JP2903098B2 - Structural design method - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION [Industrial Application Field] The present invention relates to a structural design method for performing structural design using a structural analysis based on a finite element method, and reduces the number of times of trial and error of analysis in structural design. And a structural design method for improving the design efficiency.

[Conventional technology]

As products become larger and more complex, it is important to accurately predict static and dynamic characteristics of the structure at the design stage in order to ensure reliability. For this reason, it is indispensable to sufficiently perform a structural analysis based on the finite element method at the design stage. Generally, when designing a structure, a designer often determines the shape and material by trial and error in order to satisfy the target specification. Therefore, a sensitivity analysis method has been introduced that indicates the degree to which the static and dynamic characteristics of the structure are affected when the structural parameters such as the shape and the material are changed.

When the sensitivity analysis method is used for the structural analysis based on the finite element method, when the structural parameters of each element are changed by a unit amount, the sensitivity coefficient that indicates the change in structural deformation, stress, natural frequency, and vibration response is obtained. Can be. On the other hand, the number of element divisions is enormous in order to accurately obtain the static and dynamic characteristics of a structure and to analyze a large-scale system. Actually, when the designer changes the structural parameters, the change is rarely made for each element, and the structural parameters for a plurality of elements are often changed in common. For this reason, the designer must newly obtain a combined sensitivity coefficient of a plurality of elements by combining the sensitivity coefficients of necessary elements using the sensitivity coefficients obtained for the individual elements. Therefore, when the number of elements is large, a great deal of time is required for calculation, and data management is complicated.

The literature on the structural analysis using the sensitivity analysis method includes “Sensitivity Analysis in Damped Vibration System and Prediction of Dynamic Characteristics after Design Change”, Transactions of the Japan Society of Mechanical Engineers (C), vol. 50, No. 452 (Showa 59-4). Pages 597 to 606, Vibration Model and Simulation (Applied Technology Publishing).

[Problems to be solved by the invention]

In the above-described conventional technology, obtaining a sensitivity coefficient when simultaneously changing structural parameters in a plurality of elements, or obtaining a sensitivity coefficient when simultaneously changing a plurality of structural parameters is performed as a separate operation by a designer's judgment. I needed to do it. In addition, since the amount of data is enormous, much time has been spent to determine how much the structural parameter change in which element affects the structural characteristics.

SUMMARY OF THE INVENTION The present invention has been made to solve the above problems, and an object of the present invention is to provide a structural design method that enables a designer to efficiently execute a structural design involving a structural change.

[Means for solving the problem]

In order to achieve the above object, a combination sensitivity coefficient based on a combination of elements required by a designer is automatically calculated using a sensitivity coefficient for a design parameter in each element. In addition, the sensitivity coefficients for each structural parameter in each element are stored, and the sensitivity coefficient of each element is read out at any time so that a required combination sensitivity coefficient can be obtained. Further, in order to easily express the magnitude of the combination sensitivity coefficient, the horizontal axis indicates the element number, and the vertical axis indicates the type of the structural parameter, and the magnitude of the sensitivity coefficient is indicated.

[Action]

Deformation, stress, natural frequency, and sensitivity coefficient of vibration response, which represent structural characteristics with respect to a change in the unit amount of the structural parameter in each element, are obtained in advance. Next, by using these sensitivity coefficients, the designer specifies a plurality of elements in a portion where structural change is to be considered so as to satisfy the design specifications, thereby obtaining a combination sensitivity coefficient of the plurality of elements. by this,
Designers can predict changes in structural characteristics when structural parameters of a plurality of elements are changed simultaneously. Further, the magnitude of the sensitivity coefficient for the structural parameter in each element, the magnitude of the sensitivity coefficient for the structural parameter in a plurality of elements, and the magnitude of the sensitivity coefficient when a plurality of structural parameters are simultaneously changed are simultaneously displayed in a graph. Deformation and vibration response sensitivity coefficients are determined at each node of the finite element. The stress is determined for each element.
Further, the natural frequency is obtained in a structural model to be analyzed. Thus, the designer can easily determine which part should be changed and how much to satisfy the target structural specification.

When the structure is composed of many parts and each part is composed of many finite elements, the designer can calculate the sensitivity coefficient for each part, so that the design can be easily performed for each part.

〔Example〕

Embodiments of the present invention will be described with reference to the drawings. First
The figure shows a structural model to be analyzed using the finite element method. The structural model 1 is divided into elements 2 to use the finite element method, and a node 3 of the element 2 is provided. Each element is represented by an element number i (i = 1 to N), and each node is represented by a node number 1 (1 = 1 to L).

FIG. 2 is a view showing the first embodiment of the present invention, and is a flowchart for obtaining the sensitivity coefficient of the natural frequency of the structural model 1. In step 201, as shown in FIG.
Is divided into elements and nodes are provided. In step 202, a load condition for each element and structural parameters such as a material constant and a shape / dimension method are set. The structural model 1 overall stiffness matrix [K] calculated from the structure parameters of each element i in step 203, then the thickness of the structural parameters represented by step 204 in P _j, modulus, Poisson's ratio, the cross-sectional area, A change in the rigidity matrix [K] when one of the structural parameters such as density is changed by a unit amount, that is, a differential value [∂K / ∂P _j ] of the rigidity matrix is obtained. Note that j (j = 1 to J) is a number assigned to the structural parameter. In step 205, the mass matrix [M] of the entire structural model 1 is calculated from the structural parameters of each element i, and then in step 206, the change in the mass matrix [M] when the structural parameter P _j is changed by a unit amount, ie, The differential value [∂M / ∂P _j ] of the mass matrix [M] is obtained.

In step 207, the natural frequency f ^(k) and the natural mode [Φ] of the structural model 1 are obtained from the rigidity matrix [K] and the mass matrix [M]. Here, f ^(k) indicates the natural frequency next to k. In step 208, the natural frequency f ^(k) , the natural mode [Φ], the differential values [∂K / ∂P _j ] _j and [∂M / ∂P _j ] _i
Calculating the following sensitivity coefficients for the structural parameters P _j of element i natural frequency f ^(k) of ^{(∂f (k)) / ∂P} j) i of k using. Here, the sensitivity coefficient (f ^(k) , _j ) in element i is ₁
= (∂f ^(k) / ∂P _j ) _i indicates the amount of change in the natural frequency of the structural model 1 when one of the structural parameters j is changed by a unit amount in each element.

Therefore, the structural model is composed of multiple parts or multiple finite element models (eg, beam elements, truss elements, shell elements, etc.).
It is assumed that it is composed of Here, a finite element model number m (m = 1 to M) is assigned to the finite element model. It is assumed that each of these components is modeled by a plurality of elements.
Therefore, the sensitivity coefficient obtained in step 208 is calculated as (f ^(k) , _j )
replace ^{_{m, i = (∂f (k}} ) / ∂P j) m, and _i. Further, in order to know the degree of influence of the structural parameters of each part or the finite element model on the natural frequency of the structural model, the structural model 1
Coefficient of sensitivity _{^{(f (k), j)}} m, utilizes ^{_{j = (∂f (k) /}} ∂P j) m, i. In step 209, a combination sensitivity coefficient c ^(k) _{m, j} when one structural parameter is simultaneously changed by a unit amount in a plurality of elements i1 to i2 of the element i is determined. The calculation formula at this time is It is given by equation (1). Further, the sensitivity coefficient c ^(k) _{m, i} is obtained for the combination when the plurality of structural parameters are simultaneously changed in unit amount in step 210. The calculation formula at this time is (2)
In the formula Given by The addition of the above combination calculation is a scalar calculation.

Next, in step 211, the maximum value is ^{obtained from the} sensitivity coefficients f ^(k) , _j and the combination sensitivity coefficients c ^(k) _{m, j} , c ^(k) _{m, i} by using equation (3). That is, C = ((f ^(k) , _j ) _{m, i} , c ^(k) _{m, j} , c ^(k) _{m, i} ) max (3) ｛i = 1 to n; k = 1 to K ｝ The above sensitivity coefficients (f ^(k) , _j ) _{m, i} and combination sensitivity coefficient c ^(k)
_In order to make it easy to understand the magnitude relation between _{m, j} and c ^(k) _{m, i} , a graph is displayed in step 212. Hereinafter, this display method will be described based on a display example shown in FIG. The horizontal axis indicates the part or finite element model number m and the element number i or a plurality of elements (i1 to i2). The vertical axis represents the structural parameter P _j ,
Shows the combination structure parameter ΣP _j . At this time, in order to indicate the magnitudes of the sensitivity coefficients f ^(k) _{i, j} , c ^(k) _{m, j} and c ^(k) _{m, i} of the ^k-th natural frequency, the maximum value C is set to the maximum radius. R is displayed as a circle, and the other sensitivity coefficients are displayed as circles having a radius obtained by multiplying the sensitivity coefficient by R / C. Thus, the magnitude of the sensitivity coefficient can be easily determined based on the size of the circle.

Next, as a second embodiment, a sensitivity analysis in a deformation analysis will be described with reference to a flowchart shown in FIG. In FIG. 4, element division of structural model in step 401, setting the structural parameters P _j at step 402, calculation of the stiffness matrix [K] in step 402, step 404
The calculation of the differential value ∂ [K] / jP _j with respect to the structural parameter of the mass matrix in Steps 201 to 204 in the first embodiment
Is the same as

In the next step 405, calculating a deformation [delta] _l at node l (l = 1 to L) when the load Q _l is applied is one of the structural parameters P _j to node l the structural model 1 shown in FIG. 1 I do. In step 406, changing the unit amount of structural parameters P _j of the element number i of the differential value ∂ for structural parameters P _j of the modified [delta] ₁ stiffness matrix [K] / ∂P _j and parts or finite element model number m with Then, the sensitivity coefficient (∂δ _l / ∂P _j ) _i of the deformation at the node 1 is calculated. Step 40
In FIG. 7, the combination sensitivity coefficient (C _{l, at} the node l when the unit quantities of the structural parameters of the (i1 to _i- th) elements are simultaneously changed using this sensitivity coefficient (∂δ _l / ∂P _j ) _{i j} ) Calculate _m . Also, the combination sensitivity coefficient (C _l ) at the node l when a plurality of structural parameters are changed simultaneously in step 408
Calculate _m . The addition of the above combination calculation is a scalar calculation. These calculation results are displayed in a form as shown in FIG.

FIG. 5 shows a flowchart of sensitivity analysis in vibration response analysis as a third embodiment. . Element division of the structural model in step 501, setting of structural parameters in step 502, calculation of rigidity matrix in step 503, calculation of mass matrix in step 504, differentiation of rigidity matrix for structural parameters in step 505 The calculation, the calculation of the differential value for the structural parameter of the mass matrix in Step 506, and the calculation of the natural frequency and the natural mode in Step 507 are the same as Steps 201 to 207 in the first embodiment. In step 508, the vibration response is calculated using these calculation results. Step 5
In step 09, the sensitivity coefficient of the natural frequency is obtained as in the first embodiment, and the sensitivity coefficient of the eigenmode is also obtained. Using the above computation result can be calculated sensitivity coefficient of the vibration response at the node l when the structural parameters P _j of the element number i of the component or the finite element model number m was changed unit amount in step 510. In step 511, the sensitivity coefficient of the vibration response is used (i
1 to i2) The combination sensitivity coefficient (C at the node l when the unit amount of the structural parameter of the plurality of elements is simultaneously changed
_{l, j} ) Calculate _m . In step 512, the combination sensitivity coefficient (C _l ) _m at the node 1 when a plurality of structural parameters are changed simultaneously is calculated. The addition of the above combination calculation is a complex number calculation. These calculation results are displayed in step 513 in the form as shown in FIG.

Further, the case where the sensitivity analysis is applied to the stress analysis in the structural analysis can be handled in the same manner as in the first to third embodiments.

〔The invention's effect〕

According to the present invention, when performing a structural analysis based on the finite element method, not only the sensitivity coefficient of each element but also each component constituting a structure, a plurality of finite element combination sensitivity coefficients, and a plurality of structural parameters are simultaneously determined. Since the combination sensitivity coefficient at the time of the change can also be calculated, the structure can be changed efficiently. Also, by displaying the results in a graph, it is possible to easily compare the magnitudes of the respective sensitivity coefficients, which is effective for the designer to determine which part should be changed when the structure is changed. Also, since the sensitivity coefficients obtained for each element or each node are stored, the combination sensitivity coefficients of various combinations can be freely obtained without repeating the structural analysis, and the number of calculations can be reduced. it can.

From the above, the number of trial-and-error structural analyzes required by a designer for a structural design can be significantly reduced, and design changes can be easily determined.

[Brief description of the drawings]

FIG. 1 is a diagram showing a structural model, FIG. 2 is a flowchart for analyzing a sensitivity coefficient of a natural frequency of the structural model as a first embodiment of the present invention, and FIG. 3 is a display diagram for comparing the magnitude of the sensitivity coefficient. FIG. 4 is a flowchart for analyzing a sensitivity coefficient of deformation of a structural model as a second embodiment, and FIG.
5 is a flowchart for analyzing a sensitivity coefficient of a vibration response of a structural model as an example of the embodiment. 1 ... structural model, 2 ... elements 3 ... node, P _j ... structural parameters, f ^(k) ... natural frequency, [delta] _l ... deformation, i ... element number,
j: Structural parameter number, l: Node number, m: Finite element model number.

──────────────────────────────────────────────────続 き Continuing from the front page (72) Michiyo Sakayoro, Inventor 502, Kandatecho, Tsuchiura-shi, Ibaraki Pref. Machinery Research Laboratory, Hitachi, Ltd. (58) Field surveyed (Int.Cl. ⁶ , DB name) G06F 17/50 JICST (JOIS)

Claims (2)

(57) [Claims] 1. A structural design method in which a sensitivity analysis method is applied in a structural analysis using a finite element method, wherein a structure of a finite element model constituting a structure model, such as a plate thickness, a cross-sectional area, and a longitudinal elastic modulus, is used. When the parameter is changed by unit amount,
Calculate the sensitivity coefficients representing the stress change of each element of the finite element model, the change of deformation at each node, the change of vibration response at each node, and the change of natural frequency of the structural model. A structural design method characterized by determining a combination sensitivity coefficient by variously combining a plurality of sensitivity coefficients among the coefficients, and displaying the magnitude of the combination sensitivity coefficient. 2. The structure design method according to claim 1, wherein, in obtaining said combination sensitivity coefficient, a combination sensitivity coefficient when one structural parameter is changed through a plurality of elements is obtained.