CN111753455A - Method for quickly calculating dynamic buckling of slender metal arch structure by considering geometric defects - Google Patents

Method for quickly calculating dynamic buckling of slender metal arch structure by considering geometric defects Download PDF

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CN111753455A
CN111753455A CN202010616937.7A CN202010616937A CN111753455A CN 111753455 A CN111753455 A CN 111753455A CN 202010616937 A CN202010616937 A CN 202010616937A CN 111753455 A CN111753455 A CN 111753455A
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CN111753455B (en
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杨智诚
吕建根
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Zhongkai University of Agriculture and Engineering
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Abstract

The invention discloses a method for quickly calculating the dynamic buckling of a slender metal arch structure by considering geometric defects, which comprises the following steps: carrying out parametric modeling on the metal arch structure to obtain a first modeling model; applying a first concentrated force on the first modeling model, and calculating the characteristic buckling load and the characteristic buckling mode in the front N-order plane; and introducing a first-order characteristic buckling mode as an initial geometric defect of the first modeling model, carrying out nonlinear static buckling overall process analysis on the obtained second modeling model to obtain a load-displacement change curve and a total potential energy-displacement change curve of the second modeling model, and judging the dynamic buckling critical load of the second modeling model according to the obtained curves. The method provided by the invention can determine the dynamic buckling critical load of the metal arch structure under the action of corresponding step power according to one-time nonlinear static buckling calculation, achieves the aim of quick calculation, avoids complex and time-consuming dynamic response calculation, improves the calculation efficiency and reduces the calculation cost.

Description

Method for quickly calculating dynamic buckling of slender metal arch structure by considering geometric defects
Technical Field
The invention relates to the technical field of structural dynamic buckling in structural mechanics, in particular to a method for quickly calculating the dynamic buckling of a slender metal arch structure by considering geometric defects.
Background
The method for determining the critical load of the dynamic buckling of the structure is commonly used in engineering and comprises the steps of carrying out a large amount of structural dynamic response calculation, tracking the response change of the structure under the action of the dynamic load, and when the small increment of the applied dynamic load can cause the huge change of the structural response, determining the corresponding dynamic load as the critical load of the dynamic buckling. Li and Molyneaux obtain a dynamic load displacement curve of the simplified triangular arch structure under the sudden loading through a large amount of calculation, and intuitively reflect the buckling condition of the arch structure under the dynamic loading. However, the calculation amount of the method for solving the critical load of the structural dynamic buckling is quite large, and particularly when the delayed buckling occurs, the structural dynamic response of more cycles needs to be examined to obtain a correct result, but a large amount of calculation resources and time are necessarily occupied.
For the slender metal arch structure, the arch axis line shape is changed to form an initial geometric defect because the slender metal arch structure is inevitably influenced by external factors in the processes of design, manufacture, transportation, construction and the like, the slender metal arch structure with the initial geometric defect is easy to generate dynamic buckling under the action of dynamic load, the metal bending stress is increased possibly due to large buckling deformation, and even the metal can reach the yield strength, so that the potential safety hazard exists. Therefore, a method for rapidly calculating the dynamic buckling of the elongated metal arch structure by considering the geometric defects is needed to be provided, and the influence of the geometric defects on the dynamic buckling of the metal arch structure can be considered while the calculation efficiency is solved.
Disclosure of Invention
Aiming at the problems, the invention provides a method for quickly calculating the dynamic buckling of the elongated metal arch structure by considering the geometric defects, and aims to improve the calculation efficiency of the dynamic buckling of the elongated metal arch structure, save the calculation resources and consider the influence of the initial geometric defects on the dynamic buckling of the metal arch structure.
The purpose of the invention is realized by adopting the following technical scheme: a method for rapidly calculating the dynamic buckling of an elongated metal arch structure by considering geometric defects comprises the following steps:
(1) according to the geometric characteristics and physical mechanical parameters of the metal arch structure, carrying out parametric modeling on the metal arch structure by using finite element software ANSYS to obtain a first modeling model of the metal arch structure;
(2) applying finite element software ANSYS, applying a first concentrated force on the first modeling model, and then performing characteristic buckling analysis on the first modeling model to obtain characteristic buckling load and characteristic buckling mode in the front N-order plane of the first modeling model;
(3) selecting one-order characteristic buckling mode from the characteristic buckling modes in the front N-order plane as an initial geometric defect of the first modeling model, and updating the geometric configuration of the first modeling model to obtain a second modeling model; applying a second concentrated force on the second modeling model, and then carrying out nonlinear static buckling whole-process analysis on the second modeling model to obtain a load-displacement change curve and a total potential energy-displacement change curve of the second modeling model;
(4) drawing a load-displacement change curve and a total potential energy-displacement change curve of the second modeling model in the same graph;
(5) determining whether a zero total potential energy point exists according to the total potential energy-displacement change curve, if so, determining that the zero total potential energy point in the total potential energy-displacement change curve corresponds to a point a in a load-displacement change curve based on the graph obtained in the step (4), and calculating the slope k at the point a according to the load-displacement change curveaIf k isaIf the load is less than 0, the load corresponding to the point a is the dynamic buckling critical load.
In an alternative embodiment, in step (2), the step of applying a first concentrated force to the first modeling model includes: a unit static concentration force is applied at an arbitrary position above the arch in the arch axis plane in the first modeled model.
In an optional embodiment, the step (3) specifically includes the following steps:
(31) using a command UPGEOM of finite element software ANSYS to designate a first-order characteristic buckling mode as an initial geometric defect of the first modeling model, updating the geometric configuration of the first modeling model, and obtaining a second modeling model, wherein the value range of a defect scale factor is as follows: (S/500-S/1000), wherein S is the arc length of the metal arch structure;
(32) applying a second concentrated force of a characteristic buckling load magnitude corresponding to the initial geometric defect to the second modeling model;
(32) and (3) carrying out nonlinear static buckling whole-process analysis on the second modeling model by using an ARCLEN (arc length enabled) method of a command of finite element software ANSYS to obtain a load-displacement change curve and a total potential energy-displacement change curve of the second modeling model.
In an alternative embodiment, the dynamic buckling is: dynamic buckling in the plane of the second modeled model under the action of step concentration force;
in the step (5), whether a zero total potential energy point exists is determined according to the total potential energy-displacement change curve; and if the zero total potential energy point does not exist, the dynamic buckling behavior does not exist.
In an optional embodiment, the value of N satisfies: n is more than or equal to 10.
In an alternative embodiment, the 1 st order characteristic buckling mode is selected as the initial geometric defect of the first modeled model.
The invention has the beneficial effects that: the invention provides a method for quickly calculating the dynamic buckling of a slender metal arch structure by considering geometric defects, which is characterized in that the method is based on a probability theory modal method to introduce the initial geometric defects of the metal arch structure to obtain a second modeling model of the metal arch structure, a load-displacement curve and a total potential energy curve of the second modeling model of the metal arch structure under the action of concentrated force are obtained through one-time nonlinear static buckling whole-process analysis, and then the dynamic buckling critical load of the second modeling model of the metal arch structure under the action of step concentrated force is determined according to the total potential energy change. The method avoids complex and tedious structural response calculation, quickly obtains the dynamic buckling critical load of the metal arch structure, and greatly improves the calculation efficiency.
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The invention is further illustrated by means of the attached drawings, but the embodiments in the drawings do not constitute any limitation to the invention, and for a person skilled in the art, other drawings can be obtained on the basis of the following drawings without inventive effort.
FIG. 1 is a schematic view of a circular arc solid steel arch applied over a dome provided by an embodiment of the present invention;
FIG. 2 is a vertical phase force concentration profile provided by an embodiment of the present invention;
FIG. 3 is a characteristic buckling mode of order 1 of a first modeling model of a circular arc solid steel arch provided by an embodiment of the invention;
FIG. 4 is a load-displacement curve and a total potential energy curve provided by an embodiment of the present invention;
FIG. 5 is a dome dynamic response diagram of a second modeled model of a circular solid steel arch provided by an embodiment of the present invention;
FIG. 6 is a schematic view of a circular solid steel arch applied elsewhere on the arch, according to another embodiment of the present invention;
FIG. 7 is a load-displacement curve and a total potential energy curve according to another embodiment of the present invention;
FIG. 8 is a dome dynamic response plot of a second modeled model of a circular solid steel arch provided in accordance with another embodiment of the present invention;
FIG. 9 is a schematic view of a parabolic arch applied to a dome provided by yet another embodiment of the present invention;
FIG. 10 is a load versus displacement curve and a total potential energy curve according to yet another embodiment of the present invention;
FIG. 11 is a dome dynamic response diagram of a second modeled model of a parabolic arch provided in accordance with yet another embodiment of the present invention.
Detailed Description
The invention is further described with reference to the following examples.
A method for rapidly calculating the dynamic buckling of an elongated metal arch structure by considering geometric defects comprises the following steps:
(1) according to the geometric characteristics and physical mechanical parameters of the metal arch structure, carrying out parametric modeling on the metal arch structure by using finite element software ANSYS to obtain a first modeling model of the metal arch structure;
(2) applying finite element software ANSYS, applying a first concentrated force on the first modeling model, and then performing characteristic buckling analysis on the first modeling model to obtain characteristic buckling load and characteristic buckling mode in the front N-order plane of the first modeling model;
(3) selecting one-order characteristic buckling mode from the characteristic buckling modes in the front N-order plane as an initial geometric defect of the first modeling model, and updating the geometric configuration of the first modeling model to obtain a second modeling model; applying a second concentrated force on the second modeling model, and then carrying out nonlinear static buckling whole-process analysis on the second modeling model to obtain a load-displacement change curve and a total potential energy-displacement change curve of the second modeling model;
(4) drawing a load-displacement change curve and a total potential energy-displacement change curve of the second modeling model in the same graph;
(5) determining whether a zero total potential energy point exists according to the total potential energy-displacement change curve, if so, determining that the zero total potential energy point in the total potential energy-displacement change curve corresponds to a point a in a load-displacement change curve based on the graph obtained in the step (4), and calculating the slope k at the point a according to the load-displacement change curveaIf k isaIf the load is less than 0, the load corresponding to the point a is the dynamic buckling critical load.
In an alternative embodiment, in step (2), the step of applying a first concentrated force to the first modeling model includes: a unit static concentration force is applied at an arbitrary position above the arch in the arch axis plane in the first modeled model.
In an optional embodiment, the step (3) specifically includes the following steps:
(31) using a command UPGEOM of finite element software ANSYS to designate a first-order characteristic buckling mode as an initial geometric defect of the first modeling model, updating the geometric configuration of the first modeling model, and obtaining a second modeling model, wherein the value range of a defect scale factor is as follows: (S/500-S/1000), wherein S is the arc length of the metal arch structure;
(32) applying a second concentrated force of a characteristic buckling load magnitude corresponding to the initial geometric defect to the second modeling model;
(32) and (3) carrying out nonlinear static buckling whole-process analysis on the second modeling model by using an ARCLEN (arc length enabled) method of a command of finite element software ANSYS to obtain a load-displacement change curve and a total potential energy-displacement change curve of the second modeling model.
In an alternative embodiment, the dynamic buckling is: dynamic buckling in the plane of the second modeled model under the action of step concentration force;
in the step (5), whether a zero total potential energy point exists is determined according to the total potential energy-displacement change curve; and if the zero total potential energy point does not exist, the dynamic buckling behavior does not exist.
In an optional embodiment, the value of N satisfies: n is more than or equal to 10.
In an alternative embodiment, the 1 st order characteristic buckling mode is selected as the initial geometric defect of the first modeled model.
The invention provides a method for quickly calculating the dynamic buckling of a slender metal arch structure by considering geometric defects, which is characterized in that the method is based on a probability theory modal method to introduce the initial geometric defects of the metal arch structure to obtain a second modeling model of the metal arch structure, a load-displacement curve and a total potential energy curve of the second modeling model of the metal arch structure under the action of concentrated force are obtained through one-time nonlinear static buckling whole-process analysis, and then the dynamic buckling critical load of the second modeling model of the metal arch structure under the action of step concentrated force is determined according to the total potential energy change. The method avoids complex and tedious structural response calculation, quickly obtains the dynamic buckling critical load of the metal arch structure, and greatly improves the calculation efficiency.
In order to better explain the method for rapidly calculating the dynamic buckling of the elongated metal arch structure by considering the geometric defects, the embodiment of the invention provides the following three specific application scenarios.
The first embodiment is as follows: fig. 1 shows a circular solid steel arch belonging to one of the elongated metal arch structures, whose geometrical and physico-mechanical parameters are shown in table 1:
TABLE 1 arc solid Steel Arch geometry and physical parameters
Figure BDA0002564097710000051
In this embodiment, a method for rapidly calculating dynamic buckling of a slender metal arch structure by considering geometric defects is used to calculate the critical load of dynamic buckling of the arc solid steel arch shown in fig. 1, which is specifically described as follows:
carrying out parametric modeling on the arc solid steel arch shown in the figure 1 by using finite element software ANSYS to obtain a first modeling model of the arc solid steel arch; as shown in FIG. 2, the arc solid steel arch crown can bear the concentrated force with the maximum amplitude of Q vertical step.
Applying finite element software ANSYS, applying unit vertical static concentrated force (namely first concentrated force) on the arch crown of the first modeling model of the arc solid steel arch, and then carrying out characteristic buckling analysis once to obtain the characteristic buckling load and the characteristic buckling mode in the front N-order plane of the first modeling model of the arc solid steel arch, wherein the value of N is more than or equal to 10, and preferably, N is 10, wherein the 1 st-order characteristic buckling critical load is 1.24 × 107The N, 1 st order characteristic buckling mode is shown in fig. 3.
And (3) using a command UPGEOM of finite element software ANSYS to designate a 1 st order characteristic buckling mode as an initial geometric defect to be applied to an arch axis of a first modeling model of the arc solid steel arch, updating the geometric configuration of the first modeling model, and obtaining a second modeling model, wherein the defect scale factor is S/800.
The vault application size of the second modeling model of the arc solid steel arch is 1.24 × 107N, applying an ARCLEN (arc length starting method) command of finite element software ANSYS to carry out nonlinear static buckling whole-process analysis on the second modeling model to obtain a load-displacement change curve and a total potential energy-displacement change curve of the second modeling model;
and drawing the load-displacement change curve and the total potential energy-displacement change curve of the second modeling model in the same graph, which is specifically shown in fig. 4.
Determining whether a zero total potential energy point exists according to the total potential energy-displacement change curve, if so, determining that the zero total potential energy point in the total potential energy-displacement change curve corresponds to a point a in a load-displacement change curve based on the attached figure 4, and calculating a slope k at the point a according to the load-displacement change curveaIf k isaIf < 0, the load 5.812 × 10 corresponding to the point a6Namely the dynamic buckling critical load of the arc solid steel arch under the action of the vertical step concentration force of the arch crown.
In order to verify the accuracy of calculating the dynamic buckling critical load of the arc solid steel arch shown in fig. 1 by using the method for rapidly calculating the dynamic buckling of the elongated metal arch structure by considering the geometric defects, the embodiment further calculates the dynamic buckling critical load of the arc solid steel arch shown in fig. 1 by using a conventional method for solving the structural dynamic buckling, and the result is shown in fig. 56When N is higher than N, the arch crown dynamic response of the arc solid steel arch is bounded stable response, which indicates that the arc solid steel arch does not generate dynamic buckling, and when the amplitude of the step concentration force reaches 5.833 × 106When N is higher, the arch crown dynamic response of the arc solid steel arch generates large jump, and is unbounded, which indicates that the arc solid steel arch generates dynamic buckling, and the dynamic buckling critical load of the arc solid steel arch under the action of arch crown vertical step concentration force can be determined to be 5.833 × 106N。
From the above examples, it can be seen that the critical load of dynamic buckling obtained by the method provided by the present invention is 5.812 × 106N, the critical load of dynamic buckling obtained by the traditional calculation method is 5.833 × 106And N, the error of the two is 0.36 percent, which shows that the method provided by the invention has more accurate calculation precision. It should be noted that the method for calculating the dynamic buckling of the arc solid steel arch by adopting the traditional method for solving the structural dynamic buckling consumes a large amount of time to perform dynamic response calculation, and the solving efficiency is low.
Example two: fig. 6 shows a circular arc solid steel arch belonging to one of the elongated metal arch structures, whose geometrical, physico-mechanical parameters and load deflection angles are shown in table 2:
TABLE 2 arc solid Steel Arch geometry, physical parameters and load deflection angle
Figure BDA0002564097710000061
Wherein, the load deflection angle refers to the angle of the load (namely the first concentrated force) deviating from the vault position;
in this embodiment, a method for rapidly calculating dynamic buckling of a slender metal arch structure by considering geometric defects is used to calculate the critical load of dynamic buckling of the arc solid steel arch shown in fig. 6, which is specifically described as follows:
carrying out parametric modeling on the arc solid steel arch shown in the figure 6 by using finite element software ANSYS to obtain a first modeling model of the arc solid steel arch;
applying finite element software ANSYS, applying unit static concentrated force Q (t) (namely first concentrated force) on the first modeling model of the arc solid steel arch, and then carrying out characteristic buckling analysis once to obtain characteristic buckling load and buckling mode in the front 10-order plane of the first modeling model of the arc solid steel arch, wherein the 1 st-order characteristic buckling critical load is 1.34 × 107N。
And (3) using a command UPGEOM of finite element software ANSYS to designate a 1 st order characteristic buckling mode as an initial geometric defect to be applied to an arch axis of a first modeling model of the arc solid steel arch, updating the geometric configuration of the first modeling model, and obtaining a second modeling model, wherein the defect scale factor is S/800.
A second modeling model of a circular solid steel arch was overlaid with a size of 1.34 × 107N (namely a second concentration force), and performing nonlinear static buckling whole-process analysis on the second modeling model by using an ARCLEN (arc length enabled) method of a command of finite element software ANSYS (ANSYS) to obtain a load-displacement change curve and a total potential energy-displacement change curve of the second modeling model;
and drawing a load-displacement change curve and a total potential energy-displacement change curve of the second modeling model in the same graph, specifically as shown in fig. 7.
Determining whether a zero total potential energy point exists according to the total potential energy-displacement change curve, if so, determining that the zero total potential energy point in the total potential energy-displacement change curve corresponds to a point a in a load-displacement change curve based on the attached figure 7, and calculating a slope k at the point a according to the load-displacement change curveaIf k isaIf < 0, the load 5.788 × 10 corresponding to the point a6And N is the dynamic buckling critical load of the arc solid steel arch under the action of vault step concentration force.
In order to verify the accuracy of calculating the dynamic buckling critical load of the arc solid steel arch shown in fig. 6 by using the method for rapidly calculating the dynamic buckling of the elongated metal arch structure by considering the geometric defects, the embodiment further calculates the dynamic buckling critical load of the arc solid steel arch shown in fig. 6 by using a conventional method for solving the structural dynamic buckling, and the result is shown in fig. 86When N is higher than N, the arch crown dynamic response of the arc solid steel arch is bounded stable response, which indicates that the arc solid steel arch does not generate dynamic buckling, and when the amplitude of the step concentration force reaches 5.815 × 106When N is higher, the arch crown dynamic response of the arc solid steel arch generates large jump, and is unbounded, which indicates that the arc solid steel arch generates dynamic buckling, and the dynamic buckling critical load of the arc solid steel arch under the action of the step concentration force can be determined to be 5.815 × 106N。
From the above examples, it can be seen that the critical load of dynamic buckling obtained by the method provided by the present invention is 5.788 × 106N, the critical load of dynamic buckling obtained by the traditional calculation method is 5.833 × 106And N, the error of the two is 0.47%, which shows that the method provided by the invention has relatively accurate calculation precision. It should be noted that the method for calculating the dynamic buckling of the arc solid steel arch by adopting the traditional method for solving the structural dynamic buckling consumes a large amount of time to perform dynamic response calculation, and the solving efficiency is low.
Example three: FIG. 9 showsA parabolic arch is presented, wherein the parabolic function is:
Figure BDA0002564097710000071
the parabolic arch belongs to one of slender metal arch structures, and the geometrical and physical mechanical parameters of the parabolic arch are shown in table 3:
TABLE 3 parabolic arch geometry and physical parameters
Figure BDA0002564097710000072
In this embodiment, a method for rapidly calculating dynamic buckling of a slender metal arch structure by considering geometric defects is used to calculate the critical load of dynamic buckling of a parabolic arch shown in fig. 9, which is specifically described as follows:
carrying out parametric modeling on the parabola arch shown in the figure 9 by using finite element software ANSYS to obtain a first modeling model of the parabola arch;
applying finite element software ANSYS, applying unit vertical static concentrated force (namely first concentrated force) on the arch crown of the first modeling model of the parabola arch, and then carrying out characteristic buckling analysis once to obtain characteristic buckling load and buckling mode in the front 10-order plane of the first modeling model of the parabola arch, wherein the 1 st-order characteristic buckling critical load is 9.18 × 106N。
And (3) applying a command UPGEOM of finite element software ANSYS to designate a 1 st order characteristic buckling mode as an initial geometric defect to be applied to an arch axis of a first modeling model of the parabola arch, and updating the geometric configuration of the first modeling model to obtain a second modeling model, wherein the defect scale factor is S/800.
The vault application size of the second modeled model at the parabola arch was 9.18 × 106N, applying an ARCLEN (arc length starting method) command of finite element software ANSYS to carry out nonlinear static buckling whole-process analysis on the second modeling model to obtain a load-displacement change curve and a total potential energy-displacement change curve of the second modeling model;
and drawing the load-displacement change curve and the total potential energy-displacement change curve of the second modeling model in the same graph, specifically as shown in fig. 10.
Determining whether a zero total potential energy point exists according to the total potential energy-displacement change curve, if so, determining that the zero total potential energy point in the total potential energy-displacement change curve corresponds to a point a in a load-displacement change curve based on the attached figure 4, and calculating a slope k at the point a according to the load-displacement change curveaIf k isaIf < 0, the load 3.915 × 10 corresponding to the point a6And N is the dynamic buckling critical load of the parabola arch under the action of the vertical step concentration force of the arch crown.
In order to verify the accuracy of calculating the dynamic buckling critical load of the parabolic arch shown in fig. 9 by using the method for rapidly calculating the dynamic buckling of the elongated metal arch structure by considering the geometric defects, the embodiment further calculates the dynamic buckling critical load of the parabolic arch shown in fig. 9 by using a conventional method for solving the dynamic buckling of the structure, and the result is shown in fig. 116When N is reached, the dynamic response of the arch crown of the parabola arch is a bounded stable response, which indicates that no dynamic buckling of the parabola arch occurs, and when the amplitude of the step concentration force reaches 3.950 × 106When N is higher, the arch crown dynamic response of the parabola arch jumps greatly and is unbounded, the fact that dynamic buckling of the parabola arch occurs is indicated, and the dynamic buckling critical load of the parabola arch under the action of arch crown vertical step concentration force can be determined to be 3.950 × 106N。
From the above examples, it can be seen that the critical load of dynamic buckling obtained by the method provided by the present invention is 3.915 × 106N, the critical load of dynamic buckling obtained by the traditional calculation method is 3.950 × 106And N, the error of the two is 0.88 percent, which shows that the method provided by the invention has more accurate calculation precision. It should be noted that the method for calculating the parabolic arch by adopting the traditional method for solving the structural dynamic buckling consumes a large amount of time for dynamic response calculation, and the solving efficiency is low.
Finally, it should be noted that the above embodiments are only used for illustrating the technical solutions of the present invention, and not for limiting the protection scope of the present invention, although the present invention is described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that modifications or equivalent substitutions can be made on the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention.

Claims (6)

1. A method for quickly calculating the dynamic buckling of a slender metal arch structure by considering geometric defects is characterized by comprising the following steps of:
(1) according to the geometric characteristics and physical mechanical parameters of the metal arch structure, carrying out parametric modeling on the metal arch structure by using finite element software ANSYS to obtain a first modeling model of the metal arch structure;
(2) applying finite element software ANSYS, applying a first concentrated force on the first modeling model, and then performing characteristic buckling analysis on the first modeling model to obtain characteristic buckling load and characteristic buckling mode in the front N-order plane of the first modeling model;
(3) selecting one-order characteristic buckling mode from the characteristic buckling modes in the front N-order plane as an initial geometric defect of the first modeling model, and updating the geometric configuration of the first modeling model to obtain a second modeling model; applying a second concentrated force on the second modeling model, and then carrying out nonlinear static buckling whole-process analysis on the second modeling model to obtain a load-displacement change curve and a total potential energy-displacement change curve of the second modeling model;
(4) drawing a load-displacement change curve and a total potential energy-displacement change curve of the second modeling model in the same graph;
(5) determining whether a zero total potential energy point exists according to the total potential energy-displacement change curve, if so, determining that the zero total potential energy point in the total potential energy-displacement change curve corresponds to a point a in a load-displacement change curve based on the graph obtained in the step (4), and calculating the slope k at the point a according to the load-displacement change curveaIf k isaIf the load is less than 0, the load corresponding to the point a is the dynamic buckling critical load。
2. The method for rapidly calculating the dynamic buckling of the elongated metal arch structure by considering the geometric defects according to claim 1, wherein in the step (2), a first concentrated force is applied to the first modeling model, and specifically: a unit static concentration force is applied at an arbitrary position above the arch in the arch axis plane in the first modeled model.
3. The method for rapidly calculating the dynamic buckling of the elongated metal arch structure by considering the geometric defects of the claim 1, wherein the step (3) comprises the following steps:
(31) using a command UPGEOM of finite element software ANSYS to designate a first-order characteristic buckling mode as an initial geometric defect of the first modeling model, updating the geometric configuration of the first modeling model, and obtaining a second modeling model, wherein the value range of a defect scale factor is as follows: (S/500-S/1000), wherein S is the arc length of the metal arch structure;
(32) applying a second concentrated force of a characteristic buckling load magnitude corresponding to the initial geometric defect to the second modeling model;
(32) and (3) carrying out nonlinear static buckling whole-process analysis on the second modeling model by using an ARCLEN (arc length enabled) method of a command of finite element software ANSYS to obtain a load-displacement change curve and a total potential energy-displacement change curve of the second modeling model.
4. The method for rapidly calculating the dynamic buckling of the slender metal arch structure by considering the geometrical defects of the slender metal arch structure according to claim 1, wherein the dynamic buckling is as follows: dynamic buckling in the plane of the second modeled model under the action of step concentration force;
in the step (5), whether a zero total potential energy point exists is determined according to the total potential energy-displacement change curve; and if the zero total potential energy point does not exist, the dynamic buckling behavior does not exist.
5. The method for rapidly calculating the dynamic buckling of the elongated metal arch structure by considering the geometric defects according to claim 1, wherein the value of N satisfies the following conditions: n is more than or equal to 10.
6. The method for rapidly calculating the dynamic buckling of the elongated metal arch structure by considering the geometric defects according to any one of claims 1 to 3, wherein a characteristic buckling mode of the 1 st order is selected as the initial geometric defect of the first modeling model.
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