• Structural Engineering and Mechanics
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• v.14 no.5
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• pp.575-593
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• 2002

Based on the Mindlin plate theory, a refined discrete 15-DOF triangular laminated composite plate finite element RDTMLC with the re-constitution of the shear strain is proposed. For constituting the element displacement function, the exact displacement function of the Timoshenko's laminated composite beam as the displacement on the element boundary is used to derive the element displacements. The proposed element can be used for the analysis of both moderately thick and thin laminated composite plate, and the convergence for the very thin situation can be ensured theoretically. Numerical examples presented show that the present model indeed possesses the properties of higher accuracy for anisotropic laminated composite plates and is free of locking even for extremely thin laminated plates.

• Journal of the Society of Disaster Information
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• v.12 no.1
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• pp.62-68
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• 2016

In this study, the impact problems are brought up and the formulation by isoparametric element is attempted for the purpose of analyzing the response characteristics of laminated plate receiving impact load based on the first-order shear deformation theory expanded from the Mindlin plate theory. The result of static analysis and dynamic analysis is drawn through the numerical analysis rectangular and circular plates of antisymmetric Angle-Ply laminated plate using the finite element method and the analysis on each displacement is compared.

• Structural Engineering and Mechanics
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• v.50 no.2
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• pp.181-199
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• 2014

Locking phenomenon is a mesh problem and can be staved off with mesh refinement. If the studier is not preferred going to the solution with increasing mesh size or the computer memory can stack over flow than using higher order plate finite element or using integration techniques is a solution for this problem. The purpose of this paper is to show the shear locking phenomenon can be avoided by increase low order finite element mesh size of the plates and to study shear locking-free analysis of thick plates using Mindlin's theory by using higher order displacement shape function and to determine the effects of various parameters such as the thickness/span ratio, mesh size on the linear responses of thick plates subjected to uniformly distributed loads. A computer program using finite element method is coded in C++ to analyze the plates clamped or simply supported along all four edges. In the analysis, 4-, 8- and 17-noded quadrilateral finite elements are used. It is concluded that 17-noded finite element converges to exact results much faster than 8-noded finite element, and that it is better to use 17-noded finite element for shear-locking free analysis of plates.

• Earthquakes and Structures
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• v.16 no.3
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• pp.359-368
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• 2019

This paper focuses on the study of dynamic analysis of thick plates resting on Winkler foundation. The governing equation is derived from Mindlin's theory. This study is a parametric analysis of the reflections of the thickness / span ratio, the aspect ratio and the boundary conditions on the earthquake excitations are studied. In the analysis, finite element method is used for spatial integration and the Newmark-${\beta}$ method is used for the time integration. While using finite element method, a new element is used. This element is 17-noded and it's formulation is derived from using higher order displacement shape functions. C++ program is used for the analyses. Graphs are presented to help engineers in the design of thick plates subjected to earthquake excitations. It is concluded that the 17-noded finite element is used in the earthquake analysis of thick plates. It is shown that the changes in the aspect ratio are more effective than the changes in the aspect ratio. The center displacements of the reinforced concrete thick clamped plates for b/a=1, and t/a=0.2, and for b/a=2, and t/a=0.2, reached their absolute maximum values of 0.00244 mm at 3.48 s, and of 0.00444 mm at 3.48 s, respectively.

• Structural Engineering and Mechanics
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• v.49 no.5
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• pp.661-672
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• 2014

Laminated Rectangular plates embedded in elastic foundations are used in many mechanical structures. This study presents an analytical approach for transverse bending analysis of an embedded symmetric laminated rectangular plate using Mindlin plate theory. The surrounding elastic medium is simulated using Pasternak foundation. Adopting the Mindlin plate theory, the governing equations are derived based on strain-displacement relation, energy method and Hamilton's principle. The exact analysis is performed for this case when all four ends are simply supported. The effects of the plate length, elastic medium and applied force on the plate transverse bending are shown. Results indicate that the maximum deflection of the laminated plate decreases when considering an elastic medium. In addition, the deflection of the laminated plate increases with increasing the plate width and length.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2007.04a
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• pp.465-470
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• 2007

In order to investigate the stochastic behavior of Mindlin plate under imperfection in the material and geometrical parameters, a stochastic finite element formulation is proposed. The effects of inter-correlations between random parameters on the response variability are also observed. The contribution from the random Poisson ratio is taken into account adopting a stochastic decomposition scheme. which expands the constitutive matrix into an infinite series of sub-matrices. In order to demonstrate the adequacy of the proposed scheme, a square plate with simple and fixed support is taken as an example, and the results are compared with those given in previous research in the literature as well as with the results of Monte Carlo analysis.

• Structural Engineering and Mechanics
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• v.87 no.3
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• pp.283-296
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• 2023

Free-vibration and buckling analyses of plate problems are investigated with the aid of the strain gradient notation finite element method (SGN-FEM). As SGN-FEM employs physically interpretable polynomials in developing finite elements, parasitic shear sources, which are the cause of shear locking, can be precisely identified and subsequently eliminated. This allows two mutually complementary objectives to be defined in this work, namely, evaluate the efficiency of free-vibration and buckling results provided by corrected models, and study the severity of parasitic shear effects on plate models performance. Parasitic shear are flexural terms erroneously present in shear strain polynomials. It is reviewed here that six parasitic shear terms arise during the formulation of the four-node Mindlin plate element. Two parasitic shear terms have been identified in the in-plane shear strain polynomial while other two have been identified in each of the transverse shear strain polynomials. The element is corrected a-priori, i.e., during development, by simply removing the spurious terms from the shear strain polynomials. The computational implementation of the element in its two versions, namely, containing the parasitic shear terms (PS) and corrected for parasitic shear (SG), allows for assessments of the accuracy of results and of the deleterious effects of parasitic shear in free vibration and buckling analyses. This assessment of the parasitic shear effects is a novelty of this work. Validation of the SG model is done comparing its results with analytical results and results provided by other numerical procedures. Analyses are performed for square plates with different thickness-to-length ratios and boundary conditions. Results for thin plates provided by the PS model do not converge to the correct solutions, which indicates that parasitic shear must be eliminated. That is, analysts should not rely on refinement alone. For thick plates, PS model results can be considered acceptable as deleterious effects are really critical in thin plates. On the other hand, results provided by the SG model converge well for both thin and thick plates. The effectiveness of the SG model is established via high-accuracy results obtained in several examples. It is concluded that corrected SGN-FEM models are efficient alternatives for free-vibration and buckling analysis of Mindlin plate problems, and that precise elimination of parasitic shear is a requirement for sound analyses.

• Journal of KSNVE
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• v.7 no.1
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• pp.127-134
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• 1997

The dynamic stability of classical plates and Mindlin plates subjected to pulsating follower forces is investigated in this paper. Using the finite element method, the induced equation is reduced to that of one with finite degrees of freedom. Then, the multiple scales method is applied to analyze the dynamic instability region. The effects of aspect ratio, Poisson ratio, rotary inertia and shear deformation on the dynamic stability of plates are studied in this paper.

• Structural Engineering and Mechanics
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• v.6 no.6
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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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• v.18 no.2
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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.