• Smart Structures and Systems
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• v.16 no.5
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• pp.781-806
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• 2015

A unified formulation of finite layer methods (FLMs), based on the Reissner mixed variational theorem (RMVT), is developed for the three-dimensional (3D) coupled electro-elastic analysis of simply-supported, functionally graded piezoelectric material (FGPM) plates with open- and closed-circuit surface conditions and under electro-mechanical loads. In this formulation, the material properties of the plate are assumed to obey an exponent-law varying exponentially through the thickness coordinate, 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 primary field variables of each individual layer, respectively, such as the elastic displacement, transverse shear and normal stress, electric potential, and normal electric displacement components. The relevant orders used for expanding these variables in the thickness coordinate can be freely chosen as the linear, quadratic and cubic orders. Four different mechanical/electrical loading conditions applied on the top and bottom surfaces of the plate are considered, and the corresponding coupled electro-elastic analysis of the loaded FGPM plates is undertaken. The accuracy and convergence rate of the RMVT-based FLMs are assessed by comparing their solutions with the exact 3D piezoelectricity ones available in the literature.

• Steel and Composite Structures
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• v.22 no.1
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• pp.161-182
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• 2016

A state space differential reproducing kernel (DRK) method is developed for the three-dimensional (3D) analysis of functionally graded material (FGM) axisymmetric circular plates with simply-supported and clamped edges. The strong formulation of this 3D elasticity axisymmetric problem is derived on the basis of the Reissner mixed variational theorem (RMVT), which consists of the Euler-Lagrange equations of this problem and its associated boundary conditions. The primary field variables are naturally independent of the circumferential coordinate, then interpolated in the radial coordinate using the early proposed DRK interpolation functions, and finally the state space equations of this problem are obtained, which represent a system of ordinary differential equations in the thickness coordinate. The state space DRK solutions can then be obtained by means of the transfer matrix method. The accuracy and convergence of this method are examined by comparing their solutions with the accurate ones available in the literature.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.4
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• pp.559-566
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• 2003

In this study, we present a new highly accurate two-dimensional curved composite beam element. The present element, which is based on the Hellinger-Reissner variational principle and classical lamination theory, employs consistent stress parameters corresponding to cubic displacement polynomials with additional nodeless degrees to resolve the numerical difficulties due to the spurious constraints. The stress parameters are eliminated and the nodeless degrees are condensed out to obtain the (9x9) element stiffness matrix. It should be noted that the stacking sequences without transverse deformation to the load plane makes a two dimensional analysis of curved composite beams practically useful . Several numerical examples confirm the superior locking-free behavior of the present higher-order laminated curved beam element.

• Proceedings of the Korean Society For Composite Materials Conference
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• 2000.11a
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• pp.173-176
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• 2000

Finite element model based on the Naghdi's shell theory in the general tensor-based form is formulated in the present study. Partial mixed variational functional for assumed strain is formulated in order to avoid the severe locking troubles known as transverse shear and membrane locking. The proposed assumed strain element in general tensor Naghdi's shell model provides very accurate solutions for thin shells in benchmark problems. In additions, linear elastic constitutive equations are given in the general curvilinear coordinate system including anisotropic layered structures. Thus laminated composited shell structures are easily analyzed in the present formulation.

• Journal of Aerospace System Engineering
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• v.17 no.1
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• pp.24-32
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• 2023

This paper studied HART II in descending flight using rotorcraft analysis code based on geometrically exact beam (GEB) model. The present GEB model expressed by a mixed variational formulation could capture the geometrically nonlinear behavior of the blade without arbitrary assumptions. In previous results, correlation of airloads with structural moments for HART II was not as good as blade deflections. However, in present results, predictions of airloads and structural loads are fairly correlated with measured data.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.16 no.2
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• pp.165-172
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• 2003

In this study, a new and efficient harmonic axisymmetric shell element for static and dynamic analysis Is proposed. The present element considering shear strain is based on a modified mixed variational principle in which the independent unknowns are only the Quantities prescribable at the shell edges. Unlike existing hybrid-mixed axisymmetric shell elements, the present element introduces additional nodeless degrees for displacement field Interpolation In order to enhance the numerical performance. The stress parameters are eliminated by the stationary condition and the nodeless degrees are condensed out by the Guyan reduction. Through several numerical examples, the hybrid-miked shell element with the additional nodeless degrees and the consistent stress parameters is shown to be efficient and yield very accurate results for static and vibration analysis.