Refined shear-deformation models for composite laminates with finite rotations

Başar, Yavuz; Ding, Y.; Schultz, R.

doi:10.1016/0020-7683(93)90102-d

Cited by 140 publications

(43 citation statements)

References 34 publications

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“…Numerical results obtained using the above simplified theory as compared with the full geometrically nonlinear theory for elastic structures are discussed by Başar et al [30]. It is important to note that the coordinates (x, y, z) used in Equation (1) above and throughout this paper are the material coordinates.…”

Section: Kinematics Of Deformationmentioning

confidence: 97%

Nonlinear quasi‐static finite element formulations for viscoelastic Euler–Bernoulli and Timoshenko beams

Payette

Reddy

2009

Numer Methods Biomed Eng

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SUMMARYWeak form finite element models for the nonlinear quasi-static bending and extension of initially straight viscoelastic Euler-Bernoulli and Timoshenko beams are developed using the principle of virtual work. The mechanical properties of the beams are considered to be linear viscoelastic. However, large transverse displacements, moderate rotations and small strains are allowed by retaining the von Kármán strain components of the Green-Lagrange strain tensor in the formulation. The fully discretized finite element equations are developed using the trapezoidal rule in conjunction with a two-point recurrence relation. The resulting finite element equations, therefore, necessitate data storage from the previous time step only, and not the entire deformation history. Membrane locking is eliminated from the Euler-Bernoulli formulation through the use of selective reduced Gauss-Legendre quadrature. Membrane and shear locking are both circumvented in the Timoshenko beam finite element by employing a family of high-order Lagrange polynomials. A Newton-Raphson iterative scheme is used to solve the nonlinear finite element equations.

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Section: Kinematics Of Deformationmentioning

confidence: 97%

Nonlinear quasi‐static finite element formulations for viscoelastic Euler–Bernoulli and Timoshenko beams

Payette

Reddy

2009

Numer Methods Biomed Eng

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“…11a) and Arabi 2016; Balah and Al-Ghamedy 2002;Wagner and Gruttmann 1994;Basar et al 1993;Dammak et al 2005), among others. The material and geometry properties of the shell are given in The radius equation of the hyperboloid shell is given as:…”

Section: Hyperboloidal Fg Shellmentioning

confidence: 99%

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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“…Within the present formulation it is possible to consider higher-order kinematic approximations. For laminated, sandwich type shells, signiÿcantly more accurate results can be obtained by application of a layer-wise concept [1,14,20,21] in combination with assumption (4) rather than the use of higher-order polynomials. Also the multiplicative decomposition [8,9] of the ÿrst director 1 x = d into rotational variables d = d( ) and a stretch parameter is possible, but it is not needed for the general derivation of arbitrary order shell elements.…”

Section: Actual Statementioning

confidence: 99%

A general high‐order finite element formulation for shells at large strains and finite rotations

Başar

Hanskötter

Schwab

2003

Numerical Meth Engineering

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SUMMARYFor hyperelastic shells with ÿnite rotations and large strains a p-ÿnite element formulation is presented accommodating general kinematic assumptions, interpolation polynomials and particularly general threedimensional hyperelastic constitutive laws. This goal is achieved by hierarchical, high-order shell models. The tangent sti ness matrices for the hierarchical shell models are derived by computer algebra. Both non-hierarchical, nodal as well as hierarchical element shape functions are admissible. Numerical experiments show the high-order formulation to be less prone to locking e ects.

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Refined shear-deformation models for composite laminates with finite rotations

Cited by 140 publications

References 34 publications

Nonlinear quasi‐static finite element formulations for viscoelastic Euler–Bernoulli and Timoshenko beams

Nonlinear quasi‐static finite element formulations for viscoelastic Euler–Bernoulli and Timoshenko beams

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

A general high‐order finite element formulation for shells at large strains and finite rotations

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