CN113673022A - Method for calculating relative displacement between two points of deformation structure - Google Patents
Method for calculating relative displacement between two points of deformation structure Download PDFInfo
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- CN113673022A CN113673022A CN202010412353.8A CN202010412353A CN113673022A CN 113673022 A CN113673022 A CN 113673022A CN 202010412353 A CN202010412353 A CN 202010412353A CN 113673022 A CN113673022 A CN 113673022A
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Abstract
A method for calculating relative displacement between two points of a deformed structure comprises the steps of establishing a finite element model of the deformed structure, applying constraint and boundary load to the finite element model, determining a rod unit between a first node and a second node which need to calculate the relative displacement on the finite element model, and calculating the axial force of the rod unit in the finite element model according to the constraint and the boundary load, wherein the value of the axial force is equal to the value of the relative displacement between the first node and the second node, so that the aim of directly calculating the relative displacement is fulfilled, the calculation method is convenient and fast, and the practicability is high.
Description
Technical Field
The invention relates to a relative displacement calculation method. In particular to a relative displacement calculation method based on finite element software.
Background
In the field of aviation, some antenna or remote equipment is often installed on an aircraft, and the aircraft has certain rigidity requirements on the installation position of the aircraft, wherein the deformation control requirements of some special equipment on the installation position of the aircraft body are very strict, and once the installation position of the special aircraft does not meet the specific deformation range requirements, the deformation displacement of the equipment in use exceeds the design requirements and the equipment cannot be normally used. Therefore, in the process of developing the special aircraft, the rigidity deformation of the antenna installation position needs to be accurately calculated. One of the problems with this type of stiffness deformation calculation is to calculate the relative displacement between two points on the deformed structure. If an equipment installation truss is arranged on an aircraft structure base, the end heads of the truss are respectively connected with equipment, the truss generates displacement deformation under the action of external load, so that the distance between the two pieces of equipment is changed, and due to the particularity of the equipment, the equipment cannot be normally used when the relative displacement between the two pieces of equipment exceeds a certain value.
The prior art generally calculates the relative displacement between two points of a deformation body in finite element software by the following steps: and calculating the finite element model of the structure to obtain the value difference of the distance between the two points before and after the deformation of the structure in a space reference coordinate system, namely the relative displacement of the two points. The calculation idea is direct, but displacement values of the distance between two points before and after structural deformation need to be calculated respectively, then a relative displacement result is obtained through subtraction calculation, and the calculation process is relatively complex.
Disclosure of Invention
A method for calculating the relative displacement between two points of a deformed structure is known as a theoretical model of the deformed structure, and is characterized by comprising the following steps:
1) establishing a finite element model of the deformation structure according to the theoretical model of the deformation structure, and applying constraint and boundary load to the finite element model;
2) determining a first node and a second node which need to calculate relative displacement on a finite element model;
3) establishing a pole unit between a first node and a second node;
4) defining an axial stiffness coefficient K of the rod unit to be 1, defining a cross-sectional area A of the rod unit to be 1, and defining an elastic modulus E of the rod unit to be equal to a rest distance L between a first node and a second node;
5) according to the following relation between the axial force N of the linear elastic rod unit and the relative displacement delta between the first node and the second node at two ends of the linear elastic rod unit:
substituting the definition in the step 4) into the formula to obtain that the numerical value of the axial force N of the rod unit is equal to the relative displacement delta between the first node and the second node;
6) calculating the axial force of the rod unit in the finite element model according to the constraint and the boundary load in the step 1, wherein the axial force has a value equal to the relative displacement value between the first node and the second node.
The invention has the beneficial effects that: establishing an auxiliary rod unit between relative displacement measurement nodes by establishing a finite element model; combining the length L of the rod unit, the elastic modulus E and the cross section area A of the axial rigidity coefficient K of the rod unit which is 1 are defined, and equivalent values can be provided for calculating the relative displacement between the measurement nodes through finite element calculation. The numerical value of the axial force of the auxiliary rod unit is directly equal to the relative displacement of the nodes at the two ends of the rod unit, so that the aim of directly calculating the relative displacement is fulfilled, the calculation method is convenient and fast, and the practicability is high.
The invention is explained in detail below with reference to an exemplary embodiment of the drawings.
Drawings
Fig. 1 is a schematic structural model diagram of an aircraft mounting device.
Fig. 2 is a schematic diagram of a deformation structure model of the aircraft mounting equipment.
Fig. 3 is a schematic view of the lever unit.
Fig. 4 is a schematic diagram of the gravity center positions of the first node and the second node which are mounting devices.
The numbering in the figures illustrates: the system comprises a machine body structure 1, a first equipment installation truss 2, a second equipment installation truss 3, a first node 4, a second node 5 and a rod unit 6.
Detailed Description
Referring to the attached drawings, the embodiment further illustrates the invention by taking the calculation of the displacement of the top ends of the trusses and the center of gravity of the trusses caused by deformation as an example, wherein the truss structures are installed on two adjacent equipment on an airplane body 1, and the truss structures are installed on a first equipment installation truss 2 and a second equipment installation truss 3.
The aircraft body structure 1 of the aircraft is fixedly provided with two equipment installation trusses, a first equipment installation truss 2 and a second equipment installation truss 3, and the bottoms of the equipment installation trusses are fixedly connected with the aircraft structure 1. According to design requirements, displacement values of two ends of the truss under the action of external loads F1 and F2 of the two equipment installation trusses are calculated.
The specific calculation method is as follows:
step one, establishing a finite element model according to a theoretical model of a truss structure, and applying boundary constraint and boundary load to the model; the boundary load may be a static load or a vibration load.
Secondly, determining the position of the end of the first equipment installation truss 2 as a first node 4 and the position of the end of the second equipment installation truss 3 as a second node 5 according to analysis requirements, wherein the distance between the first node and the second node in relative displacement needs to be calculated;
step three, establishing a rod unit 6 between the first node 4 and the second node 5, and measuring a distance L between the first node 4 and the second node 5 in an unstressed static state to be 2m by a measuring tool in finite element software;
step four, establishing the rod unit 6 as a virtual rod unit, called as an auxiliary rod unit, for calculating the relative displacement between the first node 4 and the second node 5, defining the axial stiffness coefficient K of the rod unit as 1, and defining the cross-sectional area A of the rod unit as 1m2According to the formula:
it can be defined that the modulus of elasticity E of the rod unit is equal to the rest distance L between the first node and the second node;
step five, according to the following relation between the axial force N of the linear elastic rod unit and the relative displacement delta between the first node and the second node at the two ends of the linear elastic rod unit:
by substituting the above definitions of the K value, the a value, and E ═ L into the formula, it is possible to obtain that the value of the axial force N of the lever unit is equal to the relative displacement δ between the first node 4 and the second node 5;
and finally, calculating the axial force of the rod unit in the finite element model according to the constraint and boundary load in the step one, wherein the value of the axial force is equal to the value of the relative displacement between the first node 4 and the second node 5, so as to obtain the relative displacement result between the first node 4 and the second node 5, and the displacement result is the displacement value of the end position of the first equipment mounting truss 2 and the end position of the second equipment mounting truss 3 under the action of the external loads F1 and F2.
Referring to fig. 4, the positions of the first node 4 and the second node 5 in the method are not limited to the positions of the ends of the deformed structure, and may be set to any position in the deformed structure according to engineering requirements, for example, the positions of the first node and the second node are the positions of the centers of gravity of two adjacent devices, or the positions of the geometric centers of two adjacent devices, or any other positions.
In establishing the finite element model and setting the stiffness parameters of the rod elements, it should be noted that the dimensions of the length, the cross-sectional area and the stiffness coefficient should correspond to each other, for example, in the above example, the dimensions of the three are m and m2And N/m, which is determined based on the units of length and force as m and N. The axial force of the rod unit thus calculated is in units of N and the relative displacement between the first and second nodes is in units of m, for example an axial force of 2N would result in a relative displacement of 2 m.
It can be seen from the above embodiments that, by using the method of the present invention, the analysis result of the relative displacement between the two points is directly equal to the axial force value of the auxiliary rod unit, so that the relative displacement result can be directly obtained through finite element analysis, and the distances between the two points before and after the structural deformation and the distances between the two points after the structural deformation are subtracted from each other to obtain the relative displacement.
Finally, it should be pointed out that: the above examples are only for illustrating the technical solutions of the present invention, and are not limited thereto. Although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions of the embodiments of the present invention.
Claims (5)
1. A method for calculating the relative displacement between two points of a deformed structure is known as a theoretical model of the deformed structure, and is characterized by comprising the following steps:
1) establishing a finite element model of the deformation structure according to the theoretical model of the deformation structure, and applying constraint and boundary load to the finite element model;
2) determining a first node and a second node which need to calculate relative displacement on a finite element model;
3) establishing a pole unit between a first node and a second node;
4) defining an axial stiffness coefficient K of the rod unit to be 1, defining a cross-sectional area A of the rod unit to be 1, and defining an elastic modulus E of the rod unit to be equal to a rest distance L between a first node and a second node;
5) according to the following relation between the axial force N of the linear elastic rod unit and the relative displacement delta between the first node and the second node at two ends of the linear elastic rod unit:
substituting the definition in the step 4) into the formula to obtain that the numerical value of the axial force N of the rod unit is equal to the relative displacement delta between the first node and the second node;
6) calculating the axial force of the rod unit in the finite element model according to the constraint and the boundary load in the step 1, wherein the axial force has a value equal to the relative displacement value between the first node and the second node.
2. The method for calculating the relative displacement between two points of a deformed structure as claimed in claim 1, wherein the positions of the first node and the second node are the vertex positions of two adjacent devices.
3. The method for calculating the relative displacement between two points of a deformed structure according to claim 1, wherein the positions of the first node and the second node are the positions of the centers of gravity of two adjacent devices.
4. The method for calculating the relative displacement between two points of a deformed structure as claimed in claim 1, wherein the positions of the first node and the second node are the geometric center positions of two adjacent devices.
5. The method for calculating the relative displacement between two points of a deformed structure according to claim 1, wherein the boundary load in the step 1) can be a static load or a vibration load.
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| CN202010412353.8A CN113673022A (en) | 2020-05-15 | 2020-05-15 | Method for calculating relative displacement between two points of deformation structure |
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Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN114741925A (en) * | 2022-04-15 | 2022-07-12 | 中铁大桥勘测设计院集团有限公司 | Method, device and equipment for calculating rod piece expansion and contraction amount and readable storage medium |
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2020
- 2020-05-15 CN CN202010412353.8A patent/CN113673022A/en active Pending
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN114741925A (en) * | 2022-04-15 | 2022-07-12 | 中铁大桥勘测设计院集团有限公司 | Method, device and equipment for calculating rod piece expansion and contraction amount and readable storage medium |
| CN114741925B (en) * | 2022-04-15 | 2023-12-29 | 中铁大桥勘测设计院集团有限公司 | Method, device and equipment for calculating rod expansion and contraction amount and readable storage medium |
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