Thin shells with finite rotations formulated in biot stresses: Theory and finite element formulation

Wriggers, Peter; Gruttmann, Friedrich

doi:10.1002/nme.1620361207

Cited by 82 publications

(49 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…8) shows the displacement components in the out-of-plane direction of the undeformed plate. Displacements agree very well with results reported in Frikha and Dammak (2017), Buechter and Ramm (1992) and Wriggers and Gruttmann (1993). Reddy (2007a, 2007b).…”

Section: Case Of Ring Platesupporting

confidence: 89%

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

Mars

Koubaa

Wali

et al. 2017

Lat. Am. j. solids struct.

View full text Add to dashboard Cite

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

Section: Case Of Ring Platesupporting

confidence: 89%

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

Mars

Koubaa

Wali

et al. 2017

Lat. Am. j. solids struct.

View full text Add to dashboard Cite

show abstract

“…For example, to compute harmonic maps into the unit sphere S 2 , Bartels and Prohl [6,7] embedded S 2 into R 3 , and used first-order Lagrangian finite elements, constraining only the vertex values to be in S 2 . In the literature on geometrically exact shells, the direction of the shell surface normal is frequently expressed as a set of angles, and the angles are discretized separately using finite elements [56]. For Cosserat continua (with values in R 3 × SO(3)), an alternative approach, used by Münch [36] and Müller [35], interpolates rotation vectors in so(3) instead of in the group of rotations SO(3).…”

Section: Introductionmentioning

confidence: 99%

Optimal A Priori Discretization Error Bounds for Geodesic Finite Elements

Hardering¹,

Sander²

2014

Found Comput Math

View full text Add to dashboard Cite

We prove optimal bounds for the discretization error of geodesic finite elements for variational partial differential equations for functions that map into a nonlinear space. For this we first generalize the well-known Céa lemma to nonlinear function spaces. In a second step we prove optimal interpolation error estimates for pointwise interpolation by geodesic finite elements of arbitrary order. These two results are both of independent interest. Together they yield optimal a priori error estimates for a large class of manifold-valued variational problems. We measure the discretization error both intrinsically using an H 1 -type Finsler norm, and with the H 1 -norm using embeddings of the codomain in a linear space. To measure the regularity of the solution we propose a nonstandard smoothness descriptor for manifold-valued functions, which bounds additional terms not captured by Sobolev norms. As an application we obtain optimal a priori error estimates for discretizations of smooth harmonic maps using geodesic finite elements, yielding the first high order scheme for this problem.

show abstract

“…10. The problem has been studied in (Buechter and Ramm, 1992;Wriggers and Gruttmann, 1993;Kim et al, 2003) among others. The line force P is applied at one end of the slit while the other end of the slit is fixed.…”

Section: The Slit Annular Plate Loaded With Line Forcementioning

confidence: 99%

Efficient Co-Rotational 3-Node Shell Element

Rama¹,

Marinković²,

Zehn³

2016

American Journal of Engineering and Applied Sciences

View full text Add to dashboard Cite

Geometric nonlinear FE-analysis of thin-walled shell structures, using a co-rotational formulation and the Cell Smoothed Discrete Shear Gap triangular shell element (CS-DSG3) is presented in this study. The CS-DSG3 element formulation uses the Mindlin-Reissner kinematic hypothesis to include transverse shear effects. In order to avoid locking effects Discrete Shear Gap (DSG) method is applied. In addition, cell based smoothing technique is adopted in order to improve accuracy and stability of the element. For the purpose of comparison, the Discrete Kirchhoff-Constant strain-Triangle (DKT-CST) is also implemented and studied in the linear static analysis. In the framework of the co-rotational FE-analysis rotations and displacements are adopted as finite, while strains are infinitesimal. Large rotation theory has been utilized to take into account the non-vectorial characteristic of rotations. Several static linear and nonlinear benchmark examples are presented and compared with commercial FE software Abaqus and analytical results. The presented approach, using CS-DSG3 element in co-rotational nonlinear analysis, illustrates very good results compared to reference solution and Abaqus results. The numerical effort can be reduced compared to Lagrange formulation with a similar accuracy for the studied cases. The formulation (including CS-DSG3 shell element) has been implemented into a test program.

show abstract

Thin shells with finite rotations formulated in biot stresses: Theory and finite element formulation

Cited by 82 publications

References 24 publications

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

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

Optimal A Priori Discretization Error Bounds for Geodesic Finite Elements

Efficient Co-Rotational 3-Node Shell Element

Contact Info

Product

Resources

About