Tensor-based finite element formulation for geometrically nonlinear analysis of shell structures

Arciniega, R.A.; Reddy, J. N.

doi:10.1016/j.cma.2006.08.014

Cited by 172 publications

(136 citation statements)

References 45 publications

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“…It is plausible that the applied load to ceramic panel is higher than that of metal due to the high stiffness of ceramic. Results shown in Fig 6 are visually in good agreement with the solutions presented by Arciniega and Reddy (2007b) as well as deflection curves in Frikha and Dammak (2017), Payette and Reddy (2014).…”

Section: Hinged Cylindrical Roof Subjected To a Concentrated Loadsupporting

confidence: 75%

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

Mars

Koubaa

Wali

et al. 2017

Lat. Am. j. solids struct.

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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...

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Section: Hinged Cylindrical Roof Subjected To a Concentrated Loadsupporting

confidence: 75%

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

Mars

Koubaa

Wali

et al. 2017

Lat. Am. j. solids struct.

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“…In the computer implementation, the Schur complement method is adopted at the element level to statically condense out all degrees of freedom interior to each element in the finite element discretization. This constitutes an important departure from the tensor based shell finite element formulation proposed previously in the work of Arciniega and Reddy [1,2], where a chart was employed to insure exact parameterization of the shell mid-surface. The present formulation requires as input the three-dimensional coordinates of the shell mid-surface as well as a set of directors (i.e., unit normal vectors to the mid-surface) for each node in the shell finite element model.…”

Section: Preliminary Commentsmentioning

confidence: 99%

“…In this section we present a degenerate solid shell finite element model using a seven parameter expansion (with respect to the curvilinear thickness coordinate) of the displacement field [8,2,1]. The use of high-order spectral/hp interpolants in the numerical implementation naturally leads to a finite element model that is completely locking free.…”

Section: Preliminary Commentsmentioning

confidence: 99%

“…In the least-squares method, we construct an unconstrained convex least-squares functional  whose minimizer corresponds with the solution of equation (2)(3)(4). To maintain practicality [4,5,31,32,33] in the numerical implementation, we construct the least-squares functional in terms of the sum of the squares of the 2 L norms of the abstract equation residuals N …”

mentioning

confidence: 99%

“…To maintain practicality [4,5,31,32,33] in the numerical implementation, we construct the least-squares functional in terms of the sum of the squares of the 2 L norms of the abstract equation residuals N …”

mentioning

confidence: 99%

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RETRACTED: Higher-order Spectral/hp Finite Element Technology for Shells and Flows of Viscous Incompressible Fluids

Vallala

Reddy

2013

MCA

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Abstract-This study deals with the use of high-order spectral/hp approximation functions in finite element models of various of nonlinear boundary-value and initial-value problems arising in the fields of structural mechanics and flows of viscous incompressible fluids. For many of these classes of problems, the high-order (typically, polynomial order 4  p ) spectral/hp finite element technology offers many computational advantages over traditional low-order (i.e., 3 < p ) finite elements. For instance, higher-order spectral/hp finite element procedures allow us to develop robust structural elements such as beams, plates, and shells in a purely displacement-based setting, which avoid all forms of numerical locking. For fluid flows, when combined with least-squares variational principles, the higher-order spectral/hp technology allows us to develop efficient finite element models that always yield a symmetric positive-definite (SPD) coefficient matrix and, hence, robust iterative solvers can be used. Also, the use of spectral/hp finite element technology results in a better conservation of physical quantities like dilatation, volume, and mass, and stable evolution of variables with time for transient flows. The present study considers the weak-form based displacement finite element models elastic shells and the least-squares finite element models of the Navier-Stokes equations governing flows of viscous incompressible fluids. Numerical solutions of several nontrivial benchmark problems are presented to illustrate the accuracy and robustness of the developed finite element technology.

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Finite Element Analysis of Composite Plates and Shells

Reddy

Arciniega

Moleiro

2010

Encyclopedia of Aerospace Engineering

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In this chapter, an overview of recent developments on finite element analysis of composite plates and shells are presented. Two major developments in the last decade by the author and his colleagues have been in the formulation of (1) least–squares finite element models of plates and (2) the weak‐form Galerkin finite element formulations of first‐order and third‐order shell theories. The least–squares formulations are based on the first‐order shear deformation theory, while the weak‐form Galerkin is based on the first‐order as well as the third‐order shear deformation theories. Results using the weak‐form Galerkin finite element model based on improved 7‐parameter first‐order theory are also included for geometrically nonlinear cases. The least–squares finite element models of plates are based on mixed formulations in which displacements as well as stress resultants are treated as the unknown field variables. The weak‐form Galerkin finite element models are displacement‐based. In the latter, a family of high‐order Lagrange interpolation functions (with equally spaced nodes and Gauss–Lobatto–Legendre nodes) is used to prevent shear locking. Numerical results are presented for a number of benchmark problems involving isotropic, laminated composite, as well as functionally graded plates and shells.

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Tensor-based finite element formulation for geometrically nonlinear analysis of shell structures

Cited by 172 publications

References 45 publications

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

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

RETRACTED: Higher-order Spectral/hp Finite Element Technology for Shells and Flows of Viscous Incompressible Fluids

Finite Element Analysis of Composite Plates and Shells

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