• Steel and Composite Structures
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• 제26권5호
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• pp.557-572
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• 2018

In this paper, a refined higher-order shear deformation theory including the stretching effect is developed for the analysis of bending analysis of the simply supported functionally graded (FG) sandwich plates resting on elastic foundation. This theory has only five unknowns, which is even less than the other shear and normal deformation theories. The theory presented is variationally consistent, without the shear correction factor. The present one has a new displacement field which introduces undetermined integral variables. Equations of motion are obtained by utilizing the Hamilton's principles and solved via Navier's procedure. The convergence and the validation of the proposed theoretical numerical model are performed to demonstrate the efficacy of the model.

• Geomechanics and Engineering
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• 제14권6호
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• pp.519-532
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• 2018

In this work, two dimensional (2D) and quasi three-dimensional (quasi-3D) HSDTs are proposed for bending and free vibration investigation of functionally graded (FG) plates using hyperbolic shape function. Unlike the existing HSDT, the proposed theories have a novel displacement field which include undetermined integral terms and contains fewer unknowns. The material properties of the plate is inhomogeneous and are considered to vary continuously in the thickness direction by three different distributions; power-law, exponential and Mori-Tanaka model, in terms of the volume fractions of the constituents. The governing equations which consider the effects of both transverse shear and thickness stretching are determined through the Hamilton's principle. The closed form solutions are deduced by employing Navier method and then fundamental frequencies are obtained by solving the results of eigenvalue problems. In-plane stress components have been determined by the constitutive equations of composite plates. The transverse stress components have been determined by integrating the 3D stress equilibrium equations in the thickness direction of the FG plate. The accuracy of the present formulation is demonstrated by comparisons with the different 2D, 3D and quasi-3D solutions available in the literature.

• Structural Engineering and Mechanics
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• 제68권1호
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• pp.53-66
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• 2018

This paper presents an analysis of the bending, buckling and free vibration of functionally graded sandwich beams resting on elastic foundation by using a refined quasi-3D theory in which both shear deformation and thickness stretching effects are included. The displacement field contains only three unknowns, which is less than the number of parameters of many other shear deformation theories. In order to homogenize the micromechanical properties of the FGM sandwich beam, the material properties are derived on the basis of several micromechanical models such as Tamura, Voigt, Reuss and many others. The principle of virtual works is used to obtain the equilibrium equations. The elastic foundation is modeled using the Pasternak mathematical model. The governing equations are obtained through the Hamilton's principle and then are solved via Navier solution for the simply supported beam. The accuracy of the proposed theory can be noticed by comparing it with other 3D solution available in the literature. A detailed parametric study is presented to show the influence of the micromechanical models on the general behavior of FG sandwich beams on elastic foundation.

• Steel and Composite Structures
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• 제41권5호
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• pp.697-711
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• 2021

In this work, a simple quasi 3-D parabolic shear deformation theory is developed to examine the bending response of antisymmetric cross-ply laminated composite plates under different types of mechanical loading. The main feature of this theory is that, in addition to including the transverse shear deformation and thickness stretching effects, it has only five-unknown variables in the displacement field modeling like Mindlin's theory (FSDT), yet satisfies the zero shear stress conditions on the top and bottom surfaces of the plate without requiring a shear correction factor. The static version of principle of virtual work was employed to derive the governing equations, while the bending problem for simply supported antisymmetric cross-ply laminated plates was solved by a Navier-type closed-form solution procedure. The adequacy of the proposed model is handled by considering the impact of side-to-thickness ratio on bending response of plate through several illustrative examples. Comparison of the obtained numerical results with the other shear deformation theories leads to the conclusion that the present model is more accurate and efficient in predicting the displacements and stresses of laminated composite plates.

• Structural Engineering and Mechanics
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• 제85권5호
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• pp.593-605
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• 2023

This work presents a comparison between analytical and finite element analysis for bending of porous sandwich functionally graded material (FGM) plates. The plate is rectangular and simply supported under static sinusoidal loading. Material properties of FGM are assumed to vary continuously across the face sheets thickness according to a power-law function in terms of the volume fractions of the constituents while the core is homogeneous. Four types of porosity are considered. A refined higher-order shear with normal deformation theory is used. The number of unknowns in this theory is five, as against six or more in other shear and normal deformation theories. This theory assumes the nonlinear variation of transverse shear stresses and satisfies its nullity in the top and bottom surfaces of the plate without the use of a shear correction factor. The governing equations of equilibrium are derived from the virtual work principle. The Navier approach is used to solve equilibrium equations. The constitutive law of the porous FGM sandwich plate is implemented for a 3D finite element through a subroutine in FORTRAN (UMAT) in Abaqus software. Results show good agreement between the finite element model and the analytical method for some results, but the analytical method keeps giving symmetric results even with the thickness stretching effect and load applied to the top surface of the sandwich.

• 대한기계학회논문집A
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• 제41권9호
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• pp.809-815
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• 2017

압력용기 재료로 사용되는 STS 304강은 저온에서 기계적 특성이 우수하지만, 다른 합금과 비교하여 중량이 무겁다. 이러한 문제를 해결하는 방안으로 STS 304강에 콜드 스트레칭(Cold stretching)공법을 사용하는 방법이 있다. 본 연구에서는 ASME 규정에 따라 제작된 콜드 스트레칭 압력용기에서 직접 채취한 콜드 스트레칭부 및 용접부 시험편을 이용하여, 상온 및 $-170^{\circ}C$에서 응력비 0.1과 0.5에 대하여 컴플라이언스법을 이용하여 피로균열진전시험을 수행하였다. 시험결과, 용접부의 피로균열진전속도는 콜드 스트레칭부에 비해 동일 응력확대계수범위에서 빠른 것을 확인하였다. 이러한 결과는 콜드스트레칭 공법을 사용하여 제작한 STS강 압력용기 개발을 위한 기초자료로 활용될 수 있을 것이다.

• Advances in materials Research
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• 제6권1호
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• pp.45-63
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• 2017

In this article, static deflection and buckling of functionally graded (FG) nanoscale beams made of porous material are carried out based on the nonlocal Timoshenko beam model which captures the small scale influences. The exact position of neutral axis is fixed, to eliminate the stretching and bending coupling due to the unsymmetrical material change along the FG nanobeams thickness. The material properties of FG beam are graded through the thickness on the basis of the power-law form, which is modified to approximate the material properties with two models of porosity phases. By employing Hamilton's principle, the nonlocal governing equations of FG nanobeams are obtained and solved analytically for simply-supported boundary conditions via the Navier-type procedure. Numerical results for deflection and buckling of FG nanoscale beams are presented and validated with those existing in the literature. The influences of small scale parameter, power law index, porosity distribution and slenderness ratio on the static and stability responses of the FG nanobeams are all explored.

• Steel and Composite Structures
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• 제27권5호
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• pp.599-611
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• 2018

In this article a four unknown quasi-3D shear deformation theory for the bending analysis of functionally graded (FG) plates is developed. The advantage of this theory is that, in addition to introducing the thickness stretching impact (${\varepsilon}_z{\neq}0$), the displacement field is modeled with only four variables, which is even less than the first order shear deformation theory (FSDT). The principle of virtual work is utilized to determine the governing equations. The obtained numerical results from the proposed theory are compared with the CPT, FSDT, and other quasi-3D HSDTs.

• Structural Engineering and Mechanics
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• 제74권3호
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• pp.365-380
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• 2020

The focus of this paper is to develop an analytical approach based on an efficient shear deformation theory with stretching effect for bending stress analysis of cross-ply laminated composite plates subjected to transverse parabolic load and line load by using a new kinematic model, in which the axial displacements involve an undetermined integral component in order to reduce the number of unknowns and a sinusoidal function in terms of the thickness coordinate to include the effect of transverse shear deformation. The present theory contains only five unknowns and satisfies the zero shear stress conditions on the top and bottom surfaces of the plate without using any shear correction factors. The governing differential equations and its boundary conditions are derived by employing the static version of principle of virtual work. Closed-form solutions for simply supported cross-ply laminated plates are obtained applying Navier's solution technique, and the numerical case studies are compared with the theoretical results to verify the utility of the proposed model. Lastly, it can be seen that the present outlined theory is more accurate and useful than some higher-order shear deformation theories developed previously to study the static flexure of laminated composite plates.

• Steel and Composite Structures
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• 제47권5호
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• pp.551-568
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• 2023

In this research, a new two-dimensional (2D) and quasi three-dimensional (quasi-3D) higher order shear deformation theory is devised to address the bending problem of functionally graded plates resting on an elastic foundation. The displacement field of the suggested theories takes into account a parabolic transverse shear deformation shape function and satisfies shear stress free boundary conditions on the plate surfaces. It is expressed as a combination of trigonometric and exponential shear shape functions. The Pasternak mathematical model is considered for the elastic foundation. The material properties vary constantly across the FG plate thickness using different distributions as power-law, exponential and Mori-Tanaka model. By using the virtual works principle and Navier's technique, the governing equations of FG plates exposed to sinusoidal and evenly distributed loads are developed. The effects of material composition, geometrical parameters, stretching effect and foundation parameters on deflection, axial displacements and stresses are discussed in detail in this work. The obtained results are compared with those reported in earlier works to show the precision and simplicity of the current formulations. A very good agreement is found between the predicted results and the available solutions of other higher order theories. Future mechanical analyses of three-dimensionally FG plate structures can use the study's findings as benchmarks.