Buckling analysis of functionally graded materials structures with enhanced solid-shell elements and transverse shear correction

In this paper, a geometrically nonlinear analysis of functionally graded material (FGM) shells is investigated using Abaqus software. A user defined subroutine (UMAT) is developed and implemented in Abaqus/Standard to study the FG shells in large displacements and rotations. The material properties are introduced according to the integration points in Abaqus via the UMAT subroutine. The predictions of static response of several non-trivial structure problems are compared to some reference solutions in order to verify the accuracy and the effectiveness of the new developed nonlinear solution procedures. All the results indicate very good performance in comparison with references. Lee et al. 2009). Typically, FG shell structures were presented using: (i) Kirchhoff-Love theory, Chi and Chung (2006), where the shear strains are assumed zero, which is not acceptable for FG shell; (ii) the First-order Shear Deformation Theory (FSDT) (Praveen and Reddy 1998;Thai and Kim 2015), which gives a correct overall assessment. Notice that the shear correction factors should be incorporated to adjust the transverse shear stiffness; (iii) the High-order Shear Deformation Theory (HSDT) (Neves et al. 2012;Wali et al. 2014Wali et al. , 2015Frikha et al. 2016) in which the equations of motion are more complicated to obtain than those of the FSDT; among other theories. KeywordsIt is certainly plausible that linear finite element (FE) models cannot be able to accurately predict the structural response presenting large elastic deformations and finite rotations. Indeed, according to Yu et al. (2015), several practical problems of FG structures require a geometrically non-linear formulation, such as the post-buckling behavior of structures used in aeronautical, aerospace as well as in mechanical and civil engineering. In such cases, it becomes crucial to develop efficient and accurate nonlinear FE models.It is well known that analytical solutions of shell problems are very limited. Hence, most of reference solutions are previously reported numerical solutions. Particularly, for FE geometric nonlinear analysis of FG shells, several research papers are surveyed (Praveen and Reddy 1998;Reddy 2000;Kattimani and Ray 2015;Duc et al. 2017; Reddy 2007a, 2007b;Alinia and Ghannadpour 2009;Phung-Van et al. 2014;Kim et al. 2008;Hajlaoui et al. 2017;Frikha and Dammak 2017;Asemi et al. 2014 andAnsari et al. 2016). In these references, a number of theoretical formulation and finite element models based on von Karman, Kirchhoff-Love, FSDT and HSDT theories were proposed to study the geometrically non-linear behavior of FGMs Structures.Hosseini Kordkheili and Naghdabadi (2007) derived a FE formulation for the geometrically nonlinear thermoelastic analysis of FGM plates and shells using the updated Lagrangian approach. Later, Zhao and Liew (2009) conducted a geometrically non-linear analysis of FGM shells under mechanical and thermal loading using the element-free kp-Ritz method. The formulation was based on the modified version of Sander's non-li...

show abstract

“…In Eq. (15), K is the shear correction matrix computed based on the work of Hajlaoui et al (2015). The weak form of the equilibrium equation, Eq.…”

Section: Initial Configuration C0mentioning

confidence: 99%

“…This element is widely used for industrial applications, as it is suitable for thin to moderately thick shell structures. Results, based on the FSDT of shell elements are obtained including an automatic calculation of the shear correction factors as in Hajlaoui et al (2015).…”

Section: Through-thickness Integration and Umat Interfacementioning

confidence: 99%

Numerical Analysis of Geometrically Non-Linear Behavior of Functionally Graded Shells

Mars

Koubaa

Wali

et al. 2017

Lat. Am. j. solids struct.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Free vibration of FGM shell structures was investigated, using an efficient 3D shell model, based on a discrete double director shell element by Wali et al (2014Wali et al ( , 2015. Hajlaoui et al (2015) derived an enhanced assumed strain solid-shell element based on first-order shear deformation concept for buckling analysis of FGM plate and shell structures. Shakeri et al (2006) studied the vibration and radial wave propagation in FGM thick hollow cylinders.…”

Section: Introductionmentioning

confidence: 99%

Effects of piezoelectric rings on electro-elasto-dynamic behaviour of functionally graded cylindrical shell

Saviz

2016

Journal of Intelligent Material Systems and Structures

View full text Add to dashboard Cite

A layer-wise finite element approach is adopted to analyse the hollow cylindrical shell made of functionally graded material with piezoelectric rings as sensor/actuator, under dynamic load. The mechanical properties of the substrate are regulated by volume fraction as a function of radial coordinate. The thickness of functionally graded material shell and piezorings is divided into mathematical sub-layers and then the general layer-wise laminate theory is formulated through introducing piecewise continuous approximations across the thickness, accounting for any discontinuity in derivatives of the displacement at the interface between the ring and cylinder. The virtual work statement including structural and electrical potential energies yields the three-dimensional governing equations which are reduced to two-dimensional differential equations, using layer-wise method. For axisymmetric case, the resulted equations are solved with one-dimensional finite element method in the axial direction. By assembling stiffness and mass matrices, the required stress and displacement continuities at each interface and between the two adjacent elements are forced. The results for free vibration and static loading are applied to study the convergence and verified by comparing them to solutions of similar existing problems. The induced deformation by piezoelectric actuators as well as the effect of rings on functionally graded material shell is investigated.

show abstract

“…For the detailed description of the ANS method, refer to Hajlaoui et al (2012Hajlaoui et al ( , 2015Hajlaoui et al ( , 2016. The compatible part is arranged in (6x1) column matrix as follows 11 22 33 12 13 23…”

Section: Compatible Strainsmentioning

confidence: 99%

“…However, for the thickness strains, 33 c E , we adopt the ANS method as in Klinkel et al (1999), Vu-Quoc and Tan (2003) and Hajlaoui et al (2012Hajlaoui et al ( , 2015Hajlaoui et al ( , 2016 and evaluated at four collocation points defined in the reference surface ( ) …”

Section: Compatible Strainsmentioning

confidence: 99%

Nonlinear Dynamics Analysis of FGM Shell Structures with a Higher Order Shear Strain Enhanced Solid-Shell Element

Hajlaoui

Triki

Frikha

et al. 2017

Lat. Am. j. solids struct.

Self Cite

View full text Add to dashboard Cite

In this paper, non-linear dynamics analysis of functionally graded material (FGM) shell structures is investigated using the higher order solid-shell element based on the Enhanced Assumed Strain (EAS). With this element, a quadratic distribution of the shear stress through the thickness is considered in an enhancing part. Material properties of the shell structure are varied continuously in the thickness direction according to the general four-parameter power-law distribution in terms of the volume fractions of the constituents. Performance and accuracy of the present higher order solid-shell element are confirmed by comparing the numerical results obtained from finite element analyses with results from the literature.

show abstract

Buckling analysis of functionally graded materials structures with enhanced solid-shell elements and transverse shear correction

Cited by 50 publications

References 44 publications

Numerical Analysis of Geometrically Non-Linear Behavior of Functionally Graded Shells

Numerical Analysis of Geometrically Non-Linear Behavior of Functionally Graded Shells

Effects of piezoelectric rings on electro-elasto-dynamic behaviour of functionally graded cylindrical shell

Nonlinear Dynamics Analysis of FGM Shell Structures with a Higher Order Shear Strain Enhanced Solid-Shell Element

Contact Info

Product

Resources

About