JP2023173937A - Analysis method, analysis device and analysis program for analyzing stress to cable - Google Patents

Abstract

[Problem] To accurately analyze stress applied to a cable while reducing analysis costs. [Solution] An analysis method for analyzing stress applied to a cable 2 including a plurality of metal wires 21, which includes an acquisition step ST1 of acquiring CAD data D1 of the cable 2, and a model of the CAD data D1 using the finite element method. A modeling step ST2, a condition setting step ST3 for setting analysis conditions for the modeled data D2, and a stress analysis step ST4 for analyzing the stress based on the analysis conditions. In ST3, the CAD data D1 is divided into a plurality of parts along the length direction of the cable 2, a part of the plurality of parts is modeled with beam elements, and the rest of the plurality of parts is modeled with solid elements. analysis method. [Selection diagram] Figure 3

Description

The present invention relates to an analysis method, an analysis device, and an analysis program for analyzing stress applied to a cable.

For example, a conductive cable for a robot arm includes a plurality of strands formed by twisting a plurality of copper wires together, and is manufactured by further twisting a plurality of strands together. Such cables follow the movements of robot arms and are repeatedly subjected to complex loads such as tension, bending, and twisting, eventually leading to breakage. Cable breakage greatly affects the lifespan of the robot arm, so it is necessary to understand the cable breakage mechanism and evaluate the lifespan before putting it into practical use.

However, there is no unified evaluation test method for evaluating the lifespan of cables, and since wire breakage occurs in individual strands, it is difficult to determine the extent of the There is a problem in that it is not possible to ascertain what kind of load the wire is subjected to before it breaks.

To solve this problem, numerical simulation methods based on the finite element method have been proposed (for example, Patent Document 1 and Non-Patent Document 1). Patent Document 1 discloses an invention related to a method for predicting the bending life of a wire bundle, in which all wires (strands) are modeled with one beam element, the bending ratio at the center of the wire is calculated, and the bending ratio is obtained in advance. The bending life is predicted based on the relationship between the bending life and the bending ratio. On the other hand, in Non-Patent Document 1, the strands or strands constituting the cable are modeled using solid elements, and the SN diagram is obtained by performing a fatigue test on the strands and under combined loads (compression, The stress in the combination of tension, bending, and torsion is analyzed.

Japanese Patent Application Publication No. 2002-260460

Tetsuo Kurashiki, Ryoto Kamitori, “Evaluation of disconnection life of composite cable for robot arm using numerical analysis and fatigue test”, Production and Technology, 2020, Vol. 72, No. 2, p. 81-84

However, in Patent Document 1, all the wires are modeled using beam elements, so accurate analysis that takes into account the state of contact between the wires cannot be performed. In addition, in Non-Patent Document 1, all the strands are modeled as solid elements, so the analysis cost is high in order to analyze the entire structure of the cable by setting the twist pitch, number of strands, number of strands, etc. The problem is that it becomes huge.

The present invention has been made to solve the above problems, and an object of the present invention is to accurately analyze stress applied to a cable while reducing analysis costs.

In order to solve the above problems, the present invention includes the following aspects.
Item 1.
An analysis method for analyzing stress applied to a cable comprising a plurality of metal wires, the method comprising:
an obtaining step of obtaining structural data of the cable;
a modeling step of modeling the structural data using a finite element method;
a condition setting step of setting analysis conditions for the modeled data;
a stress analysis step of analyzing the stress based on the analysis conditions;
Equipped with
In the modeling step,
dividing the structural data into a plurality of parts along the length direction of the cable,
An analysis method in which a part of the plurality of parts is modeled with a beam element, and the rest of the plurality of parts is modeled with a solid element.
Item 2.
2. The analysis method according to item 1, wherein a first portion including an end of the cable is modeled with a beam element, and a second portion of the cable excluding the first portion is modeled with a solid element.
Item 3.
Item 3. The analysis method according to Item 1 or 2, wherein the cable includes a plurality of strands formed by twisting a plurality of wires together, and is a composite cable formed by further twisting the plurality of strands.
Item 4.
The plurality of strands are
one or more central strands located in the center of the cable;
one or more layers of annular strand group consisting of one or more strands arranged in an annular shape surrounding the center strand;
In the modeling step,
4. The analysis method according to item 3, wherein one strand is selected from each of the center strand and the annular strand group, and each strand of the selected strand is modeled as a homogeneous material.
Item 5.
An analysis device for analyzing stress applied to a cable comprising a plurality of metal wires,
an acquisition unit that acquires structural data of the cable;
a modeling unit that models the structural data using a finite element method;
a condition setting unit that sets analysis conditions for the modeled data;
a stress analysis section that analyzes the stress based on the analysis conditions;
Equipped with
The modeling unit includes:
dividing the structural data into a plurality of parts along the length direction of the cable,
An analysis device that models a part of the plurality of parts using beam elements, and models the remainder of the plurality of parts using solid elements.
Item 6.
An analysis program that analyzes stress applied to a cable comprising multiple metal wires,
an obtaining step of obtaining structural data of the cable;
a modeling step of modeling the structural data using a finite element method;
a condition setting step of setting analysis conditions for the modeled data;
a stress analysis step of analyzing the stress based on the analysis conditions;
make the computer run
In the modeling step,
dividing the structural data into a plurality of parts along the length direction of the cable,
An analysis program that models a part of the plurality of parts using beam elements and models the remainder of the plurality of parts using solid elements.

According to the present invention, stress applied to a cable can be accurately analyzed while reducing analysis costs.

FIG. 2 is a perspective view of a robot and a partially enlarged view of a composite cable used in the robot. 1 is a block diagram showing a schematic configuration of an analysis device according to an embodiment of the present invention. It is a flow chart which shows the processing procedure of the analysis method concerning the above-mentioned embodiment. (a) is a cable modeled with solid elements, and (b) is a cable modeled with beam elements. This is an example of a modeled cable. (a) is an example of a modeled cable, and (b) is an example of analysis conditions. FIG. 3 is a diagram showing a distribution of contact situations between strands. FIG. 3 is a diagram showing the distribution of maximum principal stress. FIG. 3 is a diagram showing the distribution of maximum principal shear stress. (a) shows the cable modeled in Example 1, and (b) shows the analysis conditions in Example 1. 3 is a graph showing twisting motion of the cable in Example 1. FIG. This is the distribution of the maximum principal stress applied to the cable at the time of twisting -19 degrees in Example 1. This is the distribution of the maximum principal stress applied to the cable at the time of twisting +19 degrees in Example 1. (a) is an explanatory diagram of two specific evaluation points within the strand, and (b) is a graph showing the history of maximum principal stress at each evaluation point. FIG. 2 is a fatigue limit diagram obtained in Example 1 when the number of torsion repetitions is ¹⁰⁴ . This shows the wire breakage prediction results of Example 1, where (a) is a fatigue limit diagram in which the average stress and stress amplitude at 160 nodes in the central strand are plotted, and (b) is It is a graph which shows the ratio of the number of nodes located in a high stress area|region and a low stress area|region in the fatigue limit diagram of a). This shows the wire breakage prediction results of Example 1, in which (a) is a fatigue limit diagram in which the average stress and stress amplitude at 160 nodes in the outer strand are plotted, and (b) is a ) is a graph showing the ratio of the number of nodes located in the high stress region and the low stress region in the fatigue limit diagram. (a) shows the cable modeled in Example 2 (12×20 model), and (b) shows the analysis conditions in Example 1. (a) shows the cable (7×34 model) modeled in Example 2, and (b) shows the analysis conditions in Example 1. This is the distribution of the maximum principal stress applied to the cable (12×20 model) when twisted by -19 degrees in Example 2. This is the distribution of the maximum principal stress applied to the cable (7×34 model) at the time of twisting -19 degrees in Example 2. This is the distribution of the maximum principal stress applied to the cable (12×20 model) at the time of twisting +19 degrees in Example 2. This is the distribution of the maximum principal stress applied to the cable (7×34 model) at the time of twisting +19 degrees in Example 2. This shows the wire breakage prediction results of Example 2, (a) is a fatigue limit diagram plotting the average stress and stress amplitude at 160 nodes in the central strand of the cable (12 × 20 model), (b) is a graph showing the ratio of the number of nodes located in the high stress region and the low stress region in the fatigue limit diagram of (a). This shows the wire breakage prediction results of Example 2, and (a) is a fatigue limit diagram plotting the average stress and stress amplitude at 160 nodes in the central strand of the cable (7 x 34 model), (b) is a graph showing the ratio of the number of nodes located in the high stress region and the low stress region in the fatigue limit diagram of (a).

Embodiments of the present invention will be described below with reference to the accompanying drawings. Note that the present invention is not limited to the embodiments described below, and various changes can be made without departing from the spirit thereof.

(Cable structure)
First, the structure of the cable to be analyzed will be explained. In this embodiment, a composite cable for a robot arm is targeted for analysis.

FIG. 1 is a perspective view of a robot 1 and a partially enlarged view of a composite cable (hereinafter referred to as a cable) 2 used in the robot 1. The cable 2 is subjected to complex stresses due to operations such as rotation, bending, and turning of the wrist of the robot 1 and bending of the upper and lower arms. The cable 2 includes a plurality of strands 22 formed by twisting a plurality of copper wires 21 together, and has a structure in which the plurality of strands 22 are further twisted together. In this embodiment, the wires 21 are twisted to the right (S twist), and the strands 22 are twisted to the left (Z twist).

(Analysis device)
FIG. 2 is a block diagram showing a schematic configuration of the analysis device 3 according to this embodiment. The analysis device 3 can be configured with a general-purpose computer, and includes hardware such as a processor such as a CPU or GPU (not shown), a main storage device such as a DRAM or SRAM (not shown), and an HDD or SSD. It is equipped with an auxiliary storage device 30. The auxiliary storage device 30 stores various programs for operating the analysis device 3, such as an analysis program P1, and various data such as CAD data D1.

The analysis device 3 includes an acquisition section 31, a modeling section 32, a condition setting section 33, a stress analysis section 34, and a wire breakage prediction section 35 as functional blocks. These functional blocks can be realized in software by the processor of the analysis device 3. In this case, the processor reads the analysis program P1 stored in the auxiliary storage device 30 into the main storage device and executes it, thereby realizing each of the above sections. The analysis program P1 may be downloaded to the analysis device 3 via a communication network such as the Internet, or may be downloaded to the analysis device 3 via a computer-readable non-temporary recording medium such as a CD-ROM on which the analysis program P1 is recorded. You can install it on 3.

(Processing procedure of analysis method)
FIG. 3 is a flowchart showing the processing procedure of the analysis method according to this embodiment. Each step ST1 to ST5 of the analysis method is executed by the acquisition unit 31, modeling unit 32, condition setting unit 33, stress analysis unit 34, and wire breakage prediction unit 35 of the analysis device 3, respectively.

In step ST1 (acquisition step), the acquisition unit 31 acquires the CAD data D1 by reading the CAD data D1 from the auxiliary storage device 30. The CAD data D1 is structural data indicating the three-dimensional structure of the cable 2, and is created in advance using predetermined software.

In step ST2 (modeling step), the modeling unit 32 models the CAD data D1 using the finite element method. Specifically, the modeling unit 32 models the CAD data D1 using both beam elements and solid elements. Here, beam elements and solid elements will be explained.

FIG. 4(a) shows a cable 2 modeled with solid elements. In this example, the cable 2 is modeled as a collection of solid hexahedral elements (homogeneous material). Modeling using solid elements makes it possible to evaluate the stress and strain inside the element, but as the number of elements increases, the analysis cost increases.

Figure 4(b) shows a cable 2 modeled with beam elements. In this example, the cable 2 is modeled as a single beam (virtual single wire) having a cross-sectional shape. When modeled using beam elements, it is possible to evaluate deformation at the center of the cross section, reducing analysis costs compared to solid elements, but it is not possible to evaluate stress inside the cross section.

Therefore, in this embodiment, the cable 2 is modeled using both beam elements and solid elements. By introducing beam elements, the number of elements can be reduced and the overall deformation behavior of the cable 2 can be evaluated. Furthermore, the introduction of solid elements makes it possible to evaluate the local stress distribution of the cable 2. Thereby, the stress applied to the cable 2 can be accurately analyzed while reducing the analysis cost.

Specifically, the modeling unit 32 divides the CAD data D1 into a plurality of parts along the length direction of the cable 2, models some of the plurality of parts with beam elements, and models the plurality of parts by beam elements. The rest of the model is modeled using solid elements.

FIG. 5 is an example of the modeled cable 2 (data D2). The cable 2 is divided along its length into two first sections 2a including end portions E1 and E2, and a second section 2b at the center excluding the first section 2a. The modeling unit 32 models the first portion 2a using beam elements, and models the second portion 2b using solid elements. In this example, in the first section 2a, each strand is modeled as a virtual single wire, and in the second section 2b, each strand is modeled as a homogeneous material.

In addition, in modeling using beam elements, each strand may be made into a virtual single wire, or the entire strand may be made into a virtual single wire for some of the plurality of strands, and each strand may be made into a virtual single wire for other strands. Similarly, in modeling using solid elements, each strand may be made of a homogeneous material, or the entire strand may be made of a homogeneous material for some of the plurality of strands, and each strand of the other strands may be made of a homogeneous material.

Regarding the lengths of the first part 2a and the second part 2b, as the ratio of the second part 2b (solid element) to the first part 2a (beam element) is increased, the analysis accuracy improves, but the analysis cost also increases. increase Therefore, the lengths of the first portion 2a and the second portion 2b are appropriately set in consideration of the required analysis accuracy and analysis cost.

In step ST3 (setting step), the condition setting unit 33 sets analysis conditions for the modeled data D2. Analysis conditions include the Young's modulus of the strands, Poisson's ratio, radius, friction coefficient between strands, twist angle, etc.

FIG. 6(a) shows the modeled cable 2, and FIG. 6(b) shows an example of analysis conditions. The cable 2 has a total length of 53 mm and is divided into a first section 2a consisting of a section 25 mm from the end E1 and a section 25 mm from the end E2, and a second section 2b having a central length of 3 mm. The end E1 of the cable 2 is fixed, and the angle at which the end E2 is twisted from its initial state is defined as a twist angle.

In step ST4 (analysis step), the stress analysis section 34 analyzes the stress applied to the cable 2 based on the set analysis conditions. In this embodiment, the cable 2 is modeled using both beam elements and solid elements, so the overall deformation behavior of the cable 2 due to the beam elements and the detailed behavior within one strand using the solid elements are simultaneously measured. can be evaluated.

Examples of analysis results are shown in FIGS. 7 to 9. 7 to 9 respectively show the contact situation between the strands, the distribution of the maximum principal stress, and the distribution of the maximum principal shear stress.

In step ST5, the disconnection prediction unit 35 predicts disconnection of the cable 2 using a known method based on the analyzed stress. The predicted content is not particularly limited, but includes, for example, the possibility of wire breakage when a predetermined operation (such as a predetermined number of twisting operations) is performed on the cable 2.

(Additional notes)
The present invention is not limited to the above-mentioned embodiments, and various modifications can be made within the scope shown in the claims, and forms obtained by appropriately combining the technical means disclosed in the embodiments may also be incorporated into the present invention. Included in technical scope.

For example, in the above embodiment, the cable structure data is CAD data, but it is not limited to CAD data as long as it is data indicating the cable structure.

In addition, a typical composite cable has one or more layers of annular strands consisting of one or more central strands located at the center of the cable and one or more strands arranged in an annular shape surrounding the central strand. It is equipped with In this case, one strand may be selected from each of the center strand and the annular strand group, and each strand may be modeled as a homogeneous material in the selected strand. When a plurality of center strands exist, the stress applied to each center strand is substantially equal to each other, and the stress applied to each strand in one annular strand group is also substantially equal to each other. Therefore, by modeling each strand as a homogeneous material and analyzing the stress in detail in one strand of the center strand and one strand of each annular strand group, we can reduce the analysis cost and Disconnection can be accurately predicted.

Examples of the present invention will be described below, but the present invention is not limited to the following examples.

[Example 1]
In Example 1, the stress applied to the cable 2A, which has seven strands made by twisting 20 wires together, was analyzed. The length of cable 2A was 53 mm. As shown in FIG. 10(a), the cable 2A is divided into a first section 2a consisting of a section 25 mm from the end E1 and a section 25 mm from the end E2, and a second section 2b having a central length of 3 mm. The first portion 2a was modeled using a beam element, and the second portion 2b was modeled using a solid element.

However, unlike the embodiment shown in FIG. 6, in this example, in the first part 2a, two strands S1 and S2 out of seven strands S1 to S7 model each strand into a virtual single wire. , the other strands S3 to S7 were entirely modeled as a virtual single wire. In the second portion 2b, each of the strands S1 and S2 was modeled as a homogeneous material, and the entire strands S3 to S7 were modeled as a homogeneous material. Strand S1 is a central strand located at the center of cable 2A, and strand S2 is one strand selected from six strands S2 to S7 (circular strand group) surrounding strand S1.

Subsequently, analysis conditions were set as shown in FIG. 10(b). Note that the twist angle of ±19 degrees corresponds to the twist angle of ±180 degrees when the length of the cable 2A is 500 mm.

Subsequently, the stress applied to the cable 2A was analyzed based on the set analysis conditions. FIG. 11 shows a twisting motion on cable 2A. With end E1 fixed, a tensile load equivalent to 0.01% of the cable length is gradually applied from 0 to 1 second, and then an angle of ±19 degrees is applied to end E2 at a cycle of 4 seconds. Performed a twisting motion.

Figure 12 shows the distribution of the maximum principal stress applied to the cable 2A when twisted by -19 degrees (2 seconds), and Figure 13 shows the distribution of the maximum principal stress applied to the cable 2A when twisted by +19 degrees (4 seconds). It is. In this way, we were able to locally and precisely analyze the stress on a strand-by-strand basis.

Moreover, the specific evaluation point No. in the strand S1 shown in FIG. 14(a). 1, No. The history of the maximum principal stress in No. 2 is shown in FIG. 14(b). This shows that the stress amplitude due to twisting of the cable 2A is larger in the outer strands than in the strands near the center.

Next, a prediction of disconnection of cable 2A was made. In this example, similarly to Non-Patent Document 1, the S-N curve is obtained by performing curve regression based on the "Metallic Materials Fatigue Reliability Evaluation Criteria - S-N Curve Regression Method" by the Japan Society of Materials Science. A fatigue limit diagram (modified Goodman diagram) showing the relationship between average stress and stress amplitude was created based on the -N curve and the static strength of the copper wire.

FIG. 15 shows a fatigue limit diagram when the number of torsion repetitions is ¹⁰⁴ . Plot the average stress and stress amplitude obtained for each part of cable 2A through the stress analysis above on a fatigue limit diagram, and predict that if the position is above the fatigue limit line (high stress area), it will lead to breakage. If the wire is located below the fatigue limit line (low stress region), it is predicted that the wire will not break.

FIG. 16(a) is a fatigue limit diagram plotting the average stress and stress amplitude at 160 nodes in the central strand S1, and FIG. 16(b) is a fatigue limit diagram of FIG. 16(a). In the figure, it is a graph showing the ratio of the number of nodes located in the high stress region and the low stress region. FIG. 17(a) is a fatigue limit diagram plotting the average stress and stress amplitude at 160 nodes in the outer strand S2, and FIG. 17(b) is a fatigue limit diagram of FIG. 17(a). 2 is a graph showing the ratio of the number of nodes located in a high stress region and a low stress region in FIG.

From these results, it was predicted that the strand S1 would be more likely to break than the strand S2 because the proportion of nodes in the high stress region was greater in the strand S1 than in the strand S2. As a rule of thumb, it is known that the strands in the center are more likely to break than the strands on the outside, and the prediction results of this example match the rule of thumb.

[Example 2]
In Example 2, stress applied to cables having approximately the same number of strands but different numbers and arrangements of strands was analyzed. Specifically, Cable 2B (12 x 20 model, total of 240 strands) has 12 strands made by twisting 20 strands together, and Cable 2B has 12 strands made by twisting 20 strands together, and Cable 2B has 12 strands made by twisting 20 strands together. The stress applied to cable 2C (7x34 model, total of strands: 238) having seven strands was analyzed.

The length of cables 2B and 2C was 53 mm, which is the same as cable 2A, which is the subject of analysis in Example 1. The modeling of the cables 2B and 2C is the same as that of the cable 2A, and as shown in FIGS. 18(a) and 19(a), the first portion 2a is 25 mm from the ends E1 and E2, and the length of the center is The first part 2a was modeled with a beam element, and the second part 2b was modeled with a solid element. In cable 2B, each strand of only one strand S1 of the three central strands S1 to S3 located at the center is modeled as a virtual single wire or a homogeneous material, and in cable 2C, the central strand located at the center Only in S1, each strand was modeled as a virtual single wire or a homogeneous material.

Subsequently, the analysis conditions for the cables 2B and 2C were set as shown in FIGS. 18(b) and 19(b), respectively, and the stress applied to the cables 2B and 2C was analyzed based on the set analysis conditions. The operation for cables 2B and 2C was similar to the operation for cable 2A shown in FIG.

FIGS. 20 and 21 respectively show the distribution of the maximum principal stress applied to the cables 2B and 2C at the time of twisting by -19 degrees (2 seconds). 22 and 23 respectively show the distribution of the maximum principal stress applied to the cables 2B and 2C at the time of twisting +19 degrees (4 seconds).

Subsequently, using the same method as in Example 1, prediction of disconnection of cables 2B and 2C was performed. FIG. 24(a) is a fatigue limit diagram plotting the average stress and stress amplitude at 160 nodes in strand S1 of cable 2B, and FIG. 24(b) is a fatigue limit diagram of FIG. 24(a). In the figure, it is a graph showing the ratio of the number of nodes located in the high stress region and the low stress region. FIG. 25(a) is a fatigue limit diagram plotting the average stress and stress amplitude at 160 nodes in strand S1 of cable 2C, and FIG. 25(b) is a fatigue limit diagram of FIG. 25(a). In the figure, it is a graph showing the ratio of the number of nodes located in the high stress region and the low stress region.

From these results, it was predicted that the cable 2C would be more likely to break than the cable 2B because the ratio of nodes in the high stress region was larger in the cable 2C than in the cable 2B. It has been empirically known that in actual composite cables, the 7x34 model is more likely to break than the 12x20 model, and the prediction results of this example match the empirical rule.

The object of analysis of the present invention may be any cable including a plurality of metal wires, and is not limited to composite cables.

1 Robot 2 Cable 21 Wire 22 Strand 2A Cable 2B Cable 2C Cable 2a First part 2b Second part 3 Analysis device 30 Auxiliary storage device 31 Acquisition section 32 Modeling section 33 Condition setting section 34 Stress analysis section 35 Disconnection prediction section D1 CAD data D2 Modeled data E1 End portion E2 End portion P1 Analysis program S1 to S12 Strand

Claims (6)

An analysis method for analyzing stress applied to a cable comprising a plurality of metal wires, the method comprising:
an obtaining step of obtaining structural data of the cable;
a modeling step of modeling the structural data using a finite element method;
a condition setting step of setting analysis conditions for the modeled data;
a stress analysis step of analyzing the stress based on the analysis conditions;
Equipped with
In the modeling step,
dividing the structural data into a plurality of parts along the length direction of the cable,
An analysis method in which a part of the plurality of parts is modeled with a beam element, and the rest of the plurality of parts is modeled with a solid element. 2. The analysis method according to claim 1, wherein a first portion including an end of the cable is modeled with a beam element, and a second portion of the cable excluding the first portion is modeled with a solid element. 3. The analysis method according to claim 1, wherein the cable includes a plurality of strands formed by twisting a plurality of wires together, and is a composite cable formed by further twisting the plurality of strands. The plurality of strands are
one or more central strands located in the center of the cable;
one or more layers of annular strand group consisting of one or more strands arranged in an annular shape surrounding the center strand;
In the modeling step,
4. The analysis method according to claim 3, wherein one strand is selected from each of the center strand and the annular strand group, and each strand of the selected strand is modeled as a homogeneous material. An analysis device for analyzing stress applied to a cable comprising a plurality of metal wires,
an acquisition unit that acquires structural data of the cable;
a modeling unit that models the structural data using a finite element method;
a condition setting unit that sets analysis conditions for the modeled data;
a stress analysis section that analyzes the stress based on the analysis conditions;
Equipped with
The modeling unit includes:
dividing the structural data into a plurality of parts along the length direction of the cable,
An analysis device that models a part of the plurality of parts using beam elements, and models the remainder of the plurality of parts using solid elements. An analysis program that analyzes stress applied to a cable comprising multiple metal wires,
an obtaining step of obtaining structural data of the cable;
a modeling step of modeling the structural data using a finite element method;
a condition setting step of setting analysis conditions for the modeled data;
a stress analysis step of analyzing the stress based on the analysis conditions;
make the computer run
In the modeling step,
dividing the structural data into a plurality of parts along the length direction of the cable,
An analysis program that models a part of the plurality of parts using beam elements and models the remainder of the plurality of parts using solid elements.