U.S. patent application number 10/157499 was filed with the patent office on 2002-12-05 for analysis method using finite element method, program causing computer to execute same, and system for same.
This patent application is currently assigned to NEC CORPORATION. Invention is credited to Hirata, Ichiro.
Application Number | 20020183993 10/157499 |
Document ID | / |
Family ID | 19007513 |
Filed Date | 2002-12-05 |
United States Patent
Application |
20020183993 |
Kind Code |
A1 |
Hirata, Ichiro |
December 5, 2002 |
Analysis method using finite element method, program causing
computer to execute same, and system for same
Abstract
An FEM analysis system is provided which is capable of analyzing
with high accuracy and within a short time in a drop shock analysis
of electronic devices in which a very small mesh size is
incorporated. Processing to be performed by an optimal solution
selecting and analyzing section includes a step of checking whether
an analysis to be performed is a shock analysis, a step of
searching for a minimum mesh size when the analysis to be performed
is judged to be a shock analysis, a step of creating a simplified
analysis model using the minimum mesh size, a step of performing a
preliminary analysis on a simplified model by an implicit method
and explicit method, and a step of selecting either of the implicit
method or explicit method as an optimal analysis method by
comparing results from preliminary analysis, results from these
analyses and experiments or exact solution.
Inventors: |
Hirata, Ichiro; (Tokyo,
JP) |
Correspondence
Address: |
FOLEY AND LARDNER
SUITE 500
3000 K STREET NW
WASHINGTON
DC
20007
US
|
Assignee: |
NEC CORPORATION
|
Family ID: |
19007513 |
Appl. No.: |
10/157499 |
Filed: |
May 30, 2002 |
Current U.S.
Class: |
703/2 |
Current CPC
Class: |
G06F 30/23 20200101 |
Class at
Publication: |
703/2 |
International
Class: |
G06F 007/60 |
Foreign Application Data
Date |
Code |
Application Number |
May 31, 2001 |
JP |
2001-164730 |
Claims
What is claimed is:
1. An analysis method using a finite element method for performing
a stress analysis on an analysis model, comprising: a first step of
judging whether or not an analysis to be made is a shock analysis;
a second step of performing an analysis using an implicit method
when said analysis to be made is judged to be a shock analysis in
said first step; and a third step of performing an analysis using
an analysis method selected by an analyzer when said analysis to be
made is judged to be not a shock analysis in said first step.
2. The analysis method using the finite element method according to
claim 1, wherein a Newmark .beta. method is used as said implicit
method.
3. An analysis method using a finite element method for creating
meshes of an analysis model and for making a stress analysis of
said analysis model, said analysis method comprising: a first step
of judging whether an analysis to be made is a shock analysis; a
second step of searching for a minimum mesh size out of said meshes
of said analysis model; a third step of creating a simplified
analysis model using said minimum mesh size; a fourth step of
analyzing said simplified analysis model by using an implicit
method and an explicit method; a fifth step of selecting either of
said implicit method or said explicit method as an optimal method,
based on a result from an analysis in said fourth step; a sixth
step of having an analyzer select either of said implicit method or
said explicit method based on a result from said analysis in said
fourth step; and a seventh step of analyzing said analysis model by
using an analysis method selected in said fifth step or said sixth
step.
4. The analysis method using the finite element method according to
claim 3, wherein a Newmark .beta. method is used as said implicit
method.
5. The analysis method using the finite element method according to
claim 3, wherein, in said fifth step, when a following expression
holds, T.sub.im<T.sub.ex where said "T.sub.im" denotes analysis
time required for said implicit method and said "T.sub.ex" denotes
analysis time required for said explicit method, said implicit
method is selected while, when above said expression does not hold,
said explicit method is selected.
6. The analysis method using the finite element method according to
claim 3, wherein, in said fifth step, when a following expression
holds, abs(E-S.sub.im)<abs(E-S.sub.ex) where said "abs" denotes
an absolute value, said "S.sub.im" denotes an analysis result
containing data on displacement, stress, and distortion obtained
from said implicit method, said "S.sub.ex" denotes an analysis
result containing data on displacement, stress, and distortion
obtained from said explicit method, and said "E" denotes a result
containing data on displacement, stress, and distortion obtained
from said implicit method including an experiment value and an
exact solution of a theoretical expression and from a method other
than said explicit method, said implicit method is selected while,
when above said expression does not hold, said explicit method is
selected.
7. The analysis method using the finite element method according to
claim 3, wherein, in said sixth step, said analyzer is allowed to
select an analysis method based on a relation between analysis time
required for said implicit method said "T.sub.im" and analysis time
required for said explicit method said "T.sub.ex" and based on a
relation among an analysis result said "S.sub.im" containing
displacement, stress, and distortion obtained from said implicit
method, an analysis result said "S.sub.ex" containing displacement,
stress, and distortion obtained from said explicit method, and a
result said "E" containing displacement, stress, and distortion
obtained from said implicit method including an experiment value
and an exact solution of a theoretical expression and from a method
other than said explicit method.
8. A program for having a computer make an analysis using a finite
element method used to perform a stress analysis of an analysis
model: said program comprising: a first step of judging whether or
not an analysis to be made is a shock analysis; a second step of
performing an analysis using an implicit method when said analysis
to be made is judged to be a shock analysis in said first step; a
third step of performing an analysis by using an analysis method
selected by an analyzer when said analysis to be made is judged to
be not a shock analysis in said first step.
9. The program according to claim 8, wherein a Newmark .beta.
method is executed by a computer as said implicit method.
10. A program for having a computer execute an analysis using a
finite element method which creates meshes of an analysis model and
performs a stress analysis of said analysis model, said program
comprising: a first process of judging whether or not an analysis
to be performed is a shock analysis; a second process of searching
for a minimum mesh size out of said meshes of said analysis model;
a third process of creating a simplified analysis model using said
minimum mesh size; a fourth process of analyzing said simplified
analysis model by using an implicit method and an explicit method;
a fifth process of selecting either of said implicit method or said
explicit method as an optimal method, based on a result from said
analysis in said fourth process; a sixth process of having an
analyzer select either of said implicit method or said explicit
method based on a result from said analysis in said fourth process;
and a seventh process of analyzing said analysis model by using an
analysis method selected in said fifth process or said sixth
process.
11. The program according to claim 10, wherein a Newmark .beta.
method is executed by a computer as said implicit method.
12. The program according to claim 10, wherein, in said fifth
process, when a following expression holds, T.sub.im<T.sub.ex
where said "T.sub.im" denotes analysis time required for said
implicit method and said "T.sub.ex" denotes analysis time required
for said explicit method, said implicit method is selected while,
when above said expression does not hold, said explicit method is
selected.
13. The program according to claim 10, wherein, in said fifth
process, when a following expression holds,
abs(E-S.sub.im)<abs(E-S.sub.ex) where said "abs" denotes an
absolute value, said "S.sub.im" denotes an analysis result
containing data on displacement, stress, and distortion obtained
from said implicit method, S.sub.ex said denotes an analysis result
containing data on displacement, stress, and distortion obtained
from said explicit method, and said "E" denotes a result containing
data on displacement, stress, and distortion obtained from said
implicit method including an experiment value and an exact solution
of a theoretical expression and from a method other than said
explicit method, said implicit method is selected while, when above
said expression does not hold, said explicit method is
selected.
14. The program according to claim 10, wherein, in said sixth
process, said analyzer is allowed to select an analysis method
based on a relation between said analysis time required for said
implicit method said "T.sub.im" and said analysis time required for
said explicit method said "T.sub.ex" and based on a relation among
an analysis result said "S.sub.im" containing displacement, stress,
and distortion obtained from said implicit method, an analysis
result said "S.sub.ex" containing displacement, stress, and
distortion obtained from said explicit method, and a result said
"E" containing displacement, stress, and distortion obtained from
said implicit method including an experiment value and an exact
solution of a theoretical expression and from a method other than
said explicit method.
15. A finite element method analysis system having a unit for
creating meshes of an analysis model and having a unit for making
an analysis using a finite element method used to perform a stress
analysis on said analysis model using said finite element method,
said finite element method analysis system comprising: a first unit
to judge whether or not an analysis to be made is a shock analysis;
wherein, when said analysis to be performed by said unit for making
said analysis using said finite element method is judged by said
first unit to be a shock analysis, an analysis is made by using an
implicit method and wherein, when said analysis to be performed by
said unit making said analysis using said finite element method is
judged by said first unit to be not a shock analysis, said analysis
is made by using an analysis method selected by an analyzer.
16. The finite element method analysis system according to claim
15, wherein said unit making said analysis using said finite
element method performs a Newmark .beta. method as said implicit
method.
17. A finite element method analysis system having a unit for
creating meshes of an analysis model and having a unit for making
an analysis using a finite element method used to perform a stress
analysis on said analysis model using said finite element method,
said finite element method analysis system comprising: a first
section to judge whether or not an analysis to be performed is a
shock analysis; a second section to search for a minimum mesh size
out of said meshes of said analysis model; a third section to
create a simplified analysis model using said minimum mesh size; a
fourth section to select either of said implicit method or said
explicit method as an optimal method, based on a result from a
simplified analysis in which said simplified analysis model is
analyzed by a unit for making an analysis using a finite element
method by using an implicit method and an explicit method; a fifth
section to have an analyzer select either of said implicit method
or said explicit method as an analysis method based on a result
from said simplified analysis; and wherein said unit for making an
analysis using a finite element method analyzes said analysis model
by using said fourth section or said fifth section.
18. The finite element method analysis system according to claim
17, wherein said unit making said analysis using said finite
element method performs a Newmark .beta. method as said implicit
method.
19. The finite element method analysis system according to claim
17, wherein, said fourth section, when a following expression
holds, T.sub.im<T.sub.ex where said "T.sub.im" denotes analysis
time required for said implicit method and said "T.sub.ex" denotes
analysis time required for said explicit method, selects said
implicit method while, when above said expression does not hold,
selects said explicit method.
20. The finite element method analysis system according to claim
17, wherein, said fourth section, when a following expression
holds, abs(E-S.sub.im)<abs(E-S.sub.ex) where said "abs" denotes
an absolute value, said "S.sub.im" denotes an analysis result
containing data on displacement, stress, and distortion obtained
from said implicit method, said S.sub.ex denotes an analysis result
containing data on displacement, stress, and distortion obtained
from said explicit method, and said "E" denotes a result containing
data on displacement, stress, and distortion obtained from said
implicit method including an experiment value and an exact solution
of a theoretical expression and from a method other than said
explicit method, selects said implicit method while, when above
said expression does not hold, selects said explicit method.
21. The finite element method analysis system according to claim
17, wherein said fifth section has said analyzer select an analysis
method based on a relation between analysis time required for said
implicit method said "T.sub.im" and analysis time required for said
explicit method said "T.sub.ex" and based on a relation among an
analysis result said "S.sub.im" containing displacement, stress,
and distortion obtained from said implicit method, an analysis
result said "S.sub.ex" containing displacement, stress, and
distortion obtained from said explicit method, and a result said
"E" containing displacement, stress, and distortion obtained from
said implicit method including an experiment value and an exact
solution of a theoretical expression and from a method other than
said explicit method.
Description
BACKGROUND OF THE INVENTION
[0001] 1. Field of the Invention
[0002] The present invention relates to a drop shock analysis
system using an FEM (Finite Element Method) and more particularly
to an analysis method using the FEM for analyzing a drop shock of
an electronic device, a program for the analysis by the FEM method,
and an FEM analysis system.
[0003] The present application claims priority of Japanese Patent
Application No.2001-164730 filed on May 31, 2001, which is hereby
incorporated by reference.
[0004] 2. Description of the Related Art
[0005] Since it is expected that, by using a stress analysis (by
way of simulation) based on an FEM, a number of times of
manufacturing a prototype and of experiments can be reduced and a
development period can be shortened, the stress analysis using the
FEM is now being carried out increasingly in businesses or
universities.
[0006] The stress analysis can be classified into two types, one
being a static analysis and another being a dynamic analysis. A
method for the stress analysis can also be classified into two
types, one being an implicit method and another being an explicit
method. These two methods are different from each other in that an
expression of the implicit method contains a spring constant "k" as
a matrix, thereby forming a non-diagonal matrix and an expression
of the explicit method contains a mass "m" as a matrix, thereby
forming a diagonal matrix. Therefore, when the stress analysis is
performed, an inverse matrix calculation of the spring constant "k"
takes more time than an inverse matrix calculation of the mass "m".
Moreover, in the case of the implicit method, a simultaneous linear
equation is solved so that an equilibrium condition is satisfied
and therefore accuracy of a stress analysis is higher compared with
the explicit method, however, more time is required for the
analysis compared with the explicit method.
[0007] Each of the implicit and explicit methods has an advantage
and a disadvantage. As a result, the implicit method is used for
the static analysis not requiring so much time and the explicit
method is used, in most cases, for the dynamic analysis requiring
much time. Under present circumstances, in an automobile industry
having a most advanced drop shock (crash) analysis technology being
a field of the present invention, in particular, the stress
analysis is performed by using an explicit method-specific software
typified by PAM-SHOCK and LS-DYNA. FIG. 4 is a flowchart showing
one example of the analysis processing operation in a conventional
FEM analysis system. That is, in Step A301, whether or not an
analysis to be made is a shock analysis is judged and, if it is the
shock analysis, the explicit method provided in Step A303 is used
unconditionally and, if it is not the shock analysis, a subsequent
process is relegated to a judgement of the analyzer in Step
A304.
[0008] In such circumstances, sizes and weights of electronic
devices are being reduced rapidly in recent years and a cellular
phone or a like becomes widespread remarkably in particular,
however, a problem occurs in that, when it is dropped while
carrying it, a connected portion of an LSI chip embedded therein is
broken. In order to evaluate connection reliability of portable
electronic devices, an actual drop test is required using actual
electronic devices, however, the experiment entails high costs and
time. Therefore, a demand for reduction in costs required in such
experiments for a drop shock analysis is increasing. In an attempt
to respond to this demand, a method using a shock analysis
technique cultivated through experiences in automobiles was tried
by some universities, however, values calculated in experiments are
not in agreement with actual phenomena, for example, reaction force
(impact force) is extraordinarily larger (that is, larger by one to
two digits) than calculated values and it is therefore expected
that a new method of an analysis of a drop shock that can be used
for the analysis of electronic devices is developed.
[0009] A reason why behavior (deformation of each part) and
reaction force (impact force) are widely different from actual
phenomena when the explicit method is used for a dynamic analysis,
in particular, for a drop analysis of portable electronic devices
is explained below.
[0010] When ".DELTA.t.sub.ex" is defined to be an analysis time
interval in the explicit method and ".DELTA.t.sub.im" is defined to
be an analysis time interval in the implicit method, a constraint
in the implicit method is only a converging calculation of
displacement obtained from an equilibrium equation in every step
while the dynamic analysis is performed in the explicit method and
therefore there is a following constraint (Courant condition)
related to a minimum mesh size, longitudinal elastic modulus, and
mass density:
.DELTA.t.sub.ex<L/c Expression (3)
c=(E/.rho.).sup.1/2 Expression (4)
[0011] where "L" denotes a minimum mesh size in an analysis model,
"c" denotes a propagation speed of an elastic wave, "E" denotes a
longitudinal elastic modulus (also being called "Young's modulus")
and ".rho." denotes mass density. Thus, since the explicit method
has a property that it depends on the analysis time interval
.DELTA.t.sub.ex and since the analysis time interval
.DELTA.t.sub.ex has a constraint by a minimum mesh size "L" as
shown in the expression (3), the analysis time interval
.DELTA.t.sub.exbecomes too small in the analysis model for a
small-sized portable electronic device. Therefore, a following
expression (5) is given:
.alpha..apprxeq.v/.DELTA.t.sub.ex, F=m.alpha. Expression (5)
[0012] where ".alpha." denotes acceleration, "m" denotes a mass,
"F" denotes reaction force, and "v" denotes a drop velocity. As a
result, the calculation produces extremely large reaction force
(impact force) F and different deformation occurs.
[0013] As one example, when a body is dropped from a height of 1000
mm, due to a law of conservation of energy, a following equation
(6) is given:
v=(2gh).sup.1/2=4400 mm/s Expression (6)
[0014] where "g" denotes gravimetric acceleration and "h" denotes a
dropped height. Since a phenomenon of about 5.times.10.sup.-4
seconds is a problem in a drop of electronic devices, the
acceleration ".alpha." and the reaction force "F" have following
values.
.alpha.=4400.times.10000/5=8.times.10.sup.6 mm/s.sup.2
F=0.1.times.8.8.times.10.sup.6=880N
[0015] As a convergence stabilizing condition in the explicit
method, the analysis time interval .DELTA.t.sub.ex has to satisfy a
following relation:
.DELTA.t.sub.ex<L/c and
c=(E/.rho.).sup.1/2
[0016] If a solder ball diameter is 1.0 mm, a Young's modulus
E=19600 N/mm.sup.2, a density ".rho."=2.times.10.sup.-9
kg/mm.sup.3, c=3.2.times.10.sup.6 m/s. Here, if the solder ball
diameter is divided into four portions,
L/c=0.25/(3.2.times.10.sup.6) seconds=7.8.times.10.su- p.-8
seconds.
[0017] Therefore, in order to analyze a drop phenomenon at a speed
of 5.times.10.sup.-4 seconds, in the implicit method, by reducing
the acceleration ".alpha." to one tenth (that is, a digit is
reduced by one), its analysis is made possible, while, in the case
of the explicit method, an analysis time interval has to be reduced
to one thousands.
[0018] As described above, if an analysis time interval is same,
since a number of times of the analysis required to reach the value
of 5.times.10.sup.-4 seconds becomes same, time required for a
total analysis becomes more shorter in the explicit method in which
time required for one time analysis becomes short because of use of
an expression of a diagonal matrix compared with the implicit
method.
[0019] However, if the analysis time interval required for
satisfying conditions for stabilization in the explicit method
becomes extraordinarily smaller compared with that in the implicit
method because a fine mesh is contained like in the case of a model
for portable electronic devices, a number of times of the explicit
method (analysis time interval in the implicit method/analysis time
interval in the explicit method).times.(number of times in the
implicit method). As a result, due to an increased number of the
analysis in the explicit method, time required for the total
analysis is increased more in the explicit method compared with the
implicit method.
[0020] Moreover, in the analysis during the very short time
interval, there are some cases in which shock force increases and
deformation state is not in agreement with an actual phenomenon. In
the above example, in the case of the implicit method, a value
approaching to a result from a calculation on paper can be acquired
by using a shock force of about 980N, however, in the case of the
explicit method, about one hundred-folded shock force is
necessary.
SUMMARY OF THE INVENTION
[0021] In view of the above, it is an object of the present
invention to provide an FEM analysis system which is capable of
analyzing with high accuracy and with a short time in a drop shock
analysis of electronic devices or a like in which an analysis
result is very different from actual phenomena and in which a very
small mesh size is incorporated.
[0022] According to a first aspect of the present invention, there
is provided an analysis method using a finite element method for
performing a stress analysis on an analysis model, including:
[0023] a first step of judging whether or not an analysis to be
made is a shock analysis;
[0024] a second step of performing an analysis using an implicit
method when the analysis to be made is judged to be a shock
analysis in the first step; and
[0025] a third step of performing an analysis using an analysis
method selected by an analyzer when the analysis to be made is
judged to be not a shock analysis in the first step.
[0026] With the above configuration, whether or not an analysis to
be made is a shock analysis is judged and when it is judged to be a
shock analysis, an analysis is made using the implicit method.
Therefore, a shock analysis using the explicit method is not
performed in which a decrease in accuracy in an analysis and an
increase in analysis time occur when a mesh size is made minute and
an FEM analysis using the implicit method is made in which a result
from an analysis approaching to a real phenomena can be obtained
within a short time.
[0027] In the foregoing, a preferable mode is one wherein a Newmark
.beta. method is used as the implicit method.
[0028] According to a second aspect of the present invention, there
is provided an analysis method using a finite element method for
creating meshes of an analysis model and for making a stress
analysis of the analysis model, the analysis method including:
[0029] a first step of judging whether an analysis to be made is a
shock analysis;
[0030] a second step of searching for a minimum mesh size out of
the meshes of the analysis model;
[0031] a third step of creating a simplified analysis model using
the minimum mesh size;
[0032] a fourth step of analyzing the simplified analysis model by
using an implicit method and an explicit method;
[0033] a fifth step of selecting either of the implicit method or
the explicit method as an optimal method, based on a result from an
analysis in the fourth step;
[0034] a sixth step of having an analyzer select either of the
implicit method or the explicit method based on a result from the
analysis in the forth step; and
[0035] a seventh step of analyzing the analysis model by using an
analysis method selected in the fifth step or the sixth step.
[0036] With the above configuration, a simplified analysis model
using a minimum mesh size of an analysis model is analyzed by the
implicit method and explicit method. Based on a result from the
analysis, either of the implicit method or the explicit method is
selected as an optimal method and an FEM analysis is made by using
the selected analysis method. Moreover, the analysis method can be
selected by an analyzer and therefore it is possible to execute the
FEM analysis in consideration of demands required for an analysis
such as a desire for shortening analysis time or a desire for
placing importance on analysis accuracy.
[0037] In the foregoing, a preferable mode is one wherein a Newmark
.beta. method is used as the implicit method.
[0038] Also, a preferable mode is one wherein, in the fifth step,
when a following expression holds,
T.sub.im<T.sub.ex
[0039] Where the "T.sub.im" denotes analysis time required for the
implicit method and "T.sub.ex" denotes analysis time required for
the explicit method, the implicit method is selected while, when
above the expression does not hold, the explicit method is
selected.
[0040] Also, a preferable mode is one wherein, in the fifth step,
when a following expression holds,
abs(E-S.sub.im)<abs(E-S.sub.ex)
[0041] where the "abs" denotes an absolute value, the "S.sub.im"
denotes an analysis result containing data on displacement, stress,
and distortion obtained from the implicit method, the "S.sub.ex"
denotes an analysis result containing data on displacement, stress,
and distortion obtained from the explicit method, and the "E"
denotes a result containing data on displacement, stress, and
distortion obtained from the implicit method including an
experiment value and an exact solution of a theoretical expression
and from a method other than the explicit method, the implicit
method is selected while, when above the expression does not hold,
the explicit method is selected.
[0042] Also, a preferable mode is one wherein, in the sixth step,
the analyzer is allowed to select an analysis method based on a
relation between analysis time required for the implicit method
"T.sub.im" and analysis time required for the explicit method
"T.sub.ex" and based on a relation among an analysis result
"S.sub.im" containing displacement, stress, and distortion obtained
from the implicit method, an analysis result "S.sub.ex" containing
displacement, stress, and distortion obtained from the explicit
method, and a result "E" containing displacement, stress, and
distortion obtained from the implicit method including an
experiment value and an exact solution of a theoretical expression
and from a method other than the explicit method.
[0043] According to a third aspect of the present invention, there
is provided a program for having a computer make an analysis using
a finite element method used to perform a stress analysis of an
analysis model: the program including;
[0044] a first step of judging whether or not an analysis to be
made is a shock analysis;
[0045] a second step of performing an analysis using an implicit
method when the analysis to be made is judged to be a shock
analysis in the first step;
[0046] a third step of performing an analysis by using an analysis
method selected by an analyzer when the analysis to be made is
judged to be not a shock analysis in the first step.
[0047] In the foregoing, a preferable mode is one wherein a Newmark
.beta. method is executed by a computer as the implicit method.
[0048] According to a fourth aspect of the present invention, there
is provided a program for having a computer execute an analysis
using a finite element method which creates meshes of an analysis
model and performs a stress analysis of the analysis model, the
program including:
[0049] a first process of judging whether or not an analysis to be
performed is a shock analysis;
[0050] a second process of searching for a minimum mesh size out of
the meshes of the analysis model;
[0051] a third process of creating a simplified analysis model
using the minimum mesh size;
[0052] a fourth process of analyzing the simplified analysis model
by using an implicit method and an explicit method;
[0053] a fifth process of selecting either of the implicit method
or the explicit method as an optimal method, based on a result from
the analysis in the fourth process;
[0054] a sixth process of having an analyzer select either of the
implicit method or the explicit method based on a result from the
analysis in the fourth process; and
[0055] a seventh process of analyzing the analysis model by using
an analysis method selected in the fifth process or the sixth
process.
[0056] In the foregoing, a preferable mode is one wherein a Newmark
.beta. method is executed by a computer as the implicit method.
[0057] Also, a preferable mode is one wherein, in the fifth
process, when a following expression holds,
T.sub.im<T.sub.ex
[0058] Where the "T.sub.im" denotes analysis time required for the
implicit method and the "T.sub.ex" denotes analysis time required
for the explicit method, the implicit method is selected while,
when above the expression does not hold, the explicit method is
selected.
[0059] Also, a preferable mode is one wherein, in the fifth
process, when a following expression holds,
abs(E-S.sub.im)<abs(E-S.sub.ex)
[0060] where the "abs" denotes an absolute value, the "S.sub.im"
denotes an analysis result containing data on displacement, stress,
and distortion obtained from the implicit method, the S.sub.ex
denotes an analysis result containing data on displacement, stress,
and distortion obtained from the explicit method, and the "E"
denotes a result containing data on displacement, stress, and
distortion obtained from the implicit method including an
experiment value and an exact solution of a theoretical expression
and from a method other than the explicit method, the implicit
method is selected while, when above the expression does not hold,
the explicit method is selected.
[0061] Also, a preferable mode is one wherein, in the sixth
process, the analyzer is allowed to select an analysis method based
on a relation between the analysis time required for the implicit
method "T.sub.im" and the analysis time required for the explicit
method "T.sub.ex" and based on a relation among an analysis result
"S.sub.im" containing displacement, stress, and distortion obtained
from the implicit method, an analysis result "S.sub.ex" containing
displacement, stress, and distortion obtained from the explicit
method, and a result "E" containing displacement, stress, and
distortion obtained from the implicit method including an
experiment value and an exact solution of a theoretical expression
and from a method other than the explicit method.
[0062] According to a fifth aspect of the present invention, there
is provided a finite element method analysis system having a unit
for creating meshes of an analysis model and having a unit for
making an analysis using a finite element method used to perform a
stress analysis on the analysis model using the finite element
method, the finite element method analysis system including:
[0063] a first unit to judge whether or not an analysis to be made
is a shock analysis;
[0064] wherein, when the analysis to be performed by the unit for
making the analysis using the finite element method is judged by
the first unit to be a shock analysis, an analysis is made by using
an implicit method and wherein, when the analysis to be performed
by the unit making the analysis using the finite element method is
judged by the first unit to be not a shock analysis, the analysis
is made by using an analysis method selected by an analyzer.
[0065] In the foregoing, a preferable mode is one wherein the unit
making the analysis using the finite element method performs a
Newmark .beta. method as the implicit method.
[0066] According to a sixth aspect of the present invention, there
is provided a finite element method analysis system having a unit
for creating meshes of an analysis model and having a unit for
making an analysis using a finite element method used to perform a
stress analysis on the analysis model using the finite element
method, the finite element method analysis system including:
[0067] a first section to judge whether or not an analysis to be
performed is a shock analysis;
[0068] a second section to search for a minimum mesh size out of
the meshes of the analysis model;
[0069] a third section to create a simplified analysis model using
the minimum mesh size;
[0070] a fourth section to select either of the implicit method or
the explicit method as an optimal method, based on a result from a
simplified analysis in which the simplified analysis model is
analyzed by a unit for making an analysis using a finite element
method by using an implicit method and an explicit method;
[0071] a fifth section to have an analyzer select either of the
implicit method or the explicit method as an analysis method based
on a result from the simplified analysis; and
[0072] wherein the unit for making an analysis using a finite
element method analyzes the analysis model by using the fourth
section or the fifth section.
[0073] In the foregoing, a preferable mode is one wherein the unit
making the analysis using the finite element method performs a
Newmark .beta. method as the implicit method.
[0074] Also, a preferable mode is one wherein, the fourth section,
when a following expression holds,
T.sub.im<T.sub.ex
[0075] where the "T.sub.im" denotes analysis time required for the
implicit method and the "T.sub.ex" denotes analysis time required
for the explicit method, selects the implicit method while, when
above the expression does not hold, selects the explicit
method.
[0076] Also, a preferable mode is one wherein, the fourth section,
when a following expression holds,
abs(E-S.sub.im)<abs(E-S.sub.ex)
[0077] where the "abs" denotes an absolute value, the "S.sub.im"
denotes an analysis result containing data on displacement, stress,
and distortion obtained from the implicit method, the S.sub.ex
denotes an analysis result containing data on displacement, stress,
and distortion obtained from the explicit method, and the "E"
denotes a result containing data on displacement, stress, and
distortion obtained from the implicit method including an
experiment value and an exact solution of a theoretical expression
and from a method other than the explicit method, selects the
implicit method while, when above the expression does not hold,
selects the explicit method.
[0078] Also, a preferable mode is one wherein the fifth section has
the analyzer select an analysis method based on a relation between
analysis time required for the implicit method "T.sub.im" and
analysis time required for the explicit method "T.sub.ex" and based
on a relation among an analysis result "S.sub.im" containing
displacement, stress, and distortion obtained from the implicit
method, an analysis result "S.sub.ex" containing displacement,
stress, and distortion obtained from the explicit method, and a
result "E" containing displacement, stress, and distortion obtained
from the implicit method including an experiment value and an exact
solution of a theoretical expression and from a method other than
the explicit method.
[0079] With the above configuration, whether an analysis is made by
the explicit method or whether the analysis is made by the implicit
method can be selected according to an analysis model. Since an
analysis can be performed on an analysis model using an optimal
method, an analysis result can be obtained with high accuracy and
within a short time.
BRIEF DESCRIPTION OF THE DRAWINGS
[0080] The above and other objects, advantages, and features of the
present invention will be more apparent from the following
description taken in conjunction with the accompanying drawings in
which;
[0081] FIG. 1 is a schematic diagram showing an FEM analysis system
according to a first embodiment of the present invention;
[0082] FIG. 2 is a flowchart showing a processing operation to be
performed by an optimal solution selecting and analyzing section in
the FEM analysis system of the first embodiment of the present
invention;
[0083] FIG. 3 is a flowchart showing a processing operation to be
performed by an optimal solution selecting and analyzing section in
an FEM analysis system of the second embodiment of the present
invention; and
[0084] FIG. 4 is a flowchart showing one example of a processing
operation in a conventional FEM analysis system.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
[0085] Best modes of carrying out the present invention will be
described in further detail using various embodiments with
reference to the accompanying drawings.
First Embodiment
[0086] FIG. 1 is a schematic block diagram showing an FEM analysis
system according to an embodiment of the present invention. As
shown in FIG. 1, the FEM analysis system of the embodiment includes
an analysis model creating section 100, an analysis model data
registering section 101 to store analysis model data to a file, an
optimal solution selecting and analyzing section 102, and an
analysis data registering section 103 to store analysis data to a
file.
[0087] Rough operations of each of the above sections are as
follows.
[0088] The analysis model creating section 100, after having
performed a meshing process (that is, after having discretized a
shape using an element) based on CAD (Computer-Aided Design) data
or after having created shape data from a preprocessor to be
exclusively used for an analysis and having performed a meshing
process, adds a boundary condition required for the analysis to a
model.
[0089] The analysis model data registering section 101 registers
analysis model data created by the analysis model creating section
100 on a specified file in a storage medium 104.
[0090] The optimal solution selecting and analyzing section 102
judges which method can perform an analysis, with high accuracy and
within a short time, on analysis model data registered by the
analysis model data registering section 101, the implicit method or
the explicit method, and analyzes the data by the selected
method.
[0091] Finally, the analysis data registering section 103 registers
data analyzed by the optimal solution selecting and analyzing
section 102 on a specified file in the storage medium 104.
[0092] Next, operations of the entire FEM analysis system are
described in detail by referring to the block diagram in FIG. 1 and
to the flowchart in FIG. 2.
[0093] As shown in the schematic block diagram in FIG. 1, in the
analysis model creating section 100 of the first embodiment, after
a meshing process has been performed based on CAD data or after
shape data has been formed from a preprocessor being exclusively
used for analysis and then the meshing process has been performed,
boundary conditions required for analysis are added to a model.
[0094] Next, in the analysis model data registering section 101, an
analysis model data created by the analysis model creating section
100 is registered on a specified file in the storage medium
104.
[0095] Moreover, in the optimal solution selecting and analyzing
section 102, which method can perform an analysis, with high
accuracy and within a short time, on analysis model data registered
by the analysis model data registering section 101 on a specified
file in the storage medium 104 is judged, the implicit method or
the explicit method, and the data is analyzed using the selected
method.
[0096] Finally, in the analysis data registering section 103, data
analyzed by the optimal solution selecting and analyzing section
102 is stored in a specified file in the storage medium 104.
[0097] Especially, a method for selecting an optimal solution and
for analyzing by the optimal solution selecting and analyzing
section 102 serving as a characteristic portion of the present
invention is described by referring to the flowchart in FIG. 2.
[0098] First, in a step (A1 in FIG. 2) in which checking is made on
whether or not an analysis to be made is a shock analysis, a
judgement is made as to whether processing to be performed by the
optimal solution selecting and analyzing section 102 is a shock
analysis or not and, if the above processing is a shock analysis,
an analysis using the implicit method is executed in a step (A2 in
FIG. 2) in which the implicit method is to be performed. If the
processing is other than the shock analysis, processing is
relegated to a judgement of an analyzer in a next step (A4 in FIG.
2).
[0099] Moreover, in the optimal solution selecting and analyzing
section 102, a Newmark .beta. method is preferably used as the
implicit method. The implicit method can be roughly classified into
two types, one being the Newmark .beta. method and another being a
Houbalt method. Research by the inventor shows that, when the
Newmark .beta. method is used, a value approaching to a result from
a calculation on paper is obtained, however, when the Houbalt
method (cubic function interpolation) is used, the value becomes
near to a result from an analysis performed using the explicit
method. Therefore, though all the methods being called the implicit
method are not always suitable to a drop analysis of electronic
devices, a method that can be used for the drop analysis is not
limited to the Newmark .beta. method applied to the embodiment of
the present invention.
[0100] As explained above, in the embodiment, when a shock analysis
is performed on electronic device models or a like having a portion
with a very small mesh size, an analysis using the implicit method
is selected. Therefore, by using the FEM analysis system of the
embodiment of the present invention, unlike in the case of using
the FEM analysis system using the explicit method in which a
decrease in analysis accuracy and an increase in analysis time
occur when a mesh size becomes minute, a highly accurate analysis
result approaching to a real phenomenon can be obtained within a
short time.
Second Embodiment
[0101] Processing in an FEM analysis system of a second embodiment
is same as that of the first embodiment except processing to be
performed in an optimal solution selecting and analyzing section
102 and their descriptions are omitted accordingly. In the second
embodiment, same reference numbers are assigned to corresponding to
configurations and processing of the FEM analysis system as in the
first embodiment.
[0102] FIG. 3 is a flowchart showing processing operations to be
performed by the optimal solution selecting and analyzing section
102 in the FEM analysis of the second embodiment of the present
invention.
[0103] As shown in the flowchart in FIG. 3, the optimal solution
selecting and analyzing section 102 performs processing in Step A1
in which checking is made on whether or not an analysis to be made
is a shock analysis, processing in Step A5 in which a minimum mesh
size is searched for, processing in Step A6 in which a simplified
analysis model is created using a minimum mesh size, processing in
Step A7 in which a preliminary analysis is performed by an implicit
method and by an explicit method, processing in Step A8 in which an
analysis method is selected based on an analysis result, processing
in Step A2 in which an analysis is performed using an implicit
method, processing in Step A3 in which an analysis is performed
using an explicit method, and processing in Step A4 in which a
process is relegated to a judgement of an analyzer.
[0104] Next, operations of an entire FEM analysis system will be
described by referring to the flowchart in FIG. 3.
[0105] First, in the step (A1 in FIG. 3) in which checking is made
as to whether an analysis to be made is a shock analysis, the
analysis to be made is judged to be a shock analysis, the
processing proceeds to a step (A5 in FIG. 3) in which a minimum
mesh size is searched for and if the analysis to be made is judged
to be an analysis other than the shock analysis, the routine
proceeds to a next step (A4 in FIG. 3) in which a process is
relegated to a judgement of an analyzer and the routine is
terminated.
[0106] If an analysis to be made is judged to be a shock analysis
and the routine proceeds to a step (A5 in FIG. 3) in which a
minimum mesh size is searched for, in a step (A6 in FIG. 3) in
which a simplified analysis model is created by using a minimum
mesh size, mesh cutting processing is performed by using a minimum
mesh size obtained by an automatic mesh function is step A5 on CAD
data having a simplified shape that has been already registered and
an FEM analysis model is produced. Moreover, in a step (A7 in FIG.
3) in which an analysis is performed by using the implicit method
and the explicit method, a preliminary analysis is performed using
a simplified model based on the both the methods.
[0107] Next, an analysis method is determined in a step (A8 in FIG.
3) in which an optimal analysis method is to be selected based on a
result from a preliminary analysis. If a following expression holds
in the preliminary analysis,
T.sub.im<T.sub.ex Expression (1)
[0108] where "T.sub.im" denotes analysis time required for the
implicit method and "T.sub.ex" denotes analysis time required for
the explicit method, that is, if, in the preliminary analysis, the
analysis time required for the implicit method is shorter than that
required for the explicit method, the routine proceeds to a step
(A2 in FIG. 3) in which the analysis using the implicit method is
performed in order to perform the analysis by the implicit method.
On the other hand, if a relation between the analysis time
"T.sub.im" and the analysis time "T.sub.ex" does not satisfy the
above expression (1), that is, if the analysis time required for
the explicit method is shorter than that required for the implicit
method, the routine proceeds to a step (A3 in FIG. 3) in which an
analysis by the explicit method is performed in order to perform
the analysis by the explicit method.
[0109] Thus, by using the expression (1) as a reference for
selection of the analysis method, a method that can perform an
analysis within a short time can be selected.
[0110] Moreover, selection of the analysis method in a step (A8 in
FIG. 3) in which an optimal analysis method is selected may be made
in a way other than that using the above expression (1).
[0111] That is, if a following expression (2) holds, an analysis is
made by using a model causing the analysis to be performed in the
step (A2 in FIG. 3) in which the implicit method is used;
otherwise, the analysis is made by using a model causing the
analysis to be performed in the step (A3 in FIG. 3) in which the
explicit method is used:
abs(E-S.sub.im)<abs(E-S.sub.ex) Expression (2)
[0112] where the "abs" denotes an absolute value, "S.sub.im"
denotes an analysis result including data on displacement, stress,
distortion, or a like obtained by the implicit method in the
preliminary analysis in Step A7, "S.sub.ex" denotes an analysis
result including data on displacement, stress, distortion, or a
like obtained by the explicit method, and "E" denotes a result
obtained by an experiment including data on displacement, stress,
distortion, or a like or an exact solution obtained from a
theoretical expression.
[0113] Thus, by using an analysis method given by the expression
(2) as a reference for selection, a simplified model based on a
minimum mesh size of a model to be analyzed can be created, a
preliminary analysis can be made by actually using both methods, an
analysis method having less errors can be selected by making a
comparison between an analysis result obtained by the preliminary
analysis and a result obtained from an experiment or an exact
solution, which enable highly accurate acquirement of analysis
results.
[0114] The method that can satisfy the expressions.(1) and the
method that can satisfy the expression (2) are not always same and,
in the case of the analysis handling enormous numbers of meshes,
even if some discrepancies occur between results obtained by using
the above methods and results obtained by experiments, it is
possible to select a method which requires less time.
[0115] To respond to such cases, an analyzer may select an analysis
method by adding the step A4 in which a judgement is made by the
analyzer after the step (A8 in FIG. 3) in which an analysis method
is determined based on the analysis result and by making a
comparison between the expression (1) allowing selection of the
method in which a result can be obtained within a short time and
the expression (2) allowing selection of the method providing a
highly accurate analysis. In this case, the analyzer can select a
method that the analyzer desires from a viewpoint of analysis time
and analysis accuracy.
[0116] As described above, in the first embodiment as shown by the
flowchart in FIG. 2, if, an analysis to be performed, in step A1 in
which checking is made as to whether or not the analysis to be made
is a shock analysis, is judged to be a shock analysis, an analysis
using the implicit method is made in Step A2. While, in the second
embodiment as shown by the flowchart in FIG. 3, by performing
procedures shown in Steps A5 to A8, a simplified model based on a
minimum mesh size of a model to be analyzed is created and an
preliminary analysis is made by the implicit method or the explicit
method in a separate manner.
[0117] Thus, according to the FEM analysis system of the second
embodiment, like in the case of the first embodiment, when a shock
analysis to be performed on electronic device models or a like
having portions being very small in a mesh size is made, an
analysis result approaching to actual phenomena can be obtained
with high accuracy within a short time. Moreover, in the FEM
analysis system of the second embodiment, after a simplified model
has been created based on a minimum mesh size of a model to be
analyzed, a preliminary analysis using both the methods and
therefore an optimal method to be applied to an individual model
can be selected with high accuracy.
[0118] It is apparent that the present invention is not limited to
the above embodiments but may be changed and modified without
departing from the scope and spirit of the invention.
* * * * *