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 “Δt_{ex}” is defined to be an analysis time interval in the explicit method and “Δt_{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:
Δt _{ex} <L/c Expression (3)
c=(E/ρ)^{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 “ρ” denotes mass density. Thus, since the explicit method has a property that it depends on the analysis time interval Δt_{ex }and since the analysis time interval Δt_{ex }has a constraint by a minimum mesh size “L” as shown in the expression (3), the analysis time interval Δt_{ex}becomes too small in the analysis model for a small-sized portable electronic device. Therefore, a following expression (5) is given:
α≈v/Δt _{ex} , F=mα Expression (5)
[0012]
where “α” 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)^{1/2}=4400 mm/s Expression (6)
[0014]
where “g” denotes gravimetric acceleration and “h” denotes a dropped height. Since a phenomenon of about 5×10^{−4 }seconds is a problem in a drop of electronic devices, the acceleration “α” and the reaction force “F” have following values.
α=4400×10000/5=8×10^{6 } mm/s ^{2 }
F=0.1×8.8×10^{6}=880N
[0015]
As a convergence stabilizing condition in the explicit method, the analysis time interval Δt_{ex }has to satisfy a following relation:
Δt _{ex} <L/c and
c=(E/ρ) ^{1/2 }
[0016]
If a solder ball diameter is 1.0 mm, a Young's modulus E=19600 N/mm^{2}, a density “ρ”=2×10^{−9 }kg/mm^{3}, c=3.2×10^{6 }m/s. Here, if the solder ball diameter is divided into four portions, L/c=0.25/(3.2×10^{6}) seconds=7.8×10^{−8 }seconds.
[0017]
Therefore, in order to analyze a drop phenomenon at a speed of 5×10^{−4 }seconds, in the implicit method, by reducing the acceleration “α” 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 5×10^{−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)×(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 β 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 β 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_{im}<T_{ex }
[0039]
Where the “T_{im}” denotes analysis time required for the implicit method and “T_{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 _{im})<abs(E−S _{ex})
[0041]
where the “abs” denotes an absolute value, the “S_{im}” denotes an analysis result containing data on displacement, stress, and distortion obtained from the implicit method, the “S_{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_{im}” and analysis time required for the explicit method “T_{ex}” and based on a relation among an analysis result “S_{im}” containing displacement, stress, and distortion obtained from the implicit method, an analysis result “S_{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 β 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 β 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
_{im}
<T
_{ex }
[0058]
Where the “T_{im}” denotes analysis time required for the implicit method and the “T_{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 _{im})<abs(E−S _{ex})
[0060]
where the “abs” denotes an absolute value, the “S_{im}” denotes an analysis result containing data on displacement, stress, and distortion obtained from the implicit method, the S_{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_{im}” and the analysis time required for the explicit method “T_{ex}” and based on a relation among an analysis result “S_{im}” containing displacement, stress, and distortion obtained from the implicit method, an analysis result “S_{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 β 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 β method as the implicit method.
[0074]
Also, a preferable mode is one wherein, the fourth section, when a following expression holds,
T
_{im}
<T
_{ex }
[0075]
where the “T_{im}” denotes analysis time required for the implicit method and the “T_{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 _{im})<abs(E−S _{ex})
[0077]
where the “abs” denotes an absolute value, the “S_{im}” denotes an analysis result containing data on displacement, stress, and distortion obtained from the implicit method, the S_{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_{im}” and analysis time required for the explicit method “T_{ex}” and based on a relation among an analysis result “S_{im}” containing displacement, stress, and distortion obtained from the implicit method, an analysis result “S_{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.