• Proceedings of the Korean Society For Composite Materials Conference
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• 2004.04a
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• pp.279-283
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• 2004

Thermal postbuckling and vibration analyses of functionally graded plates (FG plates) are performed. The nonlinear finite element equation based on the first-order shear deformation plate theory is formulated for the FG plate. The von Karman strain-displacement relation is used to account for the thermal large deflection. The incremental method considering the effect of the initial deflection and the initial stress is adopted for temperature-dependent material properties of functionally graded materials. The numerical result shows characteristics of the thermal postbuckling and vibration of FG plates in the pre- and post- buckled regions.

• Steel and Composite Structures
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• v.3 no.3
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• pp.213-229
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• 2003

A high precision shear deformable triangular element has been proposed for free vibration analysis of composite trapezoidal plates. The element has twelve nodes at the three sides and four nodes inside the element. Initially the element has fifty-five degrees of freedom, which has been reduced to forty-eight by eliminating the degrees of freedom of the internal nodes through static condensation. Plates having different side ratios (b/a), boundary conditions, thickness ratios (h/a=0.01, 0.1 and 0.2), number of layers and fibre angle orientations have been analyzed by the proposed shear locking free element. Trapezoidal laminate with concentrated mass at the centre has also been analyzed. An efficient mass lumping scheme has been recommended, where the effect of rotary inertia has been included. For validation of the present element and formulation few results of isotropic trapezoidal plate and square composite laminate have been compared with those obtained from open literatures. The numerical results for composite trapezoidal laminate have been given as new results.

• Structural Engineering and Mechanics
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• v.20 no.4
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• pp.435-450
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• 2005

Here, the dynamic instability characteristics of aero-thermo-mechanically stressed functionally graded plates are investigated using finite element procedure. Temperature field is assumed to be a uniform distribution over the plate surface and varied in thickness direction only. Material properties are assumed to be temperature dependent and graded in the thickness direction according to simple power law distribution. For the numerical illustrations, silicon nitride/stainless steel is considered as functionally graded material. The aerodynamic pressure is evaluated based on first-order high Mach number approximation to the linear potential flow theory. The boundaries of the instability region are obtained using the principle of Bolotin's method and are conveniently represented in the non-dimensional excitation frequency-load amplitude plane. The variation dynamic instability width is highlighted considering various parameters such as gradient index, temperature, aerodynamic and mechanical loads, thickness and aspect ratios, and boundary condition.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.25 no.6
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• pp.505-512
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• 2012

In this paper, an efficient yet accurate method for the thermal stress analysis using a first order shear deformation theory(FSDT) is presented. The main objective herein is to systematically modify transverse shear strain energy through the mixed variational theorem(MVT). In the mixed formulation, independent transverse shear stresses are taken from the efficient higher-order zigzag plate theory, and the in-plane displacements are assumed to be those of the FSDT. Moreover, a smooth parabolic distribution through the thickness is assumed in the transverse normal displacement field in order to consider a transverse normal deformation. The resulting strain energy expression is referred to as an enhanced first order shear deformation theory, which is obtained via the mixed variational theorem with transverse normal deformation effect(EFSDTM_TN). The EFSDTM_TN has the same computational advantage as the FSDT_TN(FSDT with transverse normal deformation effect) does, which allows us to improve the through-the-thickness distributions of displacements and stresses via the recovery procedure. The thermal stresses obtained by the present theory are compared with those of the FSDT_TN and three-dimensional elasticity.

• Journal of Korean Society of Steel Construction
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• v.16 no.3 s.70
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• pp.295-303
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• 2004

In this paper, an improved four-node Reissner-Mindlin plate-bending element with enhanced assumed strain field is presented for the analysis of isotropic and laminated composite plates. To avoid the shear locking and spurious zero energy modes, the transverse shear behavior is improved by the addition of a new enhanced shear strain based on the incompatible displacement mode approach and bubble function. The "standard" enhanced strain fields (Andelfinger and Ramm, 1993) are also employed to improve the in-plane behaviors of the plate elements. The four-node quadrilateral element derived using the first-order shear deformation theory is designated as "14EASP". Several applications are investigated to assess the features and the performances of the proposed element. The results are compared with other finite element solutions and analytical solutions. Numerical examples show that the element is stable, invariant, passes the patch test, and yields good results especially in highly distorted regimes.

• Structural Engineering and Mechanics
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• v.44 no.4
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• pp.431-448
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• 2012

In this paper, the first-order shear deformation theory (FSDT) (Mindlin) for continuum incorporating surface energy is exploited to study the static behavior of ultra-thin functionally graded (FG) plates. The size-dependent mechanical response is very important while the plate thickness reduces to micro/nano scales. Bulk stresses on the surfaces are required to satisfy the surface balance conditions involving surface stresses. Unlike the classical continuum plate models, the bulk transverse normal stress is preserved here. By incorporating the surface energies into the principle of minimum potential energy, a series of continuum governing differential equations which include intrinsic length scales are derived. The modifications over the classical continuum stiffness are also obtained. To illustrate the application of the theory, simply supported micro/nano scaled rectangular films subjected to a transverse mechanical load are investigated. Numerical examples are presented to present the effects of surface energies on the behavior of functionally graded (FG) film, whose effective elastic moduli of its bulk material are represented by the simple power law. The proposed model is then used for a comparison between the continuum analysis of FG ultra-thin plates with and without incorporating surface effects. Also, the transverse shear strain effect is studied by a comparison between the FG plate behavior based on Kirchhoff and Mindlin assumptions. In our analysis the residual surface tension under unstrained conditions and the surface Lame constants are expected to be the same for the upper and lower surfaces of the FG plate. The proposed model is verified by previous work.

• Structural Engineering and Mechanics
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• v.85 no.1
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• pp.1-14
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• 2023

The use of functionally graded materials in applications involving severe thermal gradients is quickly gaining acceptance in the composite mechanics community, the aerospace and aircraft industry. In the present study, a refined sandwich plate model is applied to study the free vibration analysis of porous functionally graded material (FGM) sandwich plates with various distribution rate of porosity. Two types of common FG sandwich plates are considered. The first sandwich plate is composed of two FG material (FGM) face sheets and a homogeneous ceramic or metal core. The second one consists of two homogeneous fully metal and ceramic face sheets at the top and bottom, respectively, and a FGM core. The displacement field of the present theory is chosen based on nonlinear variations in the in-plane displacements through the thickness of the sandwich plate. 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 sandwich plates is obtained using Hamilton's principle. In order to present the effect of the variation of the porosity distribution on the dynamic behavior of the FGM sandwich plates, new mixtures are proposed which take into account different rate of porosity distribution between the ceramic and the metal. The present method is applicable to study the dynamic behavior of FGM plates and sandwich plates. The frequencies of two kinds of FGM sandwich structures are analyzed and discussed. Several numerical results have been compared with the ones available in the literature.

• Structural Engineering and Mechanics
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• v.14 no.3
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• pp.245-262
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• 2002

The free vibration analysis of stiffened laminated composite plates has been performed using the layered (zigzag) finite element method based on the first order shear deformation theory. The layers of the laminated plate is modeled using nine-node isoparametric degenerated flat shell element. The stiffeners are modeled as three-node isoparametric beam elements based on Timoshenko beam theory. Bilinear in-plane displacement constraints are used to maintain the inter-layer continuity. A special lumping technique is used in deriving the lumped mass matrices. The natural frequencies are extracted using the subspace iteration method. Numerical results are presented for unstiffened laminated plates, stiffened isotropic plates, stiffened symmetric angle-ply laminates, stiffened skew-symmetric angle-ply laminates and stiffened skew-symmetric cross-ply laminates. The effects of fiber orientations (ply angles), number of layers, stiffener depths and degrees of orthotropy are examined.

• Proceedings of the Korean Society For Composite Materials Conference
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• 1999.11a
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• pp.234-238
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• 1999

This study suggests the design of the functionally gradient composite, [0/90/0/core]$_s$ cross-ply laminate, to prevent stress concentration induced from the difference of rigidity between the bone and the artificial hip joint and to reinforce the wear property of the surface and the expectation of their mechanical properties. First, the four-point bending test is done about wet bones and dry bones to know the mechanical properties of the cortical bones. In result, the wet bone shows the viscoelastic behavior and the dry bone shows the elastic behavior. Moreover, we expect the properties of the proposed gradient composites as a function of carbon fiber volume fraction in each layer to apply Halpin-Tsai equation, CLPT(classical laminate plate theory), and Bernoulli beam theory etc. and decide the thickness ratio of each lamina in order to match Young's modulus of the anisotropic cortical bone with the proposed gradient composites.

• Structural Engineering and Mechanics
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• v.27 no.4
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• pp.457-475
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• 2007

Analysis of transverse stresses at layer interfaces in a composite laminate has always been a challenging task. Composite structures possess highly irregular material properties at layer interfaces, which cause high shear stresses. Classical Plate Theory and First Order Shear Deformation Theory (FSDT) use post computing to calculate transverse stresses. This paper presents Reissner Mixed Variational Theorem (RMVT) based finite element model to carry out layer-wise analysis of composite laminates. Selective integration scheme has been used. The formulation has been validated by solving numerical examples and comparing the results with those published in the literature.