CN114429059A - Method for evaluating stability and strength of variable cross-section curved beam - Google Patents

Method for evaluating stability and strength of variable cross-section curved beam Download PDF

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CN114429059A
CN114429059A CN202111219821.0A CN202111219821A CN114429059A CN 114429059 A CN114429059 A CN 114429059A CN 202111219821 A CN202111219821 A CN 202111219821A CN 114429059 A CN114429059 A CN 114429059A
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李兆远
于鹏
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Shenyang Aircraft Design and Research Institute Aviation Industry of China AVIC
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Abstract

The application belongs to the field of airplane structural strength, and particularly relates to a method for evaluating stability and strength of a variable cross-section curved beam. According to the method for evaluating the stability and the strength of the variable-section curved beam, the instability load and the destruction load of a variable-section curved beam test model are obtained through tests, the instability load and the destruction load of a variable-section curved beam finite element model are calculated through a finite element calculation method, the finite element calculation method for the stability of the variable-section curved beam is corrected according to test measurement results, the stability of the variable-section curved beam can be quickly evaluated, a rationalization suggestion of structural design is provided, and a basis is provided for relevant structural calculation and analysis.

Description

Method for evaluating stability and strength of variable cross-section curved beam
Technical Field
The application belongs to the field of airplane structural strength, and particularly relates to a method for evaluating stability and strength of a variable cross-section curved beam.
Background
In order to reserve an installation space for an engine and equipment of a certain airplane, a curved beam for connecting structures on two sides of an engine compartment is designed below the engine. Through preliminary analysis, the curved beam bears tensile load and compressive load at two ends, and has stability problem under the action of the compressive load, if the curved beam is unstable, the integrity of an engine cabin is damaged, and the flight safety is influenced.
At present, for the stability evaluation of the constant-section curved beam, the constant-section curved beam can be equivalently formed into a mode of combining a constant-section rod and an initial curvature column, the critical instability load of the constant-section curved beam is calculated by adopting an engineering calculation method, compared with a test result, the error between the engineering algorithm and the test result is 5.6%, and the accuracy of the constant-section curved beam engineering algorithm is high. However, for the variable cross-section curved beam, if an equal cross-section curved beam stability engineering algorithm is adopted, since the parameter relationship changes along with the change of the position of the tangent plane, the cross-section parameter relationship is uncertain, the true loaded state of the variable cross-section curved beam cannot be well reflected by adopting an engineering calculation method, and the error of the calculation result is large.
Accordingly, a technical solution is desired to overcome or at least alleviate at least one of the above-mentioned drawbacks of the prior art.
Disclosure of Invention
The application aims to provide a method for evaluating stability and strength of a variable cross-section curved beam, so as to solve at least one problem in the prior art.
The technical scheme of the application is as follows:
a method for evaluating stability and strength of a variable cross-section curved beam comprises the following steps:
step one, establishing a variable cross-section curved beam test model, and performing a test to respectively obtain an instability load and a failure load of the variable cross-section curved beam test model;
step two, establishing a variable cross section curved beam finite element model according to the variable cross section curved beam test model;
step three, calculating the instability load of the variable cross-section curved beam finite element model by adopting a buckling method and/or an implicit nonlinear method, and comparing the calculation result of the instability load with the test result to obtain a first error of the calculation result of the instability load relative to the test result;
step four, calculating the failure load of the finite element model of the variable cross-section curved beam by adopting a method of combining implicit nonlinearity and material nonlinearity, and comparing the calculation result of the failure load with the test result to obtain a second error of the calculation result of the failure load relative to the test result;
and fifthly, correcting the calculation result of the unstable load according to the first error to realize the evaluation of the stability of the variable cross-section curved beam, and correcting the calculation result of the destructive load according to the second error to realize the evaluation of the bearing capacity of the variable cross-section curved beam.
In at least one embodiment of the present application, in step one, a plurality of variable cross-section curved beam test models are obtained according to parameter differences of the rim strip thickness and the web thickness.
In at least one embodiment of the present application, in step two, a corresponding variable cross-section curved beam finite element model is established according to a plurality of variable cross-section curved beam test models.
In at least one embodiment of the present application, in step three, the calculating a destabilizing load of the variable cross-section curved beam finite element model by using a buckling method and/or an implicit nonlinear method, and comparing a calculation result of the destabilizing load with a test result to obtain a first error of the calculation result of the destabilizing load relative to the test result includes:
calculating the destabilizing load of the finite element model of the variable cross-section curved beam by adopting a buckling method, and comparing the calculation result of the destabilizing load with the test result to obtain a first error of the calculation result of the destabilizing load relative to the test result, or
And calculating the instability load of the finite element model of the variable cross-section curved beam by adopting an implicit nonlinear method, and comparing the calculation result of the instability load with the test result to obtain a first error of the calculation result of the instability load relative to the test result.
In at least one embodiment of the present application, in step three, the calculating the destabilizing load of the variable cross-section curved beam finite element model by using a buckling method and/or an implicit nonlinear method, and comparing the calculation result of the destabilizing load with the test result to obtain a first error of the calculation result of the destabilizing load relative to the test result further includes:
calculating the buckling load of the finite element model of the variable-section curved beam by adopting a buckling method, and comparing the buckling method calculation result of the buckling load with the test result to obtain the error of the buckling method calculation result of the buckling load relative to the test result;
calculating the instability load of the finite element model of the variable cross-section curved beam by adopting an implicit nonlinear method, and comparing the calculation result of the implicit nonlinear method of the instability load with the test result to obtain the error of the calculation result of the implicit nonlinear method of the instability load relative to the test result;
and comparing the error of the buckling method calculation result of the unstable load relative to the test result with the error of the implicit nonlinear method calculation result of the unstable load relative to the test result, and taking a smaller error as a first error of the calculation result of the destructive load relative to the test result.
In at least one embodiment of the present application, the comparing the error of the calculation result of the buckling method of the unstable load with respect to the test result with respect to the error of the calculation result of the implicit nonlinear method of the unstable load with respect to the test result, and the using a smaller error as the first error of the calculation result of the destructive load with respect to the test result includes:
comparing the error of the buckling method calculation result of the unstable load relative to the test result with the error of the implicit nonlinear method calculation result of the unstable load relative to the test result;
the error of the calculation result of the implicit nonlinear method for obtaining the unstable load is smaller relative to the test result;
and taking the error of the calculation result of the implicit nonlinear method of the unstable load relative to the test result as a first error.
In at least one embodiment of the present application, in step five, the correcting the calculation result of the destabilizing load according to the first error to achieve the evaluation of the stability of the variable cross-section curved beam includes:
the unstable load of the variable cross-section curved beam is calculated by an implicit nonlinear method of the unstable load/1.2.
In at least one embodiment of the present application, in step five, the correcting the calculation result of the breaking load according to the second error to achieve the evaluation of the bearing capacity of the variable cross-section curved beam includes:
the method for combining the implicit nonlinearity and the material nonlinearity of the breaking load calculates the value multiplied by 1.2.
The invention has at least the following beneficial technical effects:
according to the method for evaluating the stability and the strength of the variable-section curved beam, a finite element calculation method for the stability of the variable-section curved beam is corrected according to test measurement results, the stability of the variable-section curved beam can be quickly evaluated, a rationalization suggestion of structural design is provided, and a basis is provided for relevant structural calculation analysis.
Drawings
FIG. 1 is a schematic view of a variable cross-section curved beam according to one embodiment of the present application;
FIG. 2 is a graph illustrating the results of a buckling method for a buckling load in accordance with an embodiment of the present application;
FIG. 3 is a graph illustrating the calculation of buckling method of unstable loads according to a second embodiment of the present application;
FIG. 4 is a diagram illustrating the calculation results of a buckling method of a buckling load according to a third embodiment of the present application;
FIG. 5 is a schematic diagram illustrating a calculation result of an implicit nonlinear method for a destabilized load according to an embodiment of the present application;
FIG. 6 is a diagram illustrating the calculation result of an implicit nonlinear method for a destabilized load according to a second embodiment of the present application;
fig. 7 is a schematic diagram of a calculation result of an implicit nonlinear method for a destabilizing load according to a third embodiment of the present application.
Detailed Description
In order to make the implementation objects, technical solutions and advantages of the present application clearer, the technical solutions in the embodiments of the present application will be described in more detail below with reference to the drawings in the embodiments of the present application. In the drawings, the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The described embodiments are a subset of the embodiments in the present application and not all embodiments in the present application. The embodiments described below with reference to the drawings are exemplary and intended to be used for explaining the present application and should not be construed as limiting the present application. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present application. Embodiments of the present application will be described in detail below with reference to the accompanying drawings.
In the description of the present application, it is to be understood that the terms "center", "longitudinal", "lateral", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", and the like indicate orientations or positional relationships based on those shown in the drawings, and are used merely for convenience in describing the present application and for simplifying the description, and do not indicate or imply that the referenced device or element must have a particular orientation, be constructed in a particular orientation, and be operated, and therefore should not be construed as limiting the scope of the present application.
The present application is described in further detail below with reference to fig. 1 to 7.
The application provides a method for evaluating stability and strength of a variable cross-section curved beam, which comprises the following steps:
step one, establishing a variable cross-section curved beam test model, and performing a test to respectively obtain the instability load and the failure load of the variable cross-section curved beam test model;
step two, establishing a variable cross section curved beam finite element model according to the variable cross section curved beam test model;
step three, calculating the instability load of the variable cross-section curved beam finite element model by adopting a buckling method and/or an implicit nonlinear method, and comparing the calculation result of the instability load with the test result to obtain a first error of the calculation result of the instability load relative to the test result;
step four, calculating the failure load of the finite element model of the variable cross-section curved beam by adopting a method of combining implicit nonlinearity and material nonlinearity, and comparing the calculation result of the failure load with the test result to obtain a second error of the calculation result of the failure load relative to the test result;
and fifthly, correcting the calculation result of the unstable load according to the first error to realize the evaluation of the stability of the variable cross-section curved beam, and correcting the calculation result of the destructive load according to the second error to realize the evaluation of the bearing capacity of the variable cross-section curved beam.
According to the method for evaluating the stability and the strength of the variable cross-section curved beam, firstly, a variable cross-section curved beam test model is established, referring to fig. 1, and a test is carried out according to the variable cross-section curved beam test model to obtain the test results of the instability load and the breaking load. Advantageously, a plurality of variable cross-section curved beam test models can be obtained according to the parameter difference of the flange strip thickness and the web plate thickness, and then a corresponding variable cross-section curved beam finite element model is established according to the plurality of variable cross-section curved beam test models. In this embodiment, the finite element modeling uses msc.patran finite element analysis software to establish three kinds of variable cross-section curved beam finite element models, which are a variable cross-section curved beam, a variable cross-section reinforced curved beam 1 and a variable cross-section reinforced curved beam 2.
The method for evaluating the stability and the strength of the variable-section curved beam adopts a finite element algorithm to calculate the stability of the variable-section curved beam, adopts a buckling method and/or an implicit nonlinear method to calculate the instability load of a finite element model of the variable-section curved beam, and adopts the following calculation principles:
a buckling method comprises the following steps:
judging the instability mode according to the characteristic value:
[K0]{u*}＝{P*}
{u*}＝[K0]-1{P*}
([K0]+λ[KG]){u}＝{0}
implicit nonlinear methods:
solving by iterating and solving simultaneous equations:
[K]＝K(E，vP，u)
{P}＝[K(E，vP，u)]{u}
P＝K(u)u
and comparing and analyzing the two finite element calculation methods and the instability load point in the stability test to obtain a first error of the calculation result of the instability load relative to the test result.
In one embodiment of the present application, calculating a destabilizing load of a variable cross-section curved beam finite element model by using a buckling method and/or an implicit nonlinear method, and comparing a calculation result of the destabilizing load with a test result to obtain a first error of the calculation result of the destabilizing load relative to the test result includes:
calculating the destabilizing load of the finite element model of the variable-section curved beam by adopting a buckling method, and comparing the calculation result of the destabilizing load with the test result to obtain a first error of the calculation result of the destabilizing load relative to the test result, or
And calculating the instability load of the finite element model of the variable-section curved beam by adopting an implicit nonlinear method, and comparing the calculation result of the instability load with the test result to obtain a first error of the calculation result of the instability load relative to the test result.
In another embodiment of the present application, calculating a destabilizing load of the variable cross-section curved beam finite element model by using a buckling method and/or an implicit nonlinear method, and comparing a calculation result of the destabilizing load with a test result to obtain a first error of the calculation result of the destabilizing load relative to the test result further includes:
calculating the buckling load of the finite element model of the variable-section curved beam by adopting a buckling method, and comparing the buckling method calculation result of the buckling load with the test result to obtain the error of the buckling method calculation result of the buckling load relative to the test result;
calculating the instability load of the finite element model of the variable-section curved beam by adopting an implicit nonlinear method, and comparing the calculation result of the implicit nonlinear method of the instability load with the test result to obtain the error of the calculation result of the implicit nonlinear method of the instability load relative to the test result;
and comparing the error of the buckling method calculation result of the unstable load relative to the test result with the error of the implicit nonlinear method calculation result of the unstable load relative to the test result, and taking a smaller error as a first error of the calculation result of the destructive load relative to the test result.
Further, comparing the error of the calculation result of the buckling method of the buckling load relative to the test result with the error of the calculation result of the implicit nonlinear method of the buckling load relative to the test result, and taking the smaller error as the first error of the calculation result of the breaking load relative to the test result includes:
comparing the error of the buckling method calculation result of the unstable load relative to the test result with the error of the implicit nonlinear method calculation result of the unstable load relative to the test result;
the error of the calculation result of the implicit nonlinear method for obtaining the unstable load is smaller relative to the test result;
and taking the error of the calculation result of the implicit nonlinear method of the unstable load relative to the test result as a first error.
In this embodiment, the buckling method has the buckling instability mode calculation results shown in fig. 2 to 4, and the buckling load calculation results of three variable cross-section curved beams are as follows:
buckling method for calculating instability load
Name (R) Destabilizing load kN
Variable cross-section curved beam 36.5
Variable cross-section reinforced curved beam 1 56.2
Variable cross-section reinforced curved beam 2 73.3
The implicit nonlinear calculation result is shown in the attached figure 3, and the unstable load calculation results of the three variable cross-section curved beams are as follows:
implicit nonlinear computation of destabilizing loads
Name (R) Destabilizing load kN
Variable cross-section curved beam 36
Variable cross-section reinforced curved beam 1 48
Variable cross-section reinforced curved beam 2 63
And comparing the calculation result with the test result, wherein the implicit nonlinear calculation result is closer to the test value than the buckling result, and the implicit nonlinear calculation result is larger than the test value, and the error is within 15%.
Comparing the test value with the finite element calculation result
Figure BDA0003312152020000071
According to the method for evaluating the stability and the strength of the variable cross-section curved beam, the damage load of the variable cross-section curved beam is estimated, and tests show that the bearing capacity of the curved beam is sharply reduced after the curved beam is unstable. The accuracy of the damage load of the variable cross-section curved beam is low by only adopting an implicit nonlinear method, the finite element analysis adopts a method of combining implicit nonlinearity and material nonlinearity, the damage load calculation result of the variable cross-section curved beam is small, and the error between the calculation result and the test result is within 15%. The calculated results are given in the following table with the test values:
Figure BDA0003312152020000072
finally, obtaining the stability and strength evaluation method of the modified variable cross-section curved beam according to the comparison of the finite element calculation result and the test value, wherein,
correcting the calculation result of the unstable load according to the first error, and realizing the evaluation of the stability of the variable cross-section curved beam comprises the following steps:
the unstable load of the variable cross-section curved beam is calculated by an implicit nonlinear method of the unstable load/1.2.
Correcting the calculation result of the breaking load according to the second error, and realizing the evaluation of the bearing capacity of the variable cross-section curved beam comprises the following steps:
the method for combining the implicit nonlinearity and the material nonlinearity of the breaking load calculates the value multiplied by 1.2.
According to the method for evaluating the stability and the strength of the variable-section curved beam, the instability load and the failure load of a variable-section curved beam test model are obtained through tests, the instability load and the failure load of a variable-section curved beam finite element model are calculated through a finite element calculation method, and the finite element simulation result is corrected through comparing and analyzing the finite element simulation result and the test result of the variable-section curved beam. The method provides a basis for rapidly evaluating the stability of the variable cross-section curved beam, improving the calculation precision and the structural design rationalization level.
The above description is only for the specific embodiments of the present application, but the scope of the present application is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present application should be covered within the scope of the present application. Therefore, the protection scope of the present application shall be subject to the protection scope of the claims.

Claims (8)

1. A method for evaluating the stability and the strength of a variable cross-section curved beam is characterized by comprising the following steps:
step one, establishing a variable cross-section curved beam test model, and performing a test to respectively obtain an instability load and a failure load of the variable cross-section curved beam test model;
step two, establishing a variable cross section curved beam finite element model according to the variable cross section curved beam test model;
step three, calculating the instability load of the variable cross-section curved beam finite element model by adopting a buckling method and/or an implicit nonlinear method, and comparing the calculation result of the instability load with the test result to obtain a first error of the calculation result of the instability load relative to the test result;
step four, calculating the failure load of the finite element model of the variable cross-section curved beam by adopting a method of combining implicit nonlinearity and material nonlinearity, and comparing the calculation result of the failure load with the test result to obtain a second error of the calculation result of the failure load relative to the test result;
and fifthly, correcting the calculation result of the unstable load according to the first error to realize the evaluation of the stability of the variable cross-section curved beam, and correcting the calculation result of the destructive load according to the second error to realize the evaluation of the bearing capacity of the variable cross-section curved beam.
2. The method for evaluating the stability and the strength of the variable cross-section curved beam according to claim 1, wherein in the step one, a plurality of variable cross-section curved beam test models are obtained according to parameter differences of the flange strip thickness and the web plate thickness.
3. The method for evaluating the stability and the strength of the variable cross-section curved beam according to claim 2, wherein in the second step, a corresponding variable cross-section curved beam finite element model is established according to a plurality of variable cross-section curved beam test models.
4. The method for evaluating the stability and the strength of the variable cross-section curved beam according to claim 1, wherein in the third step, the step of calculating the destabilizing load of the finite element model of the variable cross-section curved beam by adopting a buckling method and/or an implicit nonlinear method and comparing the calculation result of the destabilizing load with the test result to obtain the first error of the calculation result of the destabilizing load relative to the test result comprises the steps of:
calculating the destabilizing load of the finite element model of the variable cross-section curved beam by adopting a buckling method, and comparing the calculation result of the destabilizing load with the test result to obtain a first error of the calculation result of the destabilizing load relative to the test result, or
And calculating the instability load of the finite element model of the variable cross-section curved beam by adopting an implicit nonlinear method, and comparing the calculation result of the instability load with the test result to obtain a first error of the calculation result of the instability load relative to the test result.
5. The method for evaluating the stability and the strength of the variable cross-section curved beam according to claim 1, wherein in the third step, the step of calculating the destabilizing load of the finite element model of the variable cross-section curved beam by using a buckling method and/or an implicit nonlinear method and comparing the calculation result of the destabilizing load with the test result to obtain the first error of the calculation result of the destabilizing load relative to the test result further comprises:
calculating the buckling load of the finite element model of the variable-section curved beam by adopting a buckling method, and comparing the buckling method calculation result of the buckling load with the test result to obtain the error of the buckling method calculation result of the buckling load relative to the test result;
calculating the instability load of the finite element model of the variable cross-section curved beam by adopting an implicit nonlinear method, and comparing the calculation result of the implicit nonlinear method of the instability load with the test result to obtain the error of the calculation result of the implicit nonlinear method of the instability load relative to the test result;
and comparing the error of the buckling method calculation result of the unstable load relative to the test result with the error of the implicit nonlinear method calculation result of the unstable load relative to the test result, and taking a smaller error as a first error of the calculation result of the destructive load relative to the test result.
6. The method for evaluating the stability and the strength of the variable cross-section curved beam according to claim 5, wherein the step of comparing the error of the calculation result of the buckling method of the buckling load relative to the test result with the error of the calculation result of the implicit nonlinear method of the buckling load relative to the test result, and the step of taking the smaller error as the first error of the calculation result of the breaking load relative to the test result comprises the steps of:
comparing the error of the buckling method calculation result of the unstable load relative to the test result with the error of the implicit nonlinear method calculation result of the unstable load relative to the test result;
the error of the calculation result of the implicit nonlinear method for obtaining the unstable load is smaller relative to the test result;
and taking the error of the calculation result of the implicit nonlinear method of the unstable load relative to the test result as a first error.
7. The method for evaluating the stability and the strength of the variable cross-section curved beam according to claim 6, wherein in the fifth step, the correcting the calculation result of the destabilizing load according to the first error to realize the evaluation of the stability of the variable cross-section curved beam comprises the following steps:
the unstable load of the variable cross-section curved beam is calculated by an implicit nonlinear method of the unstable load/1.2.
8. The method for evaluating the stability and the strength of the variable cross-section curved beam according to claim 7, wherein in the fifth step, the step of correcting the calculation result of the breaking load according to the second error to realize the evaluation of the bearing capacity of the variable cross-section curved beam comprises the following steps:
the method for combining the implicit nonlinearity and the material nonlinearity of the breaking load calculates the value multiplied by 1.2.
CN202111219821.0A 2021-10-20 2021-10-20 Method for evaluating stability and strength of variable cross-section curved beam Pending CN114429059A (en)

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