior of a simply supported FG nano plate.

• 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.

• Journal of the Korean Society for Advanced Composite Structures
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• 제1권4호
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• pp.1-5
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• 2010

In this study, it is presented analysis results of bending problems in the anisotropic cantilever thick plates and the anisotropic laminated cantilever thin plates bending problems. Finite element method in this analysis was used. Both Kirchoff's assumptions and Mindlin assumptions are used as the basic governing equations of bending problems in the anisotropic laminated plates. The analysis results are compared between the anisotropic laminated cantilever thick plates and the anisotropic laminated cantilever thin plates for the variations of thickness-width ratios.

• Journal of the Korea Academia-Industrial cooperation Society
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• 제11권6호
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• pp.2284-2291
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• 2010

In this paper, we investigate the vibration analysis of plates, using an 8-node shell element that accounts for the transverse shear strains and rotary inertia. The forced vibration analysis of plates subjected to arbitrary loading is investigated. In order to overcome membrane and shear locking phenomena, the assumed natural strain method is used. To improve an 8-node shell element for forced vibration analysis, the new combination of sampling points for assumed natural strain method was applied. The refined first-order shear deformation theory based on Reissner-Mindlin theory which allows the shear deformation without shear correction factor and rotary inertia effect to be considered is adopted for development of 8-node assumed strain shell element. In order to validate the finite element numerical solutions, the reference solutions of plates are presented. Results of the present theory show good agreement with the reference solution. In addition the effect of damping is investigated on the forced vibration analysis of plates.

• KSCE Journal of Civil and Environmental Engineering Research
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• 제13권2호
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• pp.151-160
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• 1993

This paper is concerned with formulations of the hierarchical $C^{\circ}$-plate element on the basis of Reissner-Mindlin plate theory. On reason for the development of the aforementioned element based on Integrals of Legendre shape functions is that it is still difficult to construct elements based on h-version concepts which are accurate and stable against the shear locking effects. An adaptive mesh refinement and selective p-distribution of the polynomial degree using hp-version of the finite element method are proposed to verify the superior convergence and algorithmic efficiency with the help of the simply supported L-shaped plate problems.

• Journal of the Society of Naval Architects of Korea
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• 제33권1호
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• pp.77-89
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• 1996

An enormous amount of efforts has been devoted to the development of finite elements for the bending problem of thick plates, especially based on Mindlin plate theory. Here, an approximate Constant Shear Angle Theory is usually used to take a transverse shear deformation of thick plate into consideration, which cannot be effectively considered the influence of transversal warping of cross-section with an increase of thickness. It might be the best way to represent the exact cross-sectional warping of the plate. The overall objective of this study is to develop a new formulation of plate including shear deformation and transversal warping, to perform extensive parametric studies comparing its results with those from Mindlin plate formulation, and to gain further insight into the influence of shear deformation and transversal warping of thick plate.

• KSCE Journal of Civil and Environmental Engineering Research
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• 제7권4호
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• pp.83-90
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• 1987

The applications of reduced integration technique, addition of nonconforming modes, and their coupling to the Mindlin plate elements to improve their basic behavior are reviewed and the establishment of a series of new plate elements by combined use of these schemes are presented in this paper. The element formulation is based upon quadratic Mindlin plate concept. The results obtained by new elements converged to the exact solutions very rapidly as the mesh is refined and showed reliable solutions even for severely distorted meshes. The new elements have the requisite numbers of zero eigenvalues associated with rigid body modes to avoid the spurious zero energy modes. These elements are shown to be applicable to the wide range of plate problems, giving a high accuracy for both thick and thin plates.

• Structural Engineering and Mechanics
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• 제20권4호
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• pp.477-493
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• 2005

In case of Mindlin plate, not only the bending deformation but also the shear behavior is allowed. While the bending and shear stiffness are given in the same order in terms of elastic modulus, they are in different order in case of plate thickness. Accordingly, bending and shear contributions have to be dealt with independently if the stochastic finite element analysis is performed on the Mindlin plate taking into account of the uncertain plate thickness. In this study, a formulation is suggested to give the response variability of Mindlin plate taking into account of the uncertainties in elastic modulus as well as in the thickness of plate, a geometrical parameter, and their correlation. The cubic function of thickness and the correlation between elastic modulus and thickness are incorporated into the formulation by means of the modified auto- and cross-correlation functions, which are constructed based on the general formula for n-th joint moment of random variables. To demonstrate the adequacy of the proposed formulation, a plate with various boundary conditions is taken as an example and the results are compared with those obtained by means of classical Monte Carlo simulation.