Stability problems encountered in the finite element method

Bachelor Project – Spring 2015

Under certain conditions, a radical change in behavior can be observed while employing the finite element method using the displacement formulation. Such phenomena can be described as stability problems. The objective of this project was to be able to illustrate and study the evolution of two recurrent phenomenon: zero energy modes and volumetric locking. Both behaviors were studied using Matlab, by thoroughly changing the framework of an existing code to cater to the needs of the study. Amongst a wide variety of remedies that effectively cure such stability problems, the following methods were illustrated and/or discussed:

• The effect of a reduced and full integration on a bilinear element, illustration of hour glassing modes

• The injection of an artificial hour glassing stiffness using the Frazlier method

• The mixed method , for cases near the incompressible limit

• The selective-integration method , a penalty method that allows for a good approximation of the mixed method while retaining the displacement formulation

• The B-Bar method , a generalization of the selective integration method for axisymmetric and anisotropic mediums

 

Influence of integration scheme on displacements for nearly incompressible limit – Full, Reduced and Selective.

 

Student:

Hugo Nicolas Ribet, [email protected]

Advisors:

Jaehyun Cho (LSMS), [email protected]

Jean-François Molinari (LSMS), [email protected]