System, method, and computer program product for performing transformation of rotations to translations during finite element stiffness formulation

1. A method for performing a finite element rotation transformation, comprising:

discretizing a region of an object model into finite elements;

determining an approximate rotational displacement solution for each finite element depending on the finite element type;

determining an element stiffness matrix for each finite element and global stiffness;

evaluating displacement and load column matrices for each element by substituting loads and boundary conditions; and

solving a resulting system of equations to produce translation displacements at each node of each finite element.

2. The method of claim 1 , further comprising converting the approximate rotational displacements to translations based on force displacement relations.

3. The method of claim 1 , wherein determining global stiffness includes assembling all the element stiffness matrices.

4. The method of claim 1 , wherein at least one finite element is a solid element.

5. The method of claim 1 , wherein at least one finite element is a shell element.

6. The method of claim 1 , wherein at least one finite element is a beam element.

7. The method of claim 1 , wherein the element stiffness matrix for each element includes the effect of both translation and rotation loads.

8. A data processing system having at least a processor and accessible memory, comprising:

means for discretizing a region of an object model into finite elements;

means for determining an approximate rotational displacement solution for each finite element depending on the finite element type;

means for determining an element stiffness matrix for each finite element and global stiffness;

means for evaluating displacement and load column matrices for each element by substituting loads and boundary conditions; and

means for solving a resulting system of equations to produce translation displacements at each node of each finite element.

9. The data processing system of claim 8 , further comprising means for converting the approximate rotational displacements to translations based on force displacement relations.

10. The data processing system of claim 8 , wherein determining global stiffness includes assembling all the element stiffness matrices.

11. The data processing system of claim 8 , wherein at least one finite element is a solid element.

12. The data processing system of claim 8 , wherein at least one finite element is a shell element.

13. The data processing system of claim 8 , wherein at least one finite element is a beam element.

14. The data processing system of claim 8 , wherein the element stiffness matrix for each element includes the effect of both translation and rotation loads.

15. A computer product tangibly embodied in a machine-readable medium, comprising:

instructions for discretizing a region of an object model into finite elements;

instructions for determining an approximate rotational displacement solution for each finite element depending on the finite element type;

instructions for determining an element stiffness matrix for each finite element and global stiffness;

instructions for evaluating displacement and load column matrices for each element by substituting loads and boundary conditions; and

instructions for solving a resulting system of equations to produce translation displacements at each node of each finite element.

16. The computer program product of claim 15 , further comprising instructions for converting the approximate rotational displacements to translations based on force displacement relations.

17. The computer program product of claim 15 , wherein determining global stiffness includes assembling all the element stiffness matrices.

18. The computer program product of claim 15 , wherein at least one finite element is a solid element.

19. The computer program product of claim 15 , wherein at least one finite element is a shell element.

20. The computer program product of claim 15 , wherein at least one finite element is a beam element.

21. The computer program product of claim 15 , wherein the element stiffness matrix for each element includes the effect of both translation and rotation loads.