A C1 Triangular Finite Element for Analyzing Multilayered Shell Structures

2009 ◽  
Author(s):  
F. Dau ◽  
O. Polit ◽  
M. Touratier
Keyword(s):  
Finite Element ◽  
Shell Structures ◽  
Triangular Finite Element ◽  
Multilayered Shell

scholarly journals Numerical analysis of the stress-strain state of thin shells based on a joint triangular finite element

2019 ◽  
Vol 15 (2) ◽  
pp. 117-126
Author(s):  
Yuriy V Klochkov ◽  
Anatoliy P Nikolaev ◽  
Olga V Vakhnina
Keyword(s):  
Finite Element ◽  
Middle Surface ◽  
Shell Structures ◽  
The Finite Element Method ◽  
Compatibility Conditions ◽  
Engineering Structures ◽  
Triangular Finite Element ◽  
Triangular Elements ◽  
Lagrange Functional ◽  
Derivatives Of

Relevance. The use of the finite element method for determining the stressstrain state of thin-walled elements of engineering structures predetermines their discretization into separate finite elements. Splitting irregular parts of the structure is impossible without the use of triangular areas. The triangular elements of shell structures are joint in displacements and in their derivatives only at the nodal points. Therefore, ways to improve the compatibility conditions at the boundaries of triangular elements are relevant. Aims of research. The aim of the work is to improve the compatibility conditions at the boundaries of adjacent triangular elements based on equating the derivatives of normal displacements in the middle of the boundary sides. Methods. In order to improve the compatibility conditions at the boundaries of triangular elements in this work, the Lagrange functional is used with the condition of ensuring equality in the middle of the sides of adjacent elements derived from normal displacements in the directions of perpendiculars tangent to the middle surface of the shell. Results. Using the example of analysing an elliptical shell, the efficiency of using a joint triangular finite element is shown, whose stiffness matrix is formed in accordance with the algorithm outlined in this article.

Large Nonlinear Responses of Spatially Nonhomogeneous Stochastic Shell Structures Under Nonstationary Random Excitations

2009 ◽  
Vol 9 (4) ◽  
Author(s):  
C. W. S. To
Keyword(s):  
Finite Element ◽  
Shell Structures ◽  
Random Disturbance ◽  
Hybrid Strain ◽  
Central Difference ◽  
Spherical Cap ◽  
Approximation Techniques ◽  
Nonlinear Responses ◽  
Novel Approach ◽  
Random Disturbances

A novel approach for determining large nonlinear responses of spatially homogeneous and nonhomogeneous stochastic shell structures under intensive transient excitations is presented. The intensive transient excitations are modeled as combinations of deterministic and nonstationary random excitations. The emphases are on (i) spatially nonhomogeneous and homogeneous stochastic shell structures with large spatial variations, (ii) large nonlinear responses with finite strains and finite rotations, (iii) intensive deterministic and nonstationary random disturbances, and (iv) the large responses of a specific spherical cap under intensive apex nonstationary random disturbance. The shell structures are approximated by the lower order mixed or hybrid strain based triangular shell finite elements developed earlier by the author and his associate. The novel approach consists of the stochastic central difference method, time coordinate transformation, and modified adaptive time schemes. Computed results of a temporally and spatially stochastic shell structure are presented. Computationally, the procedure is very efficient compared with those entirely or partially based on the Monte Carlo simulation, and it is free from the limitations associated with those employing the perturbation approximation techniques, such as the so-called stochastic finite element or probabilistic finite element method. The computed results obtained and those presented demonstrate that the approach is simple and easy to apply.

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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