[Getfem-users] problem with structural calculations in getfem

Dear Yves,

First of all thank you very much for debugging that two NonLin term problem. If I also may consult you regarding the following:

While looking for bugs in my electrostatic-structural implementation I confrontated a problem with quite simple structural calculation in getfem. Although this calculation gives a result that looks nice, comparing the numbers whith commercial FEM package MSC. Marc gave very different solution.

The problem is very simple (please see the picture in the attachment):

A rectange with a size 0.8 by 0.1 is clamped at the sides.

A constant distributed load P is applied on the bottom surface of this rectangle. In getfem, this load (pressure) is prescribed by source_term, with vector "V(#1)+=comp(Normal().vBase(#1))(i,:,i);", assembled on the bottom boundary. Then this vector is scaled with the actual value of the pressure. In both Marc and Getfem the corresponding nodal force is calculated on the underformed geometry of the body (hence, no follower force).

The force causes the rectangle to subside downwards and the deflection of the middle part of the rectangle is measured.

Elastic properties (used by MSC. Marc) are

Young moduls: 20

Poisson ratio: 0.3

Plain strain assumed for 2D problem

Corresponding Lame constants (used in Getfem program):

Lambda: 11.5384

Mu: 7.6923

In both programs I used linear quad elements, splitting the rectangle 32X4. Both programs use 4 Gauss points for element integration.

A similar problem was also solved in 3D for 0.8X0.1X0.1 paralellepiped structure, descretized by 32X4X4 linear hex elements.

Bellow you can see small and finite strain results from the two programs:

2D, finite strain, distributed load P=-2.0:

MSC. Marc deflection = 0.229; Getfem deflection 0.192651

2D, small strain, distributed load P=-0.4

MSC.Marc deflection = 0.2667; Getfem deflection 0.1699

3D, finite strain, distributed load P=-2.0

MSC. Marc deflection = 0.2375; Getfem deflection 0.0191458 !!!

3D, small strain, distributed load P=-0.4

MSC. Marc deflection = 0.287; Getfem delflection 0.00400608 !!!

Even if Marc results are not correct, the agreement between 2D and 3D solution is much better then in Getfem. Additionally, when doing either p- or h- refinement in Marc, the result changes only slightly, by increasing the deflection (2-3 %). When I refine the mesh in Getfem, the deflection considerably reduces which is really strange.

The source of the program with the corresponding four parameter files (2D/3D and finite/small strain cases) can be found in the attachment.

Thank you in advance,

Andriy

__________________________________________
Andriy Andreykiv (PhD, MSc)
Delft University of Technology
Faculty of Mechanical Engineering
Material Science and Marine Technology
Group: Fundamentals of Microsystems
Mekelweg 2
2628 CD Delft
The Netherlands

E-mail : address@hidden
Tel.    :   (31) 15 2786818
Fax.    :   (31) 15 2789475
www     :   http://www-tm.wbmt.tudelft.nl/~andrico
private: (31) 6 47376804

From:	Andriy Andreykiv
Subject:	[Getfem-users] problem with structural calculations in getfem
Date:	Tue, 6 Nov 2007 17:50:02 +0100