scholarly journals Investigation of porosity effect on flexural analysis of doubly curved FGM conoids

2019 ◽  
Vol 26 (1) ◽  
pp. 435-448
Author(s):  
Md Irfan Ansari ◽  
Ajay Kumar ◽  
Danuta Barnat-Hunek ◽  
Zbigniew Suchorab ◽  
Bartłomiej Kwiatkowski
Keyword(s):  
Mathematical Model ◽  
Shear Strain ◽  
Transverse Shear ◽  
Volume Fraction ◽  
Current Model ◽  
Lower Surface ◽  
Functionally Graded ◽  
Transverse Shear Strain ◽  
Flexural Analysis ◽  
Doubly Curved

AbstractThe flexural analysis of doubly curved functionally graded porous conoids was performed in the present paper. The porosities inside functionally graded materials (FGMs) can occur during the fabrication and lead to the occurrence of micro-voids in the materials. The mathematical model includes expansion of Taylor’s series up to the third degree in thickness coordinate and normal curvatures in in-plane displacement fields. Since there is a parabolic variation in transverse shear strain deformation across the thickness coordinate, the shear correction factor is not necessary. The condition of zero-transverse shear strain at upper and lower surface of conoidal shell is implemented in the present model. The improvement in the 2D mathematical model enables to solve problems of moderately thick FGM porous conoids. The distinguishing feature of the present shell from the other shells is that maximum transverse deflection does not occur at its centre. The improved mathematical model was implemented in finite element code written in FORTRAN. The obtained numerical results were compared with the results available in the literature. Once validated, the current model was employed to study the effect of porosity, boundary condition, volume fraction index, loading pattern and others geometric parameters.

Static analysis of carbon nanotube-reinforced FG shells using an efficient solid-shell element with parabolic transverse shear strain

2019 ◽  
Vol 37 (3) ◽  
pp. 823-849 ◽  
Author(s):  
Abdessalem Hajlaoui ◽  
Elouni Chebbi ◽  
Mondher Wali ◽  
Fakhreddine Dammak
Keyword(s):  
Shear Strain ◽  
Transverse Shear ◽  
Shell Element ◽  
Functionally Graded ◽  
Shell Structures ◽  
Element Formulation ◽  
Transverse Shear Strain ◽  
Solid Shell ◽  
Static Behavior ◽  
Content Type

Purpose This paper aims to study the static behavior of carbon nanotubes (CNTs) reinforced functionally graded shells using an efficient solid-shell element with parabolic transverse shear strain. Four different types of reinforcement along the thickness are considered. Design/methodology/approach Furthermore, the developed solid-shell element allows an efficient and accurate analysis of CNT-reinforced functionally graded shells under linear static conditions. Findings The validity and accuracy of the developed solid-shell element are illustrated through the solution of deflection and stress distribution problems of shell structures taken from the literature. The influences of some geometrical and material parameters on the static behavior of shell structures are discussed. Originality/value The finite element formulation is based on a modified first-order enhanced solid-shell element formulation with an imposed parabolic shear strain distribution through the shell thickness in the compatible strain part. This formulation guarantees a zero transverse shear stress on the top and bottom surfaces of the shell and the shear correction factors is no longer needed.

On the nominal transverse shear strain to characterize the severity of creasing

TAPPI Journal ◽  
2018 ◽  
Vol 17 (04) ◽  
pp. 231-240
Author(s):  
Douglas Coffin ◽  
Joel Panek
Keyword(s):  
Shear Strain ◽  
Transverse Shear ◽  
Elastic Limit ◽  
Experimental Results ◽  
Transverse Shear Strain ◽  
Maximum Strain ◽  
Machine Direction ◽  
Engineering Approach ◽  
Wide Range ◽  
Analytic Expression

A transverse shear strain was utilized to characterize the severity of creasing for a wide range of tooling configurations. An analytic expression of transverse shear strain, which accounts for tooling geometry, correlated well with relative crease strength and springback as determined from 90° fold tests. The experimental results show a minimum strain (elastic limit) that needs to be exceeded for the relative crease strength to be reduced. The theory predicts a maximum achievable transverse shear strain, which is further limited if the tooling clearance is negative. The elastic limit and maximum strain thus describe the range of interest for effective creasing. In this range, cross direction (CD)-creased samples were more sensitive to creasing than machine direction (MD)-creased samples, but the differences were reduced as the shear strain approached the maximum. The presented development provides the foundation for a quantitative engineering approach to creasing and folding operations.

Dynamic Behavior of FGM Doubly Curved Panel due to Mechanical Loading

2019 ◽  
Vol 950 ◽  
pp. 200-204
Author(s):  
Guang Ping Zou ◽  
Nadiia Dergachova
Keyword(s):  
Mechanical Loading ◽  
Volume Fraction ◽  
Equivalent Stress ◽  
Functionally Graded ◽  
Excitation Mode ◽  
Simply Supported ◽  
Curved Panel ◽  
Von Mises Equivalent Stress ◽  
Von Mises ◽  
Doubly Curved

This study presents the dynamic response analyze of a simply supported and isotropic functionally graded (FG) double curved panel under mechanical loading. The aim of the research was to investigate mechanical behavior in a FGM curved panel due to different excitation mode of dynamic loading. The novelty of this research is an investigation of von Mises equivalent stress distribution in double curved panel due to different excitation mode. Computed results are found to agree well with the results reported in the literature. Moreover, influence of volume fraction of the material is studied.

scholarly journals Vibration and Buckling Analysis of Cylindrical Shells Made of Functionally Graded Materials under Combined Static and Periodic Axial Forces

2010 ◽  
Vol 19 (2) ◽  
pp. 096369351001900 ◽  
Author(s):  
F. Ebrahimi ◽  
H.A. Sepiani
Keyword(s):  
Transverse Shear ◽  
Volume Fraction ◽  
Cylindrical Shells ◽  
Shear Deformation Theory ◽  
Deformation Mode ◽  
Functionally Graded ◽  
Power Law Distribution ◽  
Graded Materials ◽  
Axial Forces ◽  
Graded Material

In this study, a formulation for the free vibration and buckling of cylindrical shells made of functionally graded material (FGM) subjected to combined static and periodic axial loadings are presented. The properties are temperature dependent and graded in the thickness direction according to a volume fraction power law distribution. The analysis is based on two different methods of first-order shear deformation theory (FSDT) considering the transverse shear strains and the rotary inertias and the classical shell theory (CST). The results obtained show that the effect of transverse shear and rotary inertias on vibration and buckling of functionally graded cylindrical shells is dependent on the material composition, the temperature environment, the amplitude of static load, the deformation mode, and the shell geometry parameters.

scholarly journals An Efficient Beam Element Based on Quasi-3D Theory for Static Bending Analysis of Functionally Graded Beams

Materials ◽  
2019 ◽  
Vol 12 (13) ◽  
pp. 2198 ◽  
Author(s):  
Hoang Nam Nguyen ◽  
Tran Thi Hong ◽  
Pham Van Vinh ◽  
Do Van Thom
Keyword(s):  
Transverse Shear ◽  
Volume Fraction ◽  
Beam Theory ◽  
Beam Element ◽  
Functionally Graded ◽  
Shear Stresses ◽  
Functionally Graded Beam ◽  
Transverse Shear Stresses ◽  
Power Law Index ◽  
Transverse Shear Strains

In this paper, a 2-node beam element is developed based on Quasi-3D beam theory and mixed formulation for static bending of functionally graded (FG) beams. The transverse shear strains and stresses of the proposed beam element are parabolic distributions through the thickness of the beam and the transverse shear stresses on the top and bottom surfaces of the beam vanish. The proposed beam element is free of shear-looking without selective or reduced integration. The material properties of the functionally graded beam are assumed to vary according to the power-law index of the volume fraction of the constituents through the thickness of the beam. The numerical results of this study are compared with published results to illustrate the accuracy and convenience rate of the new beam element. The influence of some parametrics on the bending behavior of FGM beams is investigated.

Free vibration analysis of functionally graded double-tapered beam rotating in thermal environment considering geometric nonlinearity, shear deformability, and Coriolis effect

2017 ◽  
Vol 232 (12) ◽  
pp. 2244-2262 ◽  
Author(s):  
Suman Pal ◽  
Debabrata Das
Keyword(s):  
Mathematical Model ◽  
Free Vibration ◽  
Material Properties ◽  
Volume Fraction ◽  
Thermal Environment ◽  
Ritz Method ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Coriolis Effect ◽  
Governing Equations

The present work investigates the free vibration behavior of double-tapered functionally graded beams rotating in thermal environment, using an improved mathematical model. The functional gradation for ceramic–metal compositions, following power-law, is considered to be symmetric with respect to the mid-plane, leading to metal-rich core and ceramic-rich outer surfaces of the beam. The temperature dependence of the material properties are considered using Touloukian model. The nonlinearity in strain–displacement relationships for both the axial and transverse shear strains are considered. Firstly, the governing equations for deformed beam configuration under time-independent centrifugal loading are obtained using minimum total potential energy principle, and the solution is obtained following Ritz method. Then the free vibration problem of the centrifugally deformed beam is formulated employing Lagrange’s principle and considering tangent stiffness of the deformed beam configuration. Coriolis effect is considered in the mathematical model, and the governing equations are transformed to the state-space for obtaining an eigenvalue problem. The results for the first two modes of both chord-wise and flap-wise vibrations are presented in nondimensional plane to show the effects of taperness parameter, root-offset parameter, volume fraction exponent, operating temperature, and functionally graded material composition. The results in comparative form are presented for both temperature-dependent and temperature-independent material properties.

Sign in / Sign up

Export Citation Format

Share Document