Mesh-free method and system for modeling and analysis

• US 6,718,291 B1
• Filed: 06/22/2000
• Issued: 04/06/2004
• Est. Priority Date: 07/02/1999
• Status: Expired due to Term

• Current Assignee: Intact Solutions, LLC
• Original Assignee: Igor G. Tsukanov, Vadim Shapiro
• Inventors: Shapiro, Vadim, Tsukanov, Igor G.
• Primary Examiner(s): Broda, Esq., Samuel
• Assistant Examiner(s): PHAN, THAI Q
• Application Number:
  US09/602,070
• Time in Patent Office: 1,384 Days
• Field of Search: 703/2, 703/14, 703/18, 703/5, 707/104.1, 716/20
• US Class Current: 703/2
• CPC Class Codes: G06F 2111/10 Numerical modelling
• CPC Class Codes: G06F 30/00 Computer-aided design [CAD]
• CPC Class Codes: G06F 30/10 Geometric CAD
• CPC Class Codes: G06F 30/23 using finite element methods [FEM] or finite difference methods [FDM]

Abstract

A method and apparatus for mesh-free engineering analysis of geometric models is described. The method and apparatus, which are preferably software-based and implemented on personal computers or other programmable processing devices, represent geometric models by implicit mathematical functions. The implicit functions allow interpolation of all desired boundary conditions over the geometry without meshing, and the boundary conditions may then may be combined with a piecewise continuous model of the solution structure (i.e., the analysis problem). By solving for elements of the solution structure (its basis or coordinate functions) which satisfy the given boundary conditions either exactly or approximately, the solution structure will define the behavior and boundary conditions (exactly or approximately) throughout the geometric model.

Claims

1. A method of determining unknown field values in a CAD geometric model having known field values defined on at least one portion of the model, the field values being of one or more types, the method comprising:

a. for each portion of the model'"'"'s geometry upon which a field value is defined, constructing an implicit function which mathematically represents the portion'"'"'s geometry;

b. for each type of field value;

(1) constructing an interpolating function from the field values belonging to that type of field value and from the implicit functions representing the portions of the geometry corresponding to the field values belonging to that type of field value;

(2) constructing a composite implicit function combining the implicit functions representing the portions of the geometry corresponding to that type of field value;

(3) constructing a solution structure from

(a) the interpolating function,

(b) the composite implicit function, and

(c) predefined basis functions having unknown coefficients;

c. if more than one type of field value exists, constructing a combined solution structure by interpolating the solution structures for the different types using the composite implicit functions constructed for the different types;

d. processing the solution structure to determine the unknown coefficients of the basis functions;

e. using the coefficients to determine unknown field values.

2. The method of claim 1 further comprising the step of creating the geometric model in a CAD application.

3. The method of claim 2 further comprising the step of defining the known field values on portions of the geometric model within the CAD application.

4. The method of claim 2 further comprising the step of importing the geometric model from the CAD application.

5. The method of claim 1 wherein the geometric model is chosen from one of:

a. a constructive solid geometry model;

b. a boundary representation model;

or

c. a feature-based model.

6. The method of claim 1 wherein the geometric model is a portion of a larger CAD geometric model.

7. The method of claim 1 wherein the geometric model is a simplified approximation of a more complex CAD geometric model.

8. The method of claim 1 wherein the step of constructing an implicit function for each portion of the model'"'"'s geometry upon which a field value is defined includes:

a. for each portion, identifying one or more geometric primitives whose logical combination defines the portion; and

b. defining implicit functions which mathematically represent the primitives; and

c. combining the implicit functions, thereby obtaining the implicit function which mathematically represents the portion'"'"'s geometry.

9. The method of claim 1 wherein the step of processing the solution structure includes at least one of:

a. differentiation of the solution structure or portions thereof;

b. integration of the solution structure or portions thereof; and

c. algebraic solution for the unknown coefficients within the solution structure or portions thereof.

10. The method of claim 8 wherein the implicit functions are combined by R-functions.

11. The method of claim 1 further comprising the steps of:

a. after the unknown field values are determined, redefining the known field values; and

b. reperforrning the steps of claim 1.

12. The method of claim 1 further comprising the steps of:

a. after the unknown field values are determined, modifying the geometry of the geometric model; and

b. reperforming the steps of claim 1.

13. A method wherein the unknown field values determined by the method of claim 1 define a new geometric model upon which the method of claim 1 is repeated.

14. A method wherein the unknown field values determined by the method of claim 1 are then used as the known field values defined on the geometric model, whereupon which the method of claim 1 is repeated to determine further unknown field values.

15. A method of determining unknown field values in a CAD geometric model having known field values defined on at least one portion of the model, the method comprising:

a. for each portion of the model'"'"'s geometry upon which a field value is defined;

(1) identifying one or more geometric primitives whose logical combination defines the portion;

(2) defining implicit functions which mathematically represent the primitives;

(3) combining the implicit functions, thereby obtaining the implicit function which mathematically represents the portion'"'"'s geometry.

b. constructing a solution structure from;

(1) the implicit functions representing each portion'"'"'s geometry,

(2) the field values defined thereon, and

(3) predefined basis functions having unknown coefficients,

wherein determination of the unknown coefficients yields the unknown field values from the solution structure.

16. The method of claim 15 wherein:

a. the field values defined on the geometric model are of at least two types, and

b. the step of constructing a solution structure is performed for each type, with the solution structure for each type being constructed from;

(1) the implicit functions representing the portions of the geometry upon which that type of field value are defined,

(2) the field values defined thereon, and

(3) predefined basis functions having unknown coefficients.

17. The method of claim 16 wherein if more than one type of field value exists, the solution structure is a combined solution structure created by interpolating the solution structures for the different types using the composite implicit functions constructed for the different types.

18. A method wherein the unknown field values determined by the method of claim 15 are then used as the known field values defined on the geometric model, whereupon which the method of claim 15 is repeated to determine further unknown field values.

19. The method of claim 15 wherein the step of processing the solution structure includes at least one of:

a. differentiation of the solution structure or portions thereof;

b. integration of the solution structure or portions thereof; and

c. algebraic solution for the unknown coefficients of the solution structure or portions thereof.

20. The method of claim 15 wherein the implicit functions are combined by R-functions.

21. The method of claim 15 further comprising the step of creating the geometric model in a CAD application.

22. A method wherein the unknown field values determined by the method of claim 15 define a new geometric model upon which the method of claim 15 is repeated.

23. The method of claim 15 further comprising the steps of:

a. after the unknown field values are determined, redefining the known field values; and

b. reperforming the steps of claim 15.

24. The method of claim 15 further comprising the steps of:

a. after the unknown field values are determined, modifying the geometry of the geometric model; and

b. reperforming the steps of claim 15.

25. A method of determining unknown field values in a CAD geometric model having known field values defined on at least one portion of the model, the field values being of one or more types, the method comprising:

a. for each portion of the model'"'"'s geometry upon which a field value is defined;

(1) identifying one or more geometric primitives whose logical combination defines the portion;

(2) defining implicit functions which mathematically represent the primitives;

(3) combining the implicit functions, thereby obtaining the implicit function which mathematically represents the portion'"'"'s geometry;

b. for each type of field value, constructing a corresponding solution structure, the solution structure for each type being constructed from;

(1) the implicit functions representing the geometry of the portions of the model having the type of field value in question;

(2) the field values defined on those portions of the model, and

(3) predefined basis functions having unknown coefficients;

c. if more than one type of field value exists, constructing a combined solution structure by interpolating the solution structures for the different types over the corresponding portions of the geometric model;

d. processing the solution structure to determine the unknown coefficients of the basis functions; and

e. using the coefficients to determine unknown field values.

26. The method of claim 25 wherein the step of constructing a combined solution structure comprises:

a. for each type of field value, constructing an interpolating function from the field values belonging to that type of field value and from the implicit functions representing the portions of the geometry corresponding to the field values belonging to that type of field value;

b. interpolating the solution structures for the different types using the composite implicit functions constructed for the different types.