Special-purpose programmed computer for numerical simulation of a metal forming process having a predefined load path with corresponding mesh adjustment scheme

1. A special-purpose programmed computer system for obtaining numerically-simulated physical behaviors of a workpiece sheet metal during a metal forming process having a predefined load path comprises:

an input/output (I/O) interface;

a memory for storing computer readable code for a special-purpose finite element analysis (FEA) based application module;

at least one processor coupled to the memory, said at least one processor executing the computer readable code in the memory to cause the special-purpose FEA based application module to perform operations of:

receiving a FEA mesh model containing a plurality of finite elements to represent a workpiece sheet metal in a time-marching simulation of obtaining numerical physical behaviors of the workpiece sheet metal during a metal forming process having a predefined load path, whereby the obtained numerical physical behaviors are used for production improvements of parts used in a prototype or concept vehicle;

further receiving a total simulation time period, the predefined load path that contains a three-dimensional continuous path of a forming tool in the total simulation period, a set of mesh refinement criteria and a mesh coarsening criterion, the set of mesh refinement criteria includes a series of predetermined mesh adjustment times during the time-marching simulation, a characteristic length for establishing a three-dimensional (3-D) mesh refinement zone and a desired mesh refinement level;

(a) setting a current simulation time to an initial value;

(b) determining a current simulation period from the current simulation time and a subsequent next mesh adjustment time in the series of mesh adjustment times;

(c) using the characteristic length to establish the 3-D mesh refinement zone that contains a space encompassing a section of the predefined load path corresponding to the current simulation period;

(d) updating the FEA mesh model by refining those finite elements deemed to be located within the 3-D mesh refinement zone to the desired mesh refinement level;

(e) further updating the FEA mesh model by coarsening certain finite elements located outside of the 3-D mesh refinement zone in accordance with the mesh coarsening criterion;

(f) conducting a corresponding portion of the time-marching simulation using the updated FEA mesh model for the current simulation period until the current simulation time has reached the subsequent next mesh adjustment time; and

(g) repeating (b)-(f) until the current simulation time has passed the total simulation time period.

2. The special-purpose programmed computer system of claim 1 , wherein the plurality of finite elements comprises two-dimensional shell element.

3. The special-purpose programmed computer system of claim 1 , wherein the metal forming process having the predefined load path comprises an incremental sheet metal forming or hemming.

4. The special-purpose programmed computer system of claim 1 , wherein the space surrounding the corresponding section of the predefined load path comprises a three-dimensional tube with a semi-sphere at either end of the tube.

5. The special-purpose programmed computer system of claim 4 , wherein the tube is centered along the corresponding section of the predefined load path.

6. The special-purpose programmed computer system of claim 4 , wherein both the tube and the semi-sphere have a radius equal to the characteristic length.

7. The special-purpose programmed computer system of claim 1 , wherein said those finite elements deemed to be located within the 3-D mesh refinement zone are determined using respective centroids of said those finite elements.

8. The special-purpose programmed computer system of claim 1 , wherein said those finite elements deemed to be located within the 3-D mesh refinement zone are determined using respective corners of said those finite elements.

9. The special-purpose programmed computer system of claim 1 , wherein the mesh coarsening criterion is used for determining respective element strain gradients of a cluster of four finite elements that share a common corner node.

10. A non-transitory computer readable medium containing instructions for obtaining numerically-simulated physical behaviors of a workpiece sheet metal during a metal forming process having a predefined load path by a method comprises:

receiving, in a special-purpose programmed computer system having a special-purpose finite element analysis (FEA) based application module installed thereon, a FEA mesh model containing a plurality of finite elements to represent a workpiece sheet metal in a time-marching simulation of obtaining numerical physical behaviors of the workpiece sheet metal during a metal forming process having a predefined load path, whereby the obtained numerical physical behaviors are used for production improvements of parts used in a prototype or concept vehicle;

further receiving, in the special-purpose programmed computer system, a total simulation time period, the predefined load path that contains a three-dimensional continuous path of a forming tool in the total simulation period, a set of mesh refinement criteria and a mesh coarsening criterion, the set of mesh refinement criteria includes a series of predetermined mesh adjustment times during the time-marching simulation, a characteristic length for establishing a three-dimensional (3-D) mesh refinement zone and a desired mesh refinement level;

with the special-purpose FEA based application module,

(a) setting, with the special-purpose FEA based application module, a current simulation time to an initial value;

(b) determining, with the special-purpose FEA based application module, a current simulation period from the current simulation time and a subsequent next mesh adjustment time in the series of mesh adjustment times;

(c) using, with the special-purpose FEA based application module, the characteristic length to establish the 3-D mesh refinement zone that contains a space encompassing a section of the predefined load path corresponding to the current simulation period;

(d) updating, with the special-purpose FEA based application module, the FEA mesh model by refining those finite elements deemed to be located within the 3-D mesh refinement zone to the desired mesh refinement level;

(e) further updating the FEA mesh model by coarsening certain finite elements located outside of the 3-D mesh refinement zone in accordance with the mesh coarsening criterion;

(f) conducting, with the special-purpose FEA based application module, a corresponding portion of the time-marching simulation using the updated FEA mesh model for the current simulation period until the current simulation time has reached the subsequent next mesh adjustment time; and

(g) repeating, with the special-purpose FEA based application module, (b)-(f) until the current simulation time has passed the total simulation time period.

11. The non-transitory computer readable medium of claim 10 , wherein the plurality of finite elements comprises two-dimensional shell element.

12. The non-transitory computer readable medium of claim 10 , wherein the metal forming process having the predefined load path comprises an incremental sheet metal forming or hemming.

13. The non-transitory computer readable medium of claim 10 , wherein the space surrounding the corresponding section of the predefined load path comprises a three-dimensional tube with a semi-sphere at either end of the tube.

14. The non-transitory computer readable medium of claim 13 , wherein the tube is centered along the corresponding section of the predefined load path.

15. The non-transitory computer readable medium of claim 13 , wherein both the tube and the semi-sphere have a radius equal to the characteristic length.

16. The non-transitory computer readable medium of claim 10 , wherein said those finite elements deemed to be located within the 3-D mesh refinement zone are determined using respective centroids of said those finite elements.

17. The non-transitory computer readable medium of claim 10 , wherein said those finite elements deemed to be located within the 3-D mesh refinement zone are determined using respective corners of said those finite elements.

18. The non-transitory computer readable medium of claim 10 , wherein the mesh coarsening criterion is used for determining respective element strain gradients of a cluster of four finite elements that share a common corner node.