CN111753455B - Method for rapidly calculating dynamic buckling of slender metal arch structure by considering geometric defects - Google Patents
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Abstract
The invention discloses a method for rapidly calculating dynamic buckling of an elongated metal arch structure by considering geometric defects, which comprises the following steps: performing parameterized modeling on the metal arch structure to obtain a first modeling model; applying a first concentrated force on the first modeling model, and calculating a characteristic buckling load and a characteristic buckling mode in a 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 corresponding step dynamic action according to one-time nonlinear static buckling calculation, so that the purpose of rapid calculation is achieved, complex and time-consuming dynamic response calculation is avoided, the calculation efficiency is improved, and the calculation cost is reduced.
Description
Technical Field
The invention relates to the technical field of structural power buckling in structural mechanics, in particular to a rapid calculation method for structural power buckling of an elongated metal arch structure by considering geometric defects.
Background
The method for determining the dynamic buckling critical load of the structure is commonly used in engineering, which is to perform a large amount of structure dynamic response calculation, track 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 great change of the structure response, the corresponding dynamic load is the dynamic buckling critical load. Li and Molyneaux are calculated in a large amount to obtain a dynamic load displacement curve of the simplified triangular arch structure under the sudden load, and the buckling condition of the arch structure under the dynamic load is intuitively reflected. However, the method has quite large calculation amount for solving the critical load of the dynamic buckling of the structure, 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 great deal of calculation resources and time are required to be occupied.
For the slender metal arch structure, the slender metal arch structure is inevitably influenced by external factors in the processes of design, manufacture, transportation, construction and the like, so that the arch axis type is changed to form initial geometric defects, the slender metal arch structure with the initial geometric defects is easier to generate dynamic buckling under the action of dynamic load, the larger buckling deformation can lead to the increase of metal bending stress, even the metal can reach the yield strength, and potential safety hazards exist. Therefore, it is necessary to propose a method for rapidly calculating the dynamic buckling of an elongated metal arch structure by considering geometric defects, which can consider the influence of the geometric defects on the dynamic buckling of the metal arch structure while solving the calculation efficiency.
Disclosure of Invention
The invention provides a method for rapidly calculating the dynamic buckling of an elongated metal arch structure by considering geometric defects, aiming at improving the calculation efficiency of the dynamic buckling of the elongated metal arch structure, saving calculation resources and considering the influence of initial geometric defects on the dynamic buckling of the metal arch structure.
The aim of the invention is realized by adopting the following technical scheme: a method for rapidly calculating dynamic buckling of an elongated metal arch structure by considering geometric defects comprises the following steps:
(1) According to geometric characteristics and physical and mechanical parameters of the metal arch structure, parametric modeling is carried out 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 a characteristic buckling load and a characteristic buckling mode in a front N-order plane of the first modeling model;
(3) Selecting one of the first-order characteristic buckling modes from the front N-order in-plane characteristic buckling modes 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 overall 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 from the total potential energy-displacement curve asIf so, determining a point a of the zero total potential energy point in the total potential energy-displacement change curve corresponding to the 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 curve a If k a And (3) if the load is less than 0, the load corresponding to the point a is the critical load of dynamic buckling.
In an alternative embodiment, in step (2), said applying a first concentrated force on said first modeling model, in particular: a unit static force concentration is applied at any location above the arch in the arch axis plane in the first modeling model.
In an alternative embodiment, the step (3) specifically includes the following steps:
(31) The command UPGEOM of finite element software ANSYS is applied to specify a first-order characteristic buckling mode as an initial geometric defect of the first modeling model, the geometric configuration of the first modeling model is updated, and a second modeling model is obtained, wherein the range of values of defect scale factors is as follows: S/500-S/1000, S is the arc length of the metal arch structure;
(32) Applying a second concentrated force to the second modeling model corresponding to the characteristic buckling load magnitude of the initial geometric defect;
(32) And carrying out nonlinear static buckling overall process analysis on the second modeling model by using a command ARCLEN starting arc length method 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 modeling model under the action of the step concentrated force;
in the step (5), determining whether a zero total potential energy point exists according to the total potential energy-displacement change curve; if no zero total potential energy point exists, no dynamic buckling behavior exists.
In an alternative embodiment, the value of N satisfies the following: n is more than or equal to 10.
In an alternative embodiment, a 1 st order characteristic buckling mode is selected as the initial geometric defect of the first modeling model.
The beneficial effects of the invention are as follows: the invention provides a method for quickly calculating dynamic buckling of an elongated metal arch structure by considering geometric defects, which is based on the fact that the initial geometric defects of the metal arch structure are introduced by a probability theory modal method, a second modeling model of the metal arch structure is obtained, 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 overall process analysis, and then dynamic buckling critical load of the second modeling model of the metal arch structure under the action of the concentrated force is determined according to the total potential energy change. The method avoids complex and complicated structure response calculation, rapidly obtains the dynamic buckling critical load of the metal arch structure, and greatly improves the calculation efficiency.
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The invention will be further described with reference to the accompanying drawings, in which embodiments do not constitute any limitation of the invention, and other drawings can be obtained by one of ordinary skill in the art without inventive effort from the following drawings.
FIG. 1 is a schematic view of a solid steel arch applied to a dome in accordance with an embodiment of the present invention;
FIG. 2 is a vertical phase force concentrating calendar graph provided by an embodiment of the present invention;
FIG. 3 is a 1 st order characteristic buckling mode of a first modeling model of a circular arc solid steel arch provided by an embodiment of the present invention;
FIG. 4 is a graph of load versus displacement versus total potential energy provided by an embodiment of the present invention;
FIG. 5 is a graph of dome dynamics response of a second modeling model of a circular arc solid steel dome provided by an embodiment of the present invention;
FIG. 6 is a schematic view of a solid steel arch applied at other locations on the arch in accordance with another embodiment of the present invention;
FIG. 7 is a load-displacement versus total potential energy curve provided by another embodiment of the present invention;
FIG. 8 is a graph of dome dynamics response of a second modeling model of a circular arc solid steel dome provided by another embodiment of the present invention;
FIG. 9 is a schematic view of a parabolic arch applied over a dome provided in accordance with yet another embodiment of the present invention;
FIG. 10 is a load-displacement versus total potential energy curve provided by yet another embodiment of the present invention;
FIG. 11 is a graph of dome dynamics response of a second modeling model of a parabolic arch provided in accordance with yet another embodiment of the present invention.
Detailed Description
The invention will be further described with reference to the following examples.
A method for rapidly calculating dynamic buckling of an elongated metal arch structure by considering geometric defects comprises the following steps:
(1) According to geometric characteristics and physical and mechanical parameters of the metal arch structure, parametric modeling is carried out 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 a characteristic buckling load and a characteristic buckling mode in a front N-order plane of the first modeling model;
(3) Selecting one of the first-order characteristic buckling modes from the front N-order in-plane characteristic buckling modes 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 overall 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, and if so, determining the total potential energy based on the graph obtained in the step (4)-the zero total potential energy point in the displacement curve corresponds to point a in the load-displacement curve, from which the slope k at point a is calculated a If k a And (3) if the load is less than 0, the load corresponding to the point a is the critical load of dynamic buckling.
In an alternative embodiment, in step (2), said applying a first concentrated force on said first modeling model, in particular: a unit static force concentration is applied at any location above the arch in the arch axis plane in the first modeling model.
In an alternative embodiment, the step (3) specifically includes the following steps:
(31) The command UPGEOM of finite element software ANSYS is applied to specify a first-order characteristic buckling mode as an initial geometric defect of the first modeling model, the geometric configuration of the first modeling model is updated, and a second modeling model is obtained, wherein the range of values of defect scale factors is as follows: S/500-S/1000, S is the arc length of the metal arch structure;
(32) Applying a second concentrated force to the second modeling model corresponding to the characteristic buckling load magnitude of the initial geometric defect;
(32) And carrying out nonlinear static buckling overall process analysis on the second modeling model by using a command ARCLEN starting arc length method 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 modeling model under the action of the step concentrated force;
in the step (5), determining whether a zero total potential energy point exists according to the total potential energy-displacement change curve; if no zero total potential energy point exists, no dynamic buckling behavior exists.
In an alternative embodiment, the value of N satisfies the following: n is more than or equal to 10.
In an alternative embodiment, a 1 st order characteristic buckling mode is selected as the initial geometric defect of the first modeling model.
The invention provides a method for quickly calculating dynamic buckling of an elongated metal arch structure by considering geometric defects, which is based on the fact that the initial geometric defects of the metal arch structure are introduced by a probability theory modal method, a second modeling model of the metal arch structure is obtained, 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 overall process analysis, and then dynamic buckling critical load of the second modeling model of the metal arch structure under the action of the concentrated force is determined according to the total potential energy change. The method avoids complex and complicated structure response calculation, rapidly obtains the dynamic buckling critical load of the metal arch structure, and greatly improves the calculation efficiency.
In order to better explain the rapid calculation method of the dynamic buckling of the slender metal arch structure considering the geometric defects, the following three specific application scenes are given in the specific embodiment of the invention.
Embodiment one: fig. 1 shows a circular arc solid steel arch belonging to one of the elongated metal arch structures, the geometrical and physical mechanical parameters of which are shown in table 1:
TABLE 1 solid steel arch geometry and physical parameters for circular arcs
In this embodiment, a method for quickly calculating the dynamic buckling of the elongated metal arch structure by considering geometric defects is adopted to calculate the dynamic buckling critical load of the arc solid steel arch shown in fig. 1, and the method specifically includes the following steps:
performing parameterization modeling on the arc solid steel arch shown in fig. 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 circular arc solid steel arch vault can bear a vertical step concentrated force with the maximum amplitude of Q.
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 performing one-time characteristic buckling analysis to obtain the arc solid steel archCharacteristic buckling load and characteristic buckling mode in a first N-order plane of a first modeling model of the steel arch, wherein the value of N meets the following conditions: n is not less than 10, preferably N=10, wherein the 1 st order characteristic buckling critical load is 1.24X10 7 The N, 1 st order characteristic buckling modes are shown in FIG. 3.
The command UPGEOM of finite element software ANSYS is applied to specify that the 1 st order characteristic buckling mode is applied to an arch axis of a first modeling model of the arc solid steel arch as an initial geometric defect, and the geometric configuration of the first modeling model is updated to obtain a second modeling model, wherein the defect scale factor is S/800.
The dome application size of the second modeling model on a circular arc solid steel dome was 1.24X10 7 N vertical static concentrated force (namely second concentrated force), and applying a command ARCLEN of finite element software ANSYS to start an arc length method to perform nonlinear static buckling overall 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, and particularly showing in fig. 4.
Determining whether a zero total potential energy point exists according to the total potential energy-displacement change curve, if so, determining a point a corresponding to the zero total potential energy point in the total potential energy-displacement change curve in the load-displacement change curve based on the graph of fig. 4, and calculating the slope k at the point a according to the load-displacement change curve a If k a < 0, the load corresponding to point a is 5.812 ×10 6 The dynamic buckling critical load of the arc solid steel arch under the action of the vertical step concentrated force of the arch crown is obtained.
In order to verify the accuracy of calculating the dynamic buckling critical load of the arc solid steel arch shown in fig. 1 by the method for quickly 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 adopting the method for solving the dynamic buckling of the structure by using the traditional method, and the result is shown in fig. 5. As a result, it was found that when the amplitude of the step concentrated force was 5.208×10 6 When N, the arch power response of the arc solid steel arch is a bounded stable response, which indicates that the arc solid steel arch does not generate power buckling; when the amplitude of the concentrated force reaches 5.833 ×10 6 When N, the arch power response of the circular arc solid steel arch is greatly jumped, and the unbounded response shows that the circular arc solid steel arch is subjected to power buckling, so that the power buckling critical load of the circular arc solid steel arch under the action of the arch vertical step concentrated force can be determined as 5.833 multiplied by 10 6 N。
As can be seen from the above examples, the dynamic buckling critical load obtained by the method provided by the invention is 5.812 ×10 6 N, the dynamic buckling critical load obtained by the traditional calculation method is 5.833 multiplied by 10 6 The error of the N and the N is 0.36%, which indicates 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 circular arc solid steel arch by adopting the traditional method for solving the dynamic buckling of the structure consumes a great deal of time to carry out dynamic response calculation, and has low solving efficiency.
Embodiment two: fig. 6 shows a solid steel arc belonging to one of the elongated metal arc structures, with the geometrical, physical and mechanical parameters and load deflection angles as shown in table 2:
table 2 arc solid steel arch geometry, physical parameters and load deflection angle
Wherein, the load deflection angle refers to the angle of the load (i.e. the first concentrated force) deviating from the dome position;
in this embodiment, a method for quickly calculating the dynamic buckling of the elongated metal arch structure by considering geometric defects is adopted to calculate the dynamic buckling critical load of the arc solid steel arch shown in fig. 6, and the method specifically includes the following steps:
performing parameterization modeling on the arc solid steel arch shown in fig. 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 a unit static concentrated force Q (t) (namely a first concentrated force) on a first modeling model of the arc solid steel arch, and then performing characteristic buckling analysis once to obtain a first 10-order in-plane characteristic buckling load and buckling mode of the first modeling model of the arc solid steel arch, wherein the 1 st-order characteristic buckling critical load is 1.34 multiplied by 10 7 N。
The command UPGEOM of finite element software ANSYS is applied to specify that the 1 st order characteristic buckling mode is applied to an arch axis of a first modeling model of the arc solid steel arch as an initial geometric defect, and the geometric configuration of the first modeling model is updated to obtain a second modeling model, wherein the defect scale factor is S/800.
Applying a second modeling model of a circular arc solid steel arch with a size of 1.34×10 7 N is static concentrated force (namely second concentrated force), and a command ARCLEN of finite element software ANSYS is applied to start an arc length method to conduct nonlinear static buckling overall process analysis on the second modeling model, so that a load-displacement change curve and a total potential energy-displacement change curve of the second modeling model are obtained;
and drawing the load-displacement change curve and the total potential energy-displacement change curve of the second modeling model in the same graph, and particularly drawing the load-displacement change curve and the total potential energy-displacement change curve of the second modeling model in the same graph 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 the slope k at the point a according to the load-displacement change curve a If k a < 0, the load corresponding to point a is 5.788 ×10 6 And N is the critical load of dynamic buckling of the arc solid steel arch under the action of the vault step concentrated 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 the method for quickly calculating the dynamic buckling of the elongated metal arch structure by considering geometric defects, the embodiment further calculates the dynamic buckling critical load of the arc solid steel arch shown in fig. 6 by adopting the conventional method for solving the dynamic buckling of the structure,the results are shown in FIG. 8. As a result, when the magnitude of the concentrated force of the step is 5.306 ×10 6 When N, the arch power response of the arc solid steel arch is a bounded stable response, which indicates that the arc solid steel arch does not generate power buckling; when the amplitude of the concentrated force reaches 5.815 ×10 6 When N, the arch power response of the circular arc solid steel arch is greatly jumped, and the unbounded response shows that the circular arc solid steel arch is subjected to power buckling, so that the power buckling critical load of the circular arc solid steel arch under the action of the step concentrated force can be determined as 5.815 multiplied by 10 6 N。
As can be seen from the above examples, the dynamic buckling critical load obtained by the method provided by the invention is 5.788 ×10 6 N, the dynamic buckling critical load obtained by the traditional calculation method is 5.833 multiplied by 10 6 The error of N and N is 0.47%, 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 circular arc solid steel arch by adopting the traditional method for solving the dynamic buckling of the structure consumes a great deal of time to carry out dynamic response calculation, and has low solving efficiency.
Embodiment III: fig. 9 shows a parabolic arch, wherein the parabolic function is:
the parabolic arch belongs to one of the elongated metal arch structures, and the geometrical and physical mechanical parameters are shown in table 3:
TABLE 3 parabolic arch geometry and physical parameters
The embodiment adopts a rapid calculation method for dynamic buckling of an elongated metal arch structure by considering geometric defects to calculate the dynamic buckling critical load of the parabolic arch shown in fig. 9, and the method is as follows:
performing parametric modeling on the parabolic arch shown in fig. 9 by using finite element software ANSYS to obtain a first modeling model of the parabolic arch;
applying finite element software ANSYS, applying a unit vertical static concentrated force (namely a first concentrated force) on the vault of a first modeling model of the parabolic arch, and then performing characteristic buckling analysis once to obtain a characteristic buckling load and a buckling mode in the first 10-order plane of the first modeling model of the parabolic arch; wherein the 1 st order characteristic buckling critical load is 9.18 multiplied by 10 6 N。
The command UPGEOM of finite element software ANSYS is applied to specify that the 1 st order characteristic buckling mode is applied to an arch axis of a first modeling model of a parabolic arch as an initial geometric defect, and the geometric configuration of the first modeling model is updated to obtain a second modeling model, wherein the defect scale factor is S/800.
The dome application size on the second modeling model of parabolic arches was 9.18X10 6 N vertical static concentrated force (namely second concentrated force), and applying a command ARCLEN of finite element software ANSYS to start an arc length method to perform nonlinear static buckling overall 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, and particularly showing in fig. 10.
Determining whether a zero total potential energy point exists according to the total potential energy-displacement change curve, if so, determining a point a corresponding to the zero total potential energy point in the total potential energy-displacement change curve in the load-displacement change curve based on the graph of fig. 4, and calculating the slope k at the point a according to the load-displacement change curve a If k a < 0, the load corresponding to point a is 3.915 ×10 6 And N is the dynamic buckling critical load of the parabolic arch under the action of the vertical step concentrated force of the arch crown.
To verify the accuracy of calculating the dynamic buckling critical load of the parabolic arch shown in fig. 9 by the method for quickly calculating the dynamic buckling of the elongated metal arch structure by considering geometric defects, the embodiment further calculates the parabolic arch shown in fig. 9 by adopting the conventional method for solving the dynamic buckling of the structureThe dynamic buckling critical load of the wire arch is shown in figure 11. As a result, when the magnitude of the concentrated force of the step is 3.820 ×10 6 When N, the dome power response of the parabolic arch is a bounded stable response, which indicates that the parabolic arch does not generate power buckling; when the amplitude of the concentrated force reaches 3.950 ×10 6 When N, the vault dynamic response of the parabolic arch is greatly jumped and is unbounded, which indicates that the parabolic arch is in dynamic buckling, and the dynamic buckling critical load of the parabolic arch under the action of the vault vertical step concentrated force can be determined as 3.950 multiplied by 10 6 N。
As can be seen from the above examples, the dynamic buckling critical load obtained by the method provided by the invention is 3.915 ×10 6 N, the dynamic buckling critical load obtained by the traditional calculation method is 3.950 multiplied by 10 6 The error of N and N is 0.88%, which shows that the method provided by the invention has more accurate calculation precision. It should be noted that, the calculation of the parabolic arch by adopting the traditional method for solving the dynamic buckling of the structure consumes a great deal of time to carry out dynamic response calculation, and the solving efficiency is low, and the method provided by the invention has the advantage of quickly solving the dynamic buckling critical load of the parabolic arch.
Finally, it should be noted that the above embodiments are only for illustrating the technical solution of the present invention, and not for limiting the scope of the present invention, and although the present invention has been 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 to the technical solution of the present invention without departing from the spirit and scope of the technical solution of the present invention.
Claims (6)
1. A method for quickly calculating dynamic buckling of an elongated metal arch structure by considering geometric defects is characterized by comprising the following steps:
(1) According to geometric characteristics and physical and mechanical parameters of the metal arch structure, parametric modeling is carried out 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 a characteristic buckling load and a characteristic buckling mode in a front N-order plane of the first modeling model;
(3) Selecting one of the first-order characteristic buckling modes from the front N-order in-plane characteristic buckling modes 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 overall 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 curve a If k a And (3) if the load is less than 0, the load corresponding to the point a is the critical load of dynamic buckling.
2. The method according to claim 1, wherein in step (2), the first force is applied to the first modeling model, in particular: a unit static force concentration is applied at any location above the arch in the arch axis plane in the first modeling model.
3. The method for quickly calculating the dynamic buckling of the elongated metal arch structure taking geometrical defects into consideration according to claim 1, wherein the step (3) specifically comprises the following steps:
(31) The command UPGEOM of finite element software ANSYS is applied to specify a first-order characteristic buckling mode as an initial geometric defect of the first modeling model, the geometric configuration of the first modeling model is updated, and a second modeling model is obtained, wherein the range of values of defect scale factors is as follows: S/500-S/1000, S is the arc length of the metal arch structure;
(32) Applying a second concentrated force to the second modeling model corresponding to the characteristic buckling load magnitude of the initial geometric defect;
(32) And carrying out nonlinear static buckling overall process analysis on the second modeling model by using a command ARCLEN starting arc length method 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 quickly calculating the dynamic buckling of the elongated metal arch structure considering the geometric defects according to claim 1, wherein the dynamic buckling is as follows: dynamic buckling in the plane of the second modeling model under the action of the step concentrated force;
in the step (5), determining whether a zero total potential energy point exists according to the total potential energy-displacement change curve; if no zero total potential energy point exists, no dynamic buckling behavior exists.
5. The method for quickly calculating the dynamic buckling of the elongated metal arch structure with consideration of the geometric defects according to claim 1, wherein the value of N is as follows: n is more than or equal to 10.
6. A method of dynamic buckling quick calculation for an elongated metal arch structure with geometric defects considered according to any one of claims 1 or 3, wherein the 1 st order characteristic buckling mode is selected as the initial geometric defect of the first modeling model.
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