Shear Deformable Shell Element Research Articles

Finite element implementation of a new sandwich homogenization procedure

A new homogenization procedure for finite element (FE) analysis of sandwich shells was recently developed and presented by the authors. To the authors’ knowledge all present FE approaches to sandwich structures are incorporated into the FE formulation on the element formulation level. Unlike other formulations, the present approach works on the constitutive level. A homogenization of the sandwich shell is performed at each call of the corresponding constitutive subroutine. Thus, the sandwich nature of the problem is hidden from the main FE program. As a consequence, there is no need to develop a new shell element formulation, instead all available homogeneous shell elements in the utilized FE code can be used for the analysis of sandwich shells. This would provide versatility of the FE analysis and potentials to trade off between the level of accuracy and computational efficiency by using more accurate or simpler shell elements. Furthermore, the sandwich homogenization procedure (SHOP) can be easily coupled with a composite homogenization model to enable analysis of sandwich shells with composite faces. To validate the present approach and check its accuracy, efficiency and overall performance, it is implemented in a FE package and combined with existing first-order shear deformable shell elements for homogeneous materials. Results are obtained and herein presented for problems previously investigated experimentally and by different theoretical and numerical techniques. The presented results show good agreement with published results from far more complicated and computationally intensive analyses, which build confidence in the approach and motivate its future elaboration and development.

Advanced Modeling Strategies for the Analysis of Tile-Reinforced Composite Armor

A detailed investigation of the deformation mechanisms in tile-reinforced armored components was conducted to develop the most efficient modeling strategies for the structural analysis of large components of the Composite Armored Vehicle. The limitations of conventional finite elements with respect to the analysis of tile-reinforced structures were examined, and two complementary optimal modeling strategies were developed. These strategies are element layering and the use of a tile-adhesive superelement. Element layering is a technique that uses stacks of shear deformable shell elements to obtain the proper transverse shear distributions through the thickness of the laminate. The tile-adhesive superelement consists of a statically condensed substructure model designed to take advantage of periodicity in tile placement patterns to eliminate numerical redundancies in the analysis. Both approaches can be used simultaneously to create unusually efficient models that accurately predict the global response by incorporating the correct local deformation mechanisms.

A four-node, shear-deformable shell element developed via explicit Kirchhoff constraints

A four-node, shear-deformable shell element developed via explicit Kirchhoff constraints

Free vibration of a laminated composite shell of revolution: Effects of shear non-linearity

Effects of shear non-linearity on free vibration of a laminated composite shell of revolution are investigated using a semi-analytical method based on the Reissner–Mindlin shell theory. The coupling between symmetric and anti-symmetric vibration modes of the shell is considered in the shear deformable shell element employed in this study. The Hahn–Tsai non-linearly elastic shear stress–shear strain relation is adopted. Numerical examples are given for laminated composite circular cylindrical and conical shells with various boundary conditions. The numerical results indicate that shear non-linearity may reduce significantly the fundamental frequencies of cross-ply composite shells of revolution.

Shear deformable shell elements for large strains and rotations

Well-known finite element concepts like the Assumed Natural Strain (ANS) and the Enhanced Assumed Strain (EAS) techniques are combined to derive efficient and reliable finite elements for continuum based shell formulations. In the present study two aspects are covered: The first aspect focuses on the classical 5-parameter shell formulation with Reissner–Mindlin kinematics. The above-mentioned combinations, already discussed by Andelfinger and Ramm for the linear case of a four-node shell element, are extended to geometrical non-linearities. In addition a nine-node quadrilateral variant is presented. A geometrically non-linear version of the EAS-approach is applied which is based on the enhancement of the Green–Lagrange strains instead of the displacement gradient as originally proposed by Simo and Armero. In the second part elements are derived in a similar way for a higher order, so-called 7-parameter non-linear shell formulation which includes the thickness stretch of the shell (Büchter and Ramm). In order to avoid artificial stiffening caused by the three dimensional displacement field and termed ‘thickness locking’, special provisions for the thickness stretch have to be introduced. © 1997 John Wiley & Sons, Ltd.

Nonlinear analysis of laminates through a mindlin-type shear deformable shallow shell element

This study presents a nonlinear analysis with application to a doubly curved shallow shell element free of ‘locking’. The ‘locking’ phenomenon is eliminated by explicitly determining the shear and membrane correction factors. The element formulation utilizes the Reissner-Mindlin and Marguerre theories. The analysis of thin and moderately thick composite shells undergoing large displacements and rotations is achieved by using the corotational form of an updated Lagrangian formulation. The validity of the analysis is established by correlating present results with various benchmark cases that involve large displacements and rotations, as well as elastic stability.

NON-LINEAR ANALYSIS WITH AN AXISYMMETRIC THICK SHELL ELEMENT

The paper highlights the results of numerical experimentation with a geometrically non-linear formulation of a thick axisymmetric shell element involving non-axisymmetric deformation. The formulation itself has earlier been presented in the context of a non-linear local–global analysis of shells of revolution, where very little attention was paid to an independent evaluation of the element's performance. A Fourier decomposition of the loads and the displacements has been used in the circumferential co-ordinate, in order to describe the non-axisymmetric behavior. Due to the interaction between different harmonic terms in the non-linear analysis, the tangential stiffness matrix is no longer block-diagonal. A pseudoload method and a conjugate gradient like iterative scheme have been used to overcome the problem of a large tangent stiffness matrix, and thus most of the advantages of the semi-analytical method have been retained in the non-linear analysis. The accuracy of the predictions in the study has been benchmarked by analysing the same examples using the quadrilateral shear deformable shell element available in the commercial code NISA II. A comparison with other results available in the literature hints that the effect of transverse shear deformation should not be neglected in the geometrically non-linear analysis of shells which are traditionally considered thin. © 1997 by John Wiley & Sons, Ltd.

Free vibration of a partially fluid-filled cross-ply laminated composite circular cylindrical shell

Free vibration of a partially fluid-filled cross-ply laminated composite circular cylindrical shell is investigated using a semi-analytical procedure based on the Reissner–Mindlin theory and compressible fluid equations. The shell is modeled using unaxisymmetric shear deformable circular cylindrical shell elements. The fluid is modeled using column fluid elements. The equation of motion of the partially fluid-filled shell is derived using the Hamilton’s variational principle. Numerical examples are given for free vibrations of partially fluid-filled orthotropic and cross-ply laminated composite circular cylindrical shells with various boundary conditions. Numerical results indicate that the fluid filling can reduce significantly the natural frequencies of orthotropic and cross-ply laminated composite circular cylindrical shells.

Nonlinear elastic deformations of moderately thick laminated shells subjected to large and rapid rigid-body motion

This study presents a transient nonlinear finite element analysis within the realm of a multi-body dynamics formulation for determining the dynamic response of a moderately thick laminated shell undergoing a rapid and large rotational motion and nonlinear elastic deformations. Nonlinear strain measure and rotation, as well as the transverse shear deformation, are explicitly included in the formulation in order to capture the proper motion-induced stiffness of the laminate. The equations of motion are derived from the virtual work principle. The analysis utilizes shear deformable shallow shell element along with the co-rotational form of the updated Lagrangian formulation. The shallow shell element formulation is based on the Reissner-Mindlin and Marguerre theory.

Stochastic Finite Element Method for Laminated Composite Structures

The stochastic finite element method based on second moment method is developed for the probabilistic analysis of laminated composite structures in which physical properties have uncertainties and variability. The material properties, fiber angles, laminate thickness, and curvatures are modeled as random parameters. The first order shear deformable shell element is employed in application. Numerical results are presented for three example problems. The validity and accuracy of the method are verified through comparison of the present results with those obtained by the Monte Carlo simulation. Statistics of strains and stresses are derived very accurately by considering the randomness of the strain-displacement relation and principal material directions. The probability distribution of structural responses of composite structures can be assumed to be normal distribution, and therefore, can be evaluated quantitatively.

Postbuckling response and failure prediction of graphite-epoxy plates loaded in compression

A shear deformable (three-dimensional) shell element is used to analyze the panels. Two panels without boles and one with a bole are studied, and the resulting responses and failure modes comelated well with the experimental results.

Nonlinear analysis of laminated shells including transverse shear strains

Numerical results obtained using a doubly curved, shear deformable shell element are presented for geometrically nonlinear analysis of laminated composite shells. The element is based on an extension of Sanders' shell theory and accounts for the von Karman strains and transverse shear strains. The sample numerical results presented here for the geometrically nonlinear analysis of laminated composite shells should serve as references for future investigations.