• Advances in aircraft and spacecraft science
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• 제6권5호
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• pp.409-426
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• 2019

The aim of the present work is to study the nonlinear behavior of the laminated composite plates under transverse sinusoidal loading using a new inverse trigonometric shear deformation theory, where geometric nonlinearity in the Von-Karman sense is taken into account. In the present theory, in-plane displacements use an inverse trigonometric shape function to account the effect of transverse shear deformation. The theory satisfies the traction free boundary conditions and violates the need of shear correction factor. The governing equations of equilibrium and boundary conditions associated with present theory are obtained by using the principle of minimum potential energy. These governing equations are solved by eight nodded serendipity element having five degree of freedom per node. A square laminated composite plate is considered for the geometrically linear and nonlinear formulation. The numerical results are obtained for central deflections, in-plane stresses and transverse shear stresses. Finite element Codes are developed using MATLAB. The present results are compared with previously published results. It is concluded that the geometrically linear and nonlinear response of laminated composite plates predicted by using the present inverse trigonometric shape function is in excellent agreement with previously published results.

• Advances in materials Research
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• 제5권3호
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• pp.141-169
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• 2016

In this paper, an efficient and simple refined theory is presented for buckling analysis of functionally graded plates. The theory, which has strong similarity with classical plate theory in many aspects, accounts for a quadratic variation of the transverse shear strains across the thickness and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. The mechanical properties of functionally graded material are assumed to vary according to a power law distribution of the volume fraction of the constituents. Governing equations are derived from the principle of minimum total potential energy. The closed-form solutions of rectangular plates are obtained. Comparison studies are performed to verify the validity of present results. The effects of loading conditions and variations of power of functionally graded material, modulus ratio, aspect ratio, and thickness ratio on the critical buckling load of functionally graded plates are investigated and discussed.

• 동력기계공학회지
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• 제14권3호
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• pp.52-57
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• 2010

Interlaminar stresses near the free edges of composite laminates have been analyzed considering wall effects. Interface modeling of bonding layer was introduced to explain the wall effect. Using Lekhnitskii stress functions and the principle of complementary virtual work, the interlaminar stresses were obtained, which satisfied the traction free boundary conditions not only at the free edges, but also at the top and bottom surfaces of laminates. The interface modeling provides not singular stresses but concentrated finite interlaminar stresses. The significant amount of reductions of stresses at the free edge are observed compared to the results without interface modeling. The real stress state can be predicted accurately and the results demonstrate the usefulness of the proposed interface modeling for the strength design of composite laminates.

• Advances in concrete construction
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• 제9권1호
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• pp.43-54
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• 2020

This paper presents an innovative stress-function variational approach in formulating the interfacial shear and normal stresses in an externally bonded concrete joint using carbon fiber-reinforced plastic (CFRP) plies. The joint is subjected to surface traction loadings applied at both ends of the concrete substrate layer. By introducing two interfacial shear and normal stress functions on the CFRP-concrete interface, based on Euler-Bernoulli beam idea and static stress equations of equilibrium, the entire stress fields of the joint were determined. The complementary strain energy was minimized in order to solve the governing equation of the joint. This yields an ordinary differential equation from which the interfacial normal and shear stresses were proposed explicitly, satisfying all the multiple traction boundary conditions. Lamination theory for composite materials was also employed to obtain the interfacial stresses. The proposed approach was validated by the analytic models in the literature as well as through a comprehensive computational code generated by the authors. Furthermore, a numerical verification was carried out via the finite element software ABAQUS. In the end, a scaling analysis was conducted to analyze the interfacial stress field dependence of the joint upon effective issues using the devised code.

• 한국안전학회지
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• 제25권4호
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• pp.42-47
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• 2010

Recently, many techniques have been developed for the inspection of pipelines using guided waves. However, few researches have been made on the application of those techniques for buried underground pipes. Guided wave motions in the buried pipes are somewhat different from those of on-ground pipes which have traction-free (air) boundary condition on outer pipe walls and thus are strongly affected by the mechanical property of the surrounding soils. Therefore, it should be investigated the effect of soil properties on the guided wave behavior in buried pipe. On the other hand, the mechanical property of soil is largely depending on its moisture conditions nevertheless of other influential factors such as void ratio. In this study, the effect of moisture conditions in soils on mode attenuation of guided waves in the buried pipe is investigated. To this end, numerical study is performed to characterize mode attenuation behavior in buried pipes and the effective mode which is suitable for long range inspection is identified.

• Advances in materials Research
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• 제6권1호
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• pp.13-26
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• 2017

In this work we introduce a higher-order hyperbolic shear deformation model for bending and frees vibration analysis of functionally graded beams. In this theory and by making a further supposition, the axial displacement accounts for a refined hyperbolic distribution, and the transverse shear stress satisfies the traction-free boundary conditions on the beam boundary surfaces, so no need of any shear correction factors (SCFs). The material properties are continuously varied through the beam thickness by the power-law distribution of the volume fraction of the constituents. Based on the present refined hyperbolic shear deformation beam model, the governing equations of motion are obtained from the Hamilton's principle. Analytical solutions for simply-supported beams are developed to solve the problem. To verify the precision and validity of the present theory some numerical results are compared with the existing ones in the literature and a good agreement is showed.

• 전산구조공학
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• 제10권3호
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• pp.185-193
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• 1997

탄성 선형 경화 재료로 구성된 복합 구조물의 자유 경계면에서 나타나는 응력 특이도를 평면 변형률 상태에서 계산하였다. 자유 표면력 경계조건과 계면 연속조건을 만족해야하는 지배 탄성 방정식은 2점 경계치문제로 정의되며, 일반 고유치 문제의 해인 고유치가 응력 특이도가 될 것이다. 자유경계면 근처에서 응력 성분을 r/sup s-1/에 비례한다고 가정하여 특정한 s(고유치)를 구하는 고유치 문제를 뉴톤향상법과 사격법을 사용하여 수치적으로 해를 구하였다.

• Wind and Structures
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• 제22권3호
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• pp.291-305
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• 2016

In this paper, a refined shear deformation plate theory which eliminates the use of a shear correction factor was presented for FG sandwich plates composed of FG face sheets and an isotropic homogeneous core. The theory accounts for parabolic distribution of the transverse shear strains and satisfies the zero traction boundary conditions on the surfaces of the plate. The mechanical properties of the plate are assumed to vary continuously in the thickness direction by a simple power-law distribution in terms of the volume fractions of the constituents. Based on the present refined shear deformation plate theory, the governing equations of equilibrium are derived from the principle of virtual displacements. Numerical illustrations concern buckling behavior of FG sandwiches plates with Metal-Ceramic composition. Parametric studies are performed for varying ceramic volume fraction, volume fraction profiles, Boundary condition, and length to thickness ratios. The accuracy of the present solutions is verified by comparing the obtained results with the existing solutions.

• Steel and Composite Structures
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• 제18권1호
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• pp.187-212
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• 2015

In this paper, various four variable refined plate theories are presented to analyze vibration of temperature-dependent functionally graded (FG) plates. By dividing the transverse displacement into bending and shear parts, the number of unknowns and governing equations for the present model is reduced, significantly facilitating engineering analysis. These theories account for parabolic, sinusoidal, hyperbolic, and exponential distributions of the transverse shear strains and satisfy the zero traction boundary conditions on the surfaces of the plate without using shear correction factors. Power law material properties and linear steady-state thermal loads are assumed to be graded along the thickness. Uniform, linear, nonlinear and sinusoidal thermal conditions are imposed at the upper and lower surface for simply supported FG plates. Equations of motion are derived from Hamilton's principle. Analytical solutions for the free vibration analysis are obtained based on Fourier series that satisfy the boundary conditions (Navier's method). Non-dimensional results are compared for temperature-dependent and temperature-independent FG plates and validated with known results in the literature. Numerical investigation is conducted to show the effect of material composition, plate geometry, and temperature fields on the vibration characteristics. It can be concluded that the present theories are not only accurate but also simple in predicting the free vibration responses of temperature-dependent FG plates.

• Structural Engineering and Mechanics
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• 제65권4호
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• pp.453-464
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• 2018

In this paper, an efficient higher-order shear deformation theory is presented to analyze thermomechanical bending of temperature-dependent functionally graded (FG) plates resting on an elastic foundation. Further simplifying supposition are made to the conventional HSDT so that the number of unknowns is reduced, significantly facilitating engineering analysis. These theory account for hyperbolic distributions of the transverse shear strains and satisfy the zero traction boundary conditions on the surfaces of the plate without using shear correction factors. Power law material properties and linear steady-state thermal loads are assumed to be graded along the thickness. Nonlinear thermal conditions are imposed at the upper and lower surface for simply supported FG plates. Equations of motion are derived from the principle of virtual displacements. Analytical solutions for the thermomechanical bending analysis are obtained based on Fourier series that satisfy the boundary conditions (Navier's method). Non-dimensional results are compared for temperature-dependent FG plates and validated with those of other shear deformation theories. Numerical investigation is conducted to show the effect of material composition, plate geometry, and temperature field on the thermomechanical bending characteristics. It can be concluded that the present theory is not only accurate but also simple in predicting the thermomechanical bending responses of temperature-dependent FG plates.