Analyzing apparatus, analyzing method, and computer program

1. An analyzing system configured to output information for member shape modification for reducing deformation of a member formed by a press forming process at a position of the member, the deformation caused by springback, the analyzing apparatus system comprising:

a computer processor configured to:

obtain finite element model data for a finite element model indicating a shape of the member, material physical property data indicating material physical properties of the member, and stress distribution data indicating a stress distribution which occurs in the member; execute a finite element method to determine:

a displacement of nodes of the finite element model data caused by springback, the determination being based on (a) the finite element model data, (b) the material physical property data, and (c) the stress distribution data, thereby generating first displacement distribution data indicating a displacement distribution of the member caused by the springback; and

a displacement of nodes of the finite element model data with respect to each of a plurality of natural vibration deformation modes based on (a) the finite element model data and (b) the material physical property data, thereby generating respective second displacement distribution data, each indicating a respective displacement distribution of the member for a respective one of the plurality of natural vibration deformation modes; determine a degree of coincidence between the first displacement distribution data and each of the second displacement distribution data, the degree of coincidence indicating degree of relevance between displacement in each natural vibration deformation mode and displacement based on deformation caused by springback;

select, for candidate modifications, one or more of the natural vibration deformation modes based on the respective degrees of coincidence; and

determine a disposition of one or more beads in the finite element model data for increasing a natural frequency of at least a portion of the one or more natural vibration deformation modes, the disposition of the beads being such that, if applied, the disposition modifies the shape of the member,

a bead comprising of concaves and convexes on the surface is formed at a position of the member, the position determined based on results of a finite element analysis of the model of the member.

2. The analyzing system according to claim 1 , wherein the selection is of a predetermined number of natural vibration deformation modes in order of the respective degrees of coincidence, beginning from the natural vibration deformation mode in which the degree of coincidence is largest.

3. The analyzing system according to claim 1 , wherein the selection is performed such that only those of the natural vibration deformation modes for which the respective degree of coincidence is larger than a predetermined threshold are selected.

4. The analyzing system according to claim 1 , wherein the degree of coincidence is determined by equation (1), equation (2), or equation (3):

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wherein u ij denotes a displacement of a node j in an i-th order natural vibration deformation mode, u SBj denotes a displacement of node j in springback deformation, and a i , b i , and c i , denote the degree of coincidence between the i-th order natural vibration deformation mode and the springback deformation.

5. A computer-implemented method for reducing deformation of a member formed by a press forming process at a position of the member, the deformation caused by springback, the method comprising:

(a) obtaining, by a computer processor, finite element model data for a finite element model indicating a shape of the member, material physical property data indicating material physical properties of the member, and stress distribution data indicating a stress distribution which occurs in the member;

(b) executing, by the processor, a finite element method to determine:

(i) a displacement of nodes of the finite element model data caused by springback, the determination being based on (a) the finite element model data, (b) the material physical property data, and (c) the stress distribution data, thereby generating first displacement distribution data indicating a displacement distribution of the member caused by the springback;

(ii) a displacement of nodes of the finite element model data with respect to each of a plurality of natural vibration deformation modes based on (a) the finite element model data and (b) the material physical property data, thereby generating respective second displacement distribution data, each indicating a respective displacement

distribution of the member for a respective one of the plurality of natural vibration deformation modes;

(c) determining, by the processor, a degree of coincidence between the first displacement distribution data and each of the second displacement distribution data, the degree of coincidence indicating degree of relevance between displacement in each natural vibration deformation mode and displacement based on deformation caused by springback;

(d) selecting, by the processor for candidate modifications, one or more of the natural vibration deformation modes based on the respective degrees of coincidence; and

(e) determining a disposition of one or more beads in the finite element model data for increasing a natural frequency of at least a portion of the one or more natural vibration deformation modes, the disposition of the beads being such that, if applied, the disposition modifies the shape of the member; and

forming a bead comprising of concaves and convexes on the surface at a position of the member, the position determined based on results of a finite element analysis of the model of the member.

6. The method according to claim 5 , further comprising:

(f) re-performing step (b)(i) incorporating the bead distribution determined in step (e) into the finite element model data to obtain a new shape;

(g) comparing the new shape to a target shape; and

(h) executing instructions that cause the processor to:

if a difference between the new shape and the target shape determined in step (g) is greater that a threshold difference, re-perform steps (b)(ii)-(h); and

if the difference between the new shape and the target shape determined in step (g) is not greater than the threshold difference, output a representation of the member with the bead distribution of the last execution of step (e).

7. The method according to claim 5 , further comprising:

outputting a representation of the member with the bead distribution.

8. The method according to claim 5 , wherein the selection is of a predetermined number of natural vibration deformation modes in order of the respective degrees of coincidence, beginning from the natural vibration deformation mode in which the degree of coincidence is largest.

9. The method according to claim 5 , wherein the selection is performed such that only those of the natural vibration deformation modes for which the respective degree of coincidence is larger than a predetermined threshold are selected.

10. The computer-implemented method according to claim 5 , wherein the degree of coincidence is determined by equation (1), equation (2), or equation (3):

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wherein u ij denotes a displacement of a node j in an i-th order natural vibration deformation mode, u SBj denotes a displacement of node j in springback deformation, and a i , b i , and c i , denote the degree of coincidence between the i-th order natural vibration deformation mode and the springback deformation.

11. A non-transitory computer-readable medium on which are stored instructions that are executable by a computer processor, the instructions which, when executed by the processor, cause the processor to perform a method for reducing deformation of a member formed by a press forming process at a position caused by springback, the method comprising:

obtaining finite element model data for a finite element model indicating a shape of the member, material physical property data indicating material physical properties of the member, and stress distribution data indicating a stress distribution which occurs in the member; executing a finite element method to determine:

a displacement of nodes of the finite element model data caused by springback, the determination being based on (a) the finite element model data, (b) the material physical property data, and (c) the stress distribution data, thereby generating first displacement distribution data indicating a displacement distribution of the member caused by the springback;

a displacement of nodes of the finite element model data with respect to each of a plurality of natural vibration deformation modes based on (a) the finite element model data and (b) the material physical property data, thereby generating respective second displacement distribution data, each indicating a respective displacement distribution of the member for a respective one of the plurality of natural vibration deformation modes; determining a degree of coincidence between the first displacement distribution data and each of the second displacement distribution data, the degree of coincidence indicating degree of relevance between displacement in each natural vibration deformation mode and displacement based on deformation caused by springback; and

selecting one or more of the natural vibration deformation modes based on the respective degrees of coincidence; and

determining a disposition of one or more beads in the finite element model data for increasing a natural frequency of at least a portion of the one or more natural vibration deformation modes, the disposition of the beads being such that, if applied, the disposition modifies the shape of the member: and

forming a bead comprising of concaves and convexes on the surface at a position of the member, the position determined based on results of a finite element analysis of the model of the member.

12. The non-transitory computer-readable medium according to claim 11 , wherein the degree of coincidence is determined by equation (1), equation (2), or equation (3):

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wherein u ij denotes a displacement of a node j in an i-th order natural vibration deformation mode, u SBj denotes a displacement of node j in springback deformation, and a i , b i , and c i , denote the degree of coincidence between the i-th order natural vibration deformation mode and the springback deformation.