Tech Briefs

A New Iterative Solver for Higher-Order Elements in the Analysis of Solids

(For an update to this News, please see the ADINA News of Jul. 30, 2007.)

In many analyses of solids, the free-form meshing in ADINA is used with 3D tetrahedral elements. Then it is desirable to employ the 10-node or 11-node tetrahedral elements. These higher-order elements give much better stress predictions than the low-order 4-node tetrahedral elements. In a general analysis, meshes with 10-node and 11-node elements frequently also contain shell elements, beams, springs, bolts, etc. and in particular contact conditions. Instead of, or with, these higher-order tetrahedral elements also 20-node or 27-node brick elements might be used.

In these cases, frequently in nonlinear analysis 1 to 5 million equations need to be solved. Solutions using any direct sparse solver can then be very demanding, in terms of the solution time, memory and disk storage used.

We have developed a new iterative solver for ADINA 8.4 for such finite element systems. The iterative solver is effective when

• Systems of 1 to 5 million equations are solved;

• Mostly 10-node (11-node) tetrahedral elements and 20-node (27-node) brick elements are used in the mesh;

• Otherwise all other elements and material models, and the contact solution algorithms in ADINA can be used.

The figures below show the meshes and analysis statistics of two example solutions. It should be noted that the analyses include contact conditions, and while mostly higher-order solid elements were used, the models also contained some other structural elements.

Surely, the new iterative solver will be very useful in many linear and nonlinear analyses. Courtesy of John Deere

Model of Rear Axle
Elements used: 210,422 10-node tetrahedra; 11,640 6-node shells; 180 bolts;
1,859 2-node trusses; 82 beams; 16 springs. 3-D contact without friction.

 Total no. of equations = 1,117,489 No. of contact equations = 6,589 Total no. of solutions steps = 2 Total no. of Newton-Raphson iterations = 9 Total elapsed solution time = 18 min Memory required = 2.2 GB

Computer: Dell PC running Linux with two EM64T 3.2 GHz processors and 6 GB RAM Courtesy of John Deere

Model of Wheel
Elements used: 484,414 10-node tetrahedra; 14,707 6-node shells;
660 2-node trusses; 30 bolts. 3-D contact with friction.

 Total no. of equations = 2,441,812 No. of contact equations = 17,754 Total no. of solutions steps = 5 Total no. of Newton-Raphson iterations = 62 Total elapsed solution time = 5 hr 25 min Memory required = 4.3 GB

Computer: Dell PC running Linux with two EM64T 3.2 GHz processors and 6 GB RAM