• Structural Engineering and Mechanics
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• 제51권5호
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• pp.867-891
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• 2014

An equivalent single layer trigonometric shear deformation theory taking into account transverse shear deformation effect as well as transverse normal strain effect is presented for static flexure of cross-ply laminated composite and sandwich plates. The inplane displacement field uses sinusoidal function in terms of thickness coordinate to include the transverse shear deformation effect. The cosine function in thickness coordinate is used in transverse displacement to include the effect of transverse normal strain. The kinematics of the present theory is much richer than those of the other higher order shear deformation theories, because if the trigonometric term (involving thickness coordinate z) is expanded in power series, the kinematics of higher order theories (which are usually obtained by power series in thickness coordinate z) are implicitly taken into account to good deal of extent. Governing equations and boundary conditions of the theory are obtained using the principle of virtual work. The closed-form solutions of simply supported cross-ply laminated composite and sandwich plates have been obtained. The results of present theory are compared with those of the classical plate theory (CPT), first order shear deformation theory (FSDT), higher order shear deformation theory (HSDT) of Reddy and exact three dimensional elasticity theory wherever applicable. The results predicted by present theory are in good agreement with those of higher order shear deformation theory and the elasticity theory.

• Geomechanics and Engineering
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• 제11권5호
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• pp.671-690
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• 2016

This work presents a static flexure analysis of laminated composite plates by utilizing a higher order shear deformation theory in which the stretching effect is incorporated. The axial displacement field utilizes sinusoidal function in terms of thickness coordinate to consider the transverse shear deformation influence. The cosine function in thickness coordinate is employed in transverse displacement to introduce the influence of transverse normal strain. The highlight of the present method is that, in addition to incorporating the thickness stretching effect (${\varepsilon}_z{\neq}0$), the displacement field is constructed with only 5 unknowns, as against 6 or more in other higher order shear and normal deformation theory. Governing equations of the present theory are determined by employing the principle of virtual work. The closed-form solutions of simply supported cross-ply and angle-ply laminated composite plates have been obtained using Navier solution. The numerical results of present method are compared with those of the classical plate theory (CPT), first order shear deformation theory (FSDT), higher order shear deformation theory (HSDT) of Reddy, higher order shear and normal deformation theory (HSNDT) and exact three dimensional elasticity theory wherever applicable. The results predicted by present theory are in good agreement with those of higher order shear deformation theory and the elasticity theory. It can be concluded that the proposed method is accurate and simple in solving the static bending response of laminated composite plates.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2003년도 봄 학술발표회 논문집
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• pp.261-268
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• 2003

A first order shear deformable Loop-subdivision triangular element which can handle transverse shear deformation of moderately thick shell is developed. The developed element is general since it includes the effect of transverse shear deformation and has standard six degrees of freedom per node.(three translations and three rotations) The quartic box-spline function is employed as interpolation basis function. Numerical examples for the benchmark problems are analyzed in order to assess the performance of the newly developed subdivision shell element. Both in the uniform and in the distorted mesh configurations.

• Geomechanics and Engineering
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• 제16권2호
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• pp.141-150
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• 2018

In this current work a quasi 3D "trigonometric shear deformation theory" is proposed and discussed for the dynamic of thick orthotropic plates. Contrary to the classical "higher order shear deformation theories" (HSDT) and the "first shear deformation theory" (FSDT), the constructed theory utilizes a new displacement field which includes "undetermined integral terms" and presents only three "variables". In this model the axial displacement utilizes sinusoidal mathematical function in terms of z coordinate to introduce the shear strain impact. The cosine mathematical function in terms of z coordinate is employed in vertical displacement to introduce the impact of transverse "normal deformation". The motion equations of the model are found via the concept of virtual work. Numerical results found for frequency of "flexural mode", mode of shear and mode of thickness stretch impact of dynamic of simply supported "orthotropic" structures are compared and verified with those of other HSDTs and method of elasticity wherever considered.

• Structural Engineering and Mechanics
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• 제65권4호
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• pp.423-434
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• 2018

In present work, both the hyperbolic shear deformation theory and stress function concept are used to study the mechanical and thermal stability responses of functionally graded (FG) plates resting on elastic foundation. The accuracy of the proposed formulation is checked by comparing the computed results with those predicted by classical plate theory (CPT), first-order shear deformation theory (FSDT) and higher-order shear deformation theory (HSDT). Moreover, results demonstrate that the proposed formulation can achieve the same accuracy of the existing HSDTs which have more number of governing equations.

• Advances in aircraft and spacecraft science
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• 제7권2호
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• pp.115-134
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• 2020

This paper proposes a bending analysis for a functionally graded piezoelectric (FGP) plate through utilizing a two-variable shear deformation plate theory under simply-supported edge conditions. The number of unknown functions used in this theory is only four. The electric potential distribution is assumed to be a combination of a cosine function along the cartesian coordinate. Applying the analytical solutions of FGP plate by using Navier's approach and the principle of virtual work, the equilibrium equations are derived. The paper also discusses thoroughly the impact of applied electric voltage, plate's aspect ratio, thickness ratio and inhomogeneity parameter. Results are compared with the analytical solution obtained by classical plate theory, first-order-shear deformation theory, higher-order shear deformation plate theories and quasi-three-dimensional sinusoidal shear deformation plate theory.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2007년도 정기 학술대회 논문집
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• pp.663-668
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• 2007

An enhanced first shear deformation theory for composite plate is developed. The detailed process is as follows. Firstly, the theory is formulated by modifying higher order zigzag theory. That is, the higher order theory is separated into the warping function representing the higher order terms and lower order terms. Secondly, the relationships between higher order zig-zag field and averaged first shear deformation field based on the Reissner-Mindlin's plate theory are derived. Lastly, the effective shear modulus is calculated by minimizing error between higher order energy and first order energy. Then the governing equation of FSDT is solved by substituting shear modulus into effective shear modulus. The recovery processing with the nodal unknown obtained from governing equation is performed. The accuracy of the present proposed theory is demonstrated through numerical examples. The proposed method will serve as a powerful tool in the prediction of laminated composite plate.

• 복합신소재구조학회 논문집
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• 제1권3호
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• pp.1-9
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• 2010

본 연구에서는 Lagrangian 및 Hermite 보간함수를 혼합정식화한 유한요소법과 다양한 전단변형함수로 등방성, 대칭 적층 및 샌드위치판 모델을 제시하였다. 제시된 전단변형이론은 판의 상하면에서 전단응력이 0이 되는 다항식, 삼각함수, 쌍곡삼각함수 및 지수함수로 구성되어 있다. 모든 전단변형함수는 해석해, 정해 및 기발표된 유한요소 결과치와 비교하였으며, 합리적인 정확도를 갖는 것으로 예측되었다. 특히, 지수형태의 전단변형함수(Karama et al. 2003; Aydogu 2009)가 적층 및 샌드위치판 해석에 있어서 상대적으로 가장 우수한 결과를 보였다.

• 한국산학기술학회논문지
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• 제12권11호
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• pp.5347-5356
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• 2011

본 연구에서는 Lagrangian/Hermite 보간함수를 혼합정식화한 유한요소법과 다양한 전단변형함수로 역대칭 앵글-플라이 샌드위치판 모델을 비교하였다. 제시된 전단변형함수는 판의 상하면에서 전단응력이 0이 되는 다항식, 삼각함수, 쌍곡삼각함수 및 지수함수로 구성되어 있다. 모든 전단변형함수는 해석해(Analytical solution)와 비교하였으며, 합리적인 정확도를 갖는 것으로 예측되었다. 특히, 지수형태의 전단변형함수가 복합면재를 갖는 샌드위치판 해석에 있어서 상대적으로 가장 우수한 결과를 보였다.

• Korea-Australia Rheology Journal
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• 제15권2호
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• pp.63-73
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• 2003

An experimental technique was developed to determine the strain-rate in a tensile specimen. Then one can calculate the transient isothermal elongational viscosity. Both shear and elongational viscosities were measured to study the effect of shear and elongational fields on the flow properties. The comparison between these viscosities shows that the onset of rapid viscosity growth as crystallization solidification proceeds occurs at about the same value of time at very small deformation rates (0.0028 and 0.0047 $s^{-1}$). The comparison of these measured viscosities as functions of shear and elongational Hencky strains also reveals that the onset of rapid viscosity growths starts at critical Hencky strain values. The behaviour of steady shear viscosity as function of temperature sweep was also explored at three different low shear rates. Finally, the influence of changing oscillatory frequencies and strain rates was also investigated.