A marching cubes based failure surface propagation concept for three-dimensional finite elements with non-planar embedded strong discontinuities of higher-order kinematics

2013 ◽  
Vol 96 (6) ◽  
pp. 339-372 ◽  
Author(s):  
Christian Linder ◽  
Xiaoxuan Zhang
Keyword(s):  
Finite Elements ◽  
Three Dimensional ◽  
Failure Surface ◽  
Higher Order ◽  
Marching Cubes ◽  
Strong Discontinuities

Analysis of Three-Dimensional Piezo-Electric Beams via a Unified Formulation

2013 ◽  
Vol 745 ◽  
pp. 101-118 ◽  
Author(s):  
Gaetano Giunta ◽  
Yao Koutsawa ◽  
Salim Belouettar
Keyword(s):  
Finite Elements ◽  
Cross Section ◽  
Electrical Potential ◽  
Three Dimensional ◽  
Higher Order ◽  
Computational Costs ◽  
Generic Term ◽  
Mass Matrices ◽  
Out Of Plane ◽  
Piezo Electric

A Unified Formulation for deriving several higher-order theories and related finite elements for beams is presented within this paper.Three-dimensional structures with piezo-electric layers are considered.Static and free vibration analyses are carried out.Models' main unknowns are the displacements and the electric potential.They are approximated above the beam cross-section via Lagrange's polynomials in a layer-wise sense.Finite elements stiffness and mass matrices are derived in a nucleal form using d'Alembert's Principle.This nucleal form is representative of the generic term in the approximating expansion of the displacements and electric potential over the cross-section.It is, therefore, invariant versus the theory expansion order and the element nodes' number.In such a manner, higher-order displacements-based theories that account for non-classical effectssuch as transverse shear deformations and cross-section in- and out-of-plane warping are straightforwardly formulated.Results are given in terms of displacements, electrical potential and stresses.Comparison with three-dimensional finite elements models are provided, showing thataccurate results can be obtained with reduced computational costs.

Sign in / Sign up

Export Citation Format

Share Document