Sandwich shell finite element for dynamic explicit analysis

2002 ◽  
Vol 54 (5) ◽  
pp. 763-787 ◽  
Author(s):  
Ala Tabiei ◽  
Romil Tanov
Keyword(s):  
Finite Element ◽  
Sandwich Shell ◽  
Explicit Analysis ◽  
Shell Finite Element

New Formulation for Composite Sandwich Shell Finite Element

1999 ◽  
Author(s):  
Ala Tabiei ◽  
Romil Tanov
Keyword(s):  
Finite Element ◽  
Shell Element ◽  
Core Material ◽  
Element Formulation ◽  
Sandwich Shell ◽  
Composite Sandwich ◽  
Computationally Intensive ◽  
Shell Finite Element ◽  
New Formulation ◽  
Shear Deformable

Abstract Sandwich shell finite element formulation is developed and presented. The sandwich shell element formulation allows for orthotropic faces and core material. The sandwich shell element is based on first shell order shear deformable theory utilized by most shell finite elements for isotropic materials. Consequently, the presented procedure can be adopted for any shell element available in commercial finite element packages. The formulation is based on the equalities of stress and moment resultants between a sandwich shell element and a typical homogenous shell element. The developed element is implemented in the nonlinear finite element code DYNA3D to validate and check its accuracy, efficiency and overall performance. The predicted results show good agreement with results obtained from far more complicated and computationally intensive 3-D analyses.

Sandwich Shell Finite Element for Dynamic Explicit Analysis

2000 ◽  
Author(s):  
Ala Tabiei ◽  
Romil Tanov ◽  
Victor Birman
Keyword(s):  
Finite Element ◽  
Transverse Shear ◽  
Critical Time ◽  
Shell Element ◽  
Shear Stresses ◽  
Sandwich Shell ◽  
Time Step ◽  
Third Order ◽  
Explicit Analysis ◽  
Sandwich Shells

Abstract This work presents the finite element (FE) formulation and implementation of a higher order shear deformable shell element for dynamic explicit analysis of composite and sandwich shells. The formulation is developed using a displacement based third order shear deformation shell theory. Using the differential equilibrium equations and the interlayer requirements, a treatment is developed for the transverse shear, resulting in a continuous, piecewise quartic distribution of the transverse shear stresses through the shell thickness. The FE implementation is cast into a 4-noded quadrilateral shell element with 9 degrees of freedom (DOF) per node. Only C0 continuity of the displacement functions is required in the shell plane, which makes the present formulation applicable to the most common 4-noded bilinear isoparametric shell elements. Expressions are developed for the critical time step of the explicit time integration for orthotropic homogeneous and layered shells based on the developed third order formulation. To assess the performance of the present shell element it is implemented in the general nonlinear explicit dynamic FE code DYNA3D. Several problems are solved and results are compared to other theoretical and numerical results. The developed sandwich shell element is much more computationally efficient for modeling sandwich shells than solid elements.

Post-buckling inelastic analysis of thin-walled metal members using the Generalised Beam Theory

2019 ◽  
Author(s):  
Miguel Abambres ◽  
Dinar Camotim ◽  
Miguel Abambres
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Beam Theory ◽  
Flow Theory ◽  
Promising Alternative ◽  
Inelastic Analysis ◽  
Post Buckling ◽  
Thin Walled ◽  
Shell Finite Element ◽  
Generalised Beam Theory

A 2nd order inelastic Generalised Beam Theory (GBT) formulation based on the J2 flow theory is proposed, being a promising alternative to the shell finite element method. Its application is illustrated for an I-section beam and a lipped-C column. GBT results were validated against ABAQUS, namely concerning equilibrium paths, deformed configurations, and displacement profiles. It was concluded that the GBT modal nature allows (i) precise results with only 22% of the number of dof required in ABAQUS, as well as (ii) the understanding (by means of modal participation diagrams) of the behavioral mechanics in any elastoplastic stage of member deformation .

First and Second Order Elastoplastic Analyses of Thin-Walled Metal Members using Generalized Beam Theory

2018 ◽  
Author(s):  
Miguel Abambres
Keyword(s):  
Finite Element ◽  
Stainless Steel ◽  
Cross Section ◽  
Beam Theory ◽  
Second Order ◽  
Flow Rule ◽  
Non Linear ◽  
Thin Walled ◽  
Shell Finite Element ◽  
Generalized Beam Theory

Original Generalized Beam Theory (GBT) formulations for elastoplastic first and second order (postbuckling) analyses of thin-walled members are proposed, based on the J2 theory with associated flow rule, and valid for (i) arbitrary residual stress and geometric imperfection distributions, (ii) non-linear isotropic materials (e.g., carbon/stainless steel), and (iii) arbitrary deformation patterns (e.g., global, local, distortional, shear). The cross-section analysis is based on the formulation by Silva (2013), but adopts five types of nodal degrees of freedom (d.o.f.) – one of them (warping rotation) is an innovation of present work and allows the use of cubic polynomials (instead of linear functions) to approximate the warping profiles in each sub-plate. The formulations are validated by presenting various illustrative examples involving beams and columns characterized by several cross-section types (open, closed, (un) branched), materials (bi-linear or non-linear – e.g., stainless steel) and boundary conditions. The GBT results (equilibrium paths, stress/displacement distributions and collapse mechanisms) are validated by comparison with those obtained from shell finite element analyses. It is observed that the results are globally very similar with only 9% and 21% (1st and 2nd order) of the d.o.f. numbers required by the shell finite element models. Moreover, the GBT unique modal nature is highlighted by means of modal participation diagrams and amplitude functions, as well as analyses based on different deformation mode sets, providing an in-depth insight on the member behavioural mechanics in both elastic and inelastic regimes.

Some new results and current challenges in the finite element analysis of shells

Acta Numerica ◽  
2001 ◽  
Vol 10 ◽  
pp. 215-250 ◽  
Author(s):  
Dominique Chapelle
Keyword(s):  
Finite Element ◽  
Shell Theory ◽  
Shell Structures ◽  
Engineering Practice ◽  
Element Analysis ◽  
Shell Elements ◽  
Shell Models ◽  
The Finite Element Analysis ◽  
Shell Finite Element ◽  
Mathematical Analyses

This article, a companion to the article by Philippe G. Ciarlet on the mathematical modelling of shells also in this issue of Acta Numerica, focuses on numerical issues raised by the analysis of shells.Finite element procedures are widely used in engineering practice to analyse the behaviour of shell structures. However, the concept of ‘shell finite element’ is still somewhat fuzzy, as it may correspond to very different ideas and techniques in various actual implementations. In particular, a significant distinction can be made between shell elements that are obtained via the discretization of shell models, and shell elements – such as the general shell elements – derived from 3D formulations using some kinematic assumptions, without the use of any shell theory. Our first objective in this paper is to give a unified perspective of these two families of shell elements. This is expected to be very useful as it paves the way for further thorough mathematical analyses of shell elements. A particularly important motivation for this is the understanding and treatment of the deficiencies associated with the analysis of thin shells (among which is the locking phenomenon). We then survey these deficiencies, in the framework of the asymptotic behaviour of shell models. We conclude the article by giving some detailed guidelines to numerically assess the performance of shell finite elements when faced with these pathological phenomena, which is essential for the design of improved procedures.

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