Computational Mechanics Forum

Hello,

Recently I faced two questions in course that I am attending:

1) Outline the salient features of different higher order shell theories.

2)Explain why some shell theories are not suitable as the basis of element formulation.

3) Discuss any limitations of elements being used in relation to their underlying formulation ( e.g use of shallow shell theory or cylindrical shell theory).

Engineering Strain vs Logarithmic strain I would like to have your (experts) interpretation on Engineering strain and Logarithmic strain.  Based on what I’ve studied, I would request your comments on what I state below in regard to Engineering strain and logarithmic strain: 

I’m trying to program geometric non linear analysis (finite element)-for a shallow truss element.I am using the book by Crisfield for the purpose. Basically, I am using the incremental approach for analysis.And I am struck with a problem.The problem is that my Structural stiffness matrix (after application of Boundary conditions) is singular i.e. it’s determinant value is “0”.

What is the difference between Eulerian and Lagrangian coordinates?

I have read that, Eulerian coordinates correspond to spatial points and Lagrangian correspond to material points.

A material point corresponds to a spatial coordinate in initial configuration?

I'm , however, not able to get the diference between the two.Can anyone explain?

In conventional linear finite element analysis, what do we use?Lagrangian or Eulerian mesh?

This is a very fundmantal question.

What is the physical significance of stress invariants?

I understand that the stress invariant J2 of the deviatoric stress tensor is used to ecpress the yield criteria-but this is same as Von Mises yield criteria-I want to know what is so special about-stess invariants?

I understand that these invariants remain unaltered by rotation/transformation of the axis-is this the only reason for being so special or there i any other reason as well?

Hi

Isotropic hardening means, sigma_yield ll be same under both the tension (sigma_tension_yield) and compression loading(sigma_comp_yield). and the total sigma_y=sigma_tensio_yield+sigma_comp_yield.

In the case of isotropic hardening, If you increase the tensile yield strength by some means, at the same time your compressive stress ll also get increased. Hence, you get a increased radius of the yield surface. with the same shape with increased size of yield surface. and your total sigma_y ll no more remain constant. It ll get increased.