Geometrically non-linear formulation for the three dimensional solid-shell transition finite elements

1982 ◽  
Vol 15 (5) ◽  
pp. 549-566 ◽  
Author(s):  
Karan S. Surana
Keyword(s):  
Finite Elements ◽  
Three Dimensional ◽  
Linear Formulation ◽  
Solid Shell ◽  
Non Linear

Free Undamped Vibration of Geometrically Non-Linear Cable Structures

1997 ◽  
Author(s):  
Alan S. K. Kwan
Keyword(s):  
Finite Elements ◽  
Mass Matrix ◽  
Three Dimensional ◽  
Geometrically Nonlinear ◽  
Theoretical Derivation ◽  
Cable Structures ◽  
Non Linear ◽  
Membrane Models ◽  
High Degree ◽  
Axial Element

The stiffness relationship and the distributed mass matrix for a geometrically nonlinear three dimensional straight axial element is derived for use in prestressed cablenet structures. The justification for the use of a linearised stiffness relationship is provided through a theoretical derivation. Results using this simple element have shown a high degree of correlation with results to those available in the literature obtained with more complex curved finite elements, analogous membrane models and other techniques.

scholarly journals AN EFFICIENT CO-ROTATIONAL FEM FORMULATION USING A PROJECTOR MATRIX

2016 ◽  
Vol 14 (2) ◽  
pp. 227 ◽  
Author(s):  
Viet Anh Nguyen ◽  
Manfred Zehn ◽  
Dragan Marinković
Keyword(s):  
Finite Elements ◽  
Deformation Gradient ◽  
Three Dimensional ◽  
Nonlinear Problems ◽  
Internal Force ◽  
Linear Analysis ◽  
Efficient Computation ◽  
Tangent Stiffness Matrix ◽  
Non Linear ◽  
Internal Force Vector

Co-rotational finite element (FE) formulations can be seen as a very efficient approach to resolving geometrically nonlinear problems in the field of structural mechanics. A number of co-rotational FE formulations have been well documented for shell and beam structures in the available literature. The purpose of this paper is to present a co-rotational FEM formulation for fast and highly efficient computation of large three-dimensional elastic deformations. On the one hand, the approach aims at a simple way of separating the element rigid-body rotation and the elastic deformational part by means of the polar decomposition of deformation gradient. On the other hand, a consistent linearization is introduced to derive the internal force vector and the tangent stiffness matrix based on the total Lagrangian formulation. It results in a non-linear projector matrix. In this way, it ensures the force equilibrium of each element and enables a relatively straightforward upgrade of the finite elements for linear analysis to the finite elements for geometrically non-linear analysis. In this work, a simple 4-node tetrahedral element is used. To demonstrate the efficiency and accuracy of the proposed formulation, nonlinear results from ABAQUS are used as a reference.

Sign in / Sign up

Export Citation Format

Share Document