• Earthquakes and Structures
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• v.11 no.1
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• pp.63-82
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• 2016

In this study, the bending and dynamic behaviors of laminated composite plates is examined by using a refined shear deformation theory and developed for a bending analysis of orthotropic laminated composite plates under various boundary conditions. The displacement field of the present theory is chosen based on nonlinear variations in the in-plane displacements through the thickness of the plate. By dividing the transverse displacement into the bending and shear parts and making further assumptions, the number of unknowns and equations of motion of the present theory is reduced and hence makes them simple to use. In the analysis, the equation of motion for simply supported thick laminated rectangular plates is obtained through the use of Hamilton's principle. Numerical results for the bending and dynamic behaviors of antisymmetric cross-ply laminated plate under various boundary conditions are presented. The validity of the present solution is demonstrated by comparison with solutions available in the literature. Numerical results show that the present theory can archive accuracy comparable to the existing higher order shear deformation theories that contain more number of unknowns.

• Archives of Plastic Surgery
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• v.39 no.4
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• pp.284-290
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• 2012

Open reduction and anatomic reduction can create better function for the temporomandibular joint, compared with closed treatment in mandible fracture surgery. Therefore, the double miniplate fixation technique via mini-retromandibular incision was used in order to make the most stable fixation when performing subcondylar fracture surgery. Those approaches provide good visualization of the subcondyle from the posterior edge of the ramus, allow the surgeon to work perpendicularly to the fracture, and enable direct fracture management. Understanding the biomechanical load in the fixation of subcondylar fractures is also necessary in order to optimize fixation methods. Therefore, we measured the biomechanical loads of four different plate fixation techniques in the experimental model regarding mandibular subcondylar fractures. It was found that the loads measured in the two-plate fixation group with one dynamic compression plate (DCP) and one adaption plate showed the highest deformation and failure loads among the four fixation groups. The loads measured in the one DCP plate fixation group showed higher deformation and failure loads than the loads measured in the two adaption plate fixation group. Therefore, we conclude that the selection of the high profile plate (DCP) is also important in order to create a stable load in the subcondylar fracture.

• Structural Engineering and Mechanics
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• v.70 no.5
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• pp.601-621
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• 2019

This study presents a comprehensive nonlinear dynamic approach to investigate the linear and nonlinear vibration of sandwich plates fabricated from functionally graded materials (FGMs) resting on an elastic foundation. Higher-order shear deformation theory and Hamilton's principle are employed to obtain governing equations. The Runge-Kutta method is employed together with the commercially available mathematical software MAPLE 14 to solve the set of nonlinear dynamic governing equations. Method validity is evaluated by comparing the results of this study and those of previous research. Good agreement is achieved. The effects of temperature change on frequencies are investigated considering various temperatures and various volume fraction index values, N. As the temperature increased, the plate frequency decreased, whereas with increasing N, the plate frequency increased. The effects of the side-to-thickness ratio, c/h, on natural frequencies were investigated. With increasing c/h, the frequencies increased nonlinearly. The effects of foundation stiffness on nonlinear vibration of the sandwich plate were also studied. Backbone curves presenting the variation of maximum displacement with respect to plate frequency are presented to provide insight into the nonlinear vibration and dynamic behavior of FGM sandwich plates.

• Steel and Composite Structures
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• v.22 no.2
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• pp.257-276
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• 2016

In this paper, a new simple higher-order shear deformation theory for bending and free vibration analysis of functionally graded (FG) plates is developed. The significant feature of this formulation is that, in addition to including a sinusoidal variation of transverse shear strains through the thickness of the plate, it deals with only three unknowns as the classical plate theory (CPT), instead of five as in the well-known first shear deformation theory (FSDT) and higher-order shear deformation theory (HSDT). A shear correction factor is, therefore, not required. Equations of motion are derived from Hamilton's principle. Analytical solutions for the bending and free vibration analysis are obtained for simply supported plates. The accuracy of the present solutions is verified by comparing the obtained results with those predicted by classical theory, first-order shear deformation theory, and higher-order shear deformation theory. Verification studies show that the proposed theory is not only accurate and simple in solving the bending and free vibration behaviours of FG plates, but also comparable with the other higher-order shear deformation theories which contain more number of unknowns.

• Structural Engineering and Mechanics
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• v.73 no.1
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• pp.97-108
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• 2020

This study presents a 4 node, 11 DOF/node plate element based on higher order shear deformation theory for lamina composite plates. The theory accounts for parabolic distribution of the transverse shear strain through the thickness of the plate. Differential field equations of composite plates are obtained from energy methods using virtual work principle. Differential field equations of composite plates are obtained from energy methods using virtual work principle. These equations were transformed into the operator form and then transformed into functions with geometric and dynamic boundary conditions with the help of the Gâteaux differential method, after determining that they provide the potential condition. Boundary conditions were determined by performing variational operations. By using the mixed finite element method, plate element named HOPLT44 was developed. After coding in FORTRAN computer program, finite element matrices were transformed into system matrices and various analyzes were performed. The current results are verified with those results obtained in the previous work and the new results are presented in tables and graphs.

• Structural Engineering and Mechanics
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• v.60 no.4
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• pp.547-565
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• 2016

In this work a new 3-unknown non-polynomial shear deformation theory for the buckling and vibration analyses of functionally graded material (FGM) sandwich plates is presented. The present theory accounts for non-linear in plane displacement and constant transverse displacement through the plate thickness, complies with plate surface boundary conditions, and in this manner a shear correction factor is not required. The main advantage of this theory is that, in addition to including the shear deformation effect, the displacement field is modelled with only 3 unknowns as the case of the classical plate theory (CPT) and which is even less than the first order shear deformation theory (FSDT). The plate properties are assumed to vary according to a power law distribution of the volume fraction of the constituents. Equations of motion are derived from the Hamilton's principle. Analytical solutions of natural frequency and critical buckling load for functionally graded sandwich plates are obtained using the Navier solution. The results obtained for plate with various thickness ratios using the present non-polynomial plate theory are not only substantially more accurate than those obtained using the classical plate theory, but are almost comparable to those obtained using higher order theories with more number of unknown functions.

• Structural Engineering and Mechanics
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• v.5 no.6
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• pp.853-865
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• 1997

The design of robust plate and shell elements has been a very challenging area for several decades. The main difficulty has been the shear locking phenomenon in plate elements and the shear and membrane locking phenomena together in the shell elements. Among the various artifices or devices which are used to develop elements free of these problems is the field-consistency approach. In this paper this approach is reviewed, It turns out that not only Mindlin type elements but also elements based on higher-order theories could be developed using the technique.

• Proceedings of the KSME Conference
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• 2000.11a
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• pp.426-431
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• 2000

A decoupled thermo-piezoelectric-mechanical model of composite laminates with surface bonded piezoelectric actuators, subjected to externally applied load, temperature change load, electric field load is developed. The governing differential equations are obtained by applying the principle of free energy and variational techniques. A higher order zigzag theory displacement field is employed to accurately capture the transverse shear and normal effects in laminated composite plates of arbitrary thickness.

• Structural Engineering and Mechanics
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• v.19 no.3
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• pp.297-320
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• 2005

In recent years the pure displacement formulation for plate elements has not been as popular as other formulations. We revisit the pure displacement formulation for shear-deformable plate elements and propose a family of N-node, displacement-compatible, fully-integrated, pure-displacement, triangular, Mindlin plate elements, MIN-N. The development has been motivated by the relative simplicity of the pure displacement formulation and by the success of the existing 3-node plate element, MIN3. The formulation of MIN3 is generalized to obtain the MIN-N family, which possesses complete, fully compatible kinematic fields, in which the interpolation functions for transverse displacement are one degree higher than those for rotations. General element-level formulas for the thin-limit Kirchhoff constraints are developed. The 6-node, 18 degree-of-freedom element MIN6, with cubic displacement and quadratic rotations, is implemented and tested extensively. Numerical results show that MIN6 exhibits good performance for both static and dynamic analyses in the linear, elastic regime. The results illustrate that the fully-integrated MIN6 element has excellent performance in the thin limit, even for coarse meshes, and that it does not require shear relaxation.

• Journal of Korean Society of Steel Construction
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• v.9 no.4 s.33
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• pp.601-609
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• 1997

Bending and vibration results for a laminated plate base on a simplified higher-order plate theory with four variables are presented. Assuming a constant in-plane rotation tensor through the thickness in Reddy's higher-order shear deformation theory it is shown that a simpler higher-order theory can be obtained with the reduction of one variable without significant loss in the accuracy. This simple higher-order shear deformation theory is then used for predicting the natural frequencies and deflection of simply-supported laminated composite plates. The results obtained for antisymmetrical laminated composite plates compare favorably with third-order and first-order shear deformation theory. The information presented should be useful to composite-structure designers, to researchers seeking to obtain better correlation between theory and experiment and to numerical analysts in checking out their programs.