CN114036677B - Method for analyzing bearing capacity of plate steel structure - Google Patents

Method for analyzing bearing capacity of plate steel structure Download PDF

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CN114036677B
CN114036677B CN202111346993.4A CN202111346993A CN114036677B CN 114036677 B CN114036677 B CN 114036677B CN 202111346993 A CN202111346993 A CN 202111346993A CN 114036677 B CN114036677 B CN 114036677B
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bearing capacity
plate
steel structure
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ultimate bearing
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李志辉
康孝先
梁杰
强士中
张子彬
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Ultra High Speed Aerodynamics Institute China Aerodynamics Research and Development Center
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Abstract

The invention discloses a method for analyzing bearing capacity of a plate steel structure, which comprises the following steps: step one, setting a plate steel structure as a set of a series of elastic boundary plates, and finishing the initial condition setting of the plate steel structure; fitting based on a unified algorithm of the ultimate bearing capacity of the elastic boundary plate to obtain an ultimate bearing capacity formula of the plate steel structure; and thirdly, fitting and solving a undetermined constant C by utilizing a real measured value of the ultimate bearing capacity of the steel plate structure, and completing the analysis of the bearing capacity of the steel plate structure. The invention provides a method for analyzing the bearing capacity of a plate steel structure, wherein buckling stress in an effective width formula is equivalent to buckling stress of any elastic boundary plate, so that a unified algorithm of the ultimate bearing capacity of the elastic boundary plate can be regarded as that the effective width formula is popularized to the unified formula of the ultimate bearing capacity of the plate steel structure under the in-plane load effect, the defect that the elastic plastic analysis prediction of the structure by a Monte Carlo random finite element method is inaccurate is overcome, and the method has better applicability and reliability.

Description

Method for analyzing bearing capacity of plate steel structure
Technical Field
The invention relates to the field of mechanics, in particular to a method for analyzing the bearing capacity of a plate steel structure, which provides an important reference basis for the analysis of the derailment of a large spacecraft.
Background
Structural bearing capacity research is always the key point and the difficulty of research in the mechanical field, structural static stability is studied for many years as a problem, the problem is not fully known at present, and the design method is mostly based on an empirical formula. In the traditional design method, the elastic limit of the structure is the basis of the design method, but the strength design is not reliable only by the safety coefficient, buckling is caused by the structural structure, even instability is caused, if the connection of the structure and the support in the buckling direction are enough, the buckling of the structure only reduces the bearing capacity, otherwise, the instability can cause serious consequences, and the collapse of the structure can also be caused.
In aerospace application, because of the complexity of the external environment of the spacecraft structure, the numerical simulation is more complex than that of the structure in common civil engineering, and the problems of power, force-thermal coupling, collision/friction/chemical reaction of space gas molecules and the like of the structure are particularly considered, while the plate steel structure is a relatively common structure in the spacecraft structure and is an important object for research and simulation in the academic community. The out-of-orbit and reentry atmosphere crash of the large spacecraft with the service expiration needs to be evaluated in detail in advance, and the unified theory and numerical simulation method of the plate steel structure is popularized and applied to the out-of-orbit and merle-down analysis of the large spacecraft, so as to prepare for the risk forecast of the out-of-orbit and merle-down and reentry of the satellite of the subsequent freight spacecraft, space station and large plate cabin truss structure.
With the rapid development of the finite element method, the numerical method is no longer a difficult task to solve the ultimate bearing capacity of the pressed simply supported plate. Among them, the monte carlo random finite element method is the more mainstream method. Through forty years of research and development, the Monte Carlo random finite element method is widely applied and tested in the aspect of structural bearing capacity research, and particularly, reliable simulation results are obtained in metal shell stress analysis when the aircraft flows around in the field of simulating lean transition. However, while the Monte Carlo random finite element method has great success on the stress simulation of a metal structure in an air flow, the requirement of the method on time and position space grid division limits the problem that a finite element algorithm for calculating response deformation of a material surface force/heat fusion metal truss structure by the method has inaccurate structural elastoplastic analysis prediction in a pneumatic environment of a simulated near-continuous sliding transition flow region, and the defect causes inaccurate simulation effect of a full-flow-area flight track landing area in the process of researching the attenuation and reentry of an on-orbit and service expiration orbit of a large-sized spacecraft, so that an algorithm which meets the use precision of engineering and can simulate the bearing force of a plate steel part of the spacecraft in the full-flow-area flight is needed.
Disclosure of Invention
It is an object of the present invention to address at least the above problems and/or disadvantages and to provide at least the advantages described below.
To achieve these objects and other advantages and in accordance with the purpose of the invention, a method of analyzing a bearing capacity of a sheet steel structure, comprising:
step one, setting a plate steel structure as a set of a series of elastic boundary plates, and finishing the initial condition setting of the plate steel structure;
fitting based on a unified algorithm of the ultimate bearing capacity of the elastic boundary plate to obtain an ultimate bearing capacity formula of the plate steel structure;
and thirdly, fitting and solving a undetermined constant C by utilizing a real measured value of the ultimate bearing capacity of the steel plate structure, and completing the analysis of the bearing capacity of the steel plate structure.
Preferably, in the first step, the initial condition setting of the sheet steel structure is configured to include:
with elastic boundary plates under a complex set of loads (sigma) x 、σ y And τ) the equivalent buckling stress of its elastic boundary plate when buckling occurs
Figure GDA0004140940850000021
Is the formula one:
Figure GDA0004140940850000022
；
wherein the vertical section stress of the elastic boundary plate in the x or y direction is sigma x 、σ y Shear stress is tau;
let sigma be x 、σ y Equal proportion of tau is increased by lambda times until the elastic boundary plate reaches the bearing capacity limit state, then the elastic boundary plate is loaded in complex (lambda sigma x 、λσ y And λτ) is appliedWhen reaching the ultimate bearing capacity state, the equivalent ultimate bearing capacity
Figure GDA0004140940850000023
Expressed as equation two:
Figure GDA0004140940850000024
。
preferably, the ultimate bearing capacity formula of the elastic boundary plate in the unified algorithm is expressed as formula three:
Figure GDA0004140940850000031
；
wherein C is i Constant, i=1, 2,3, σ u Is the ultimate stress, sigma y Is of yield strength, sigma cr Is buckling stress;
in the third formula
Figure GDA0004140940850000032
The term cannot describe the true data curve, so the ultimate bearing capacity formula IV of the plate steel structure is obtained based on the formula III assumption:
Figure GDA0004140940850000033
。
preferably, in the third step, the undetermined constant C in the plate steel structure ultimate bearing capacity formula is obtained by fitting according to the plate steel structure ultimate bearing capacity real measurement value, the plate steel structure ultimate bearing capacity formula is used as a generalized effective width formula, and the undetermined constant C is applied to ultimate bearing capacity analysis of the plate steel structure to obtain an ultimate bearing capacity unified formula five of the plate steel structure:
Figure GDA0004140940850000034
wherein when
Figure GDA0004140940850000035
In the case of taking->
Figure GDA0004140940850000036
The invention at least comprises the following beneficial effects: the buckling stress in the effective width formula is equivalent to buckling stress of any elastic boundary plate, so that the unified algorithm of the ultimate bearing capacity of the elastic boundary plate can be regarded as the unified formula of the ultimate bearing capacity of the effective width formula when being popularized to the ultimate bearing capacity of the plate steel structure under the in-plane load effect.
Additional advantages, objects, and features of the invention will be set forth in part in the description which follows and in part will become apparent to those having ordinary skill in the art upon examination of the following or may be learned from practice of the invention.
Drawings
FIG. 1 is a diagram of a computational model of an embodiment of the present invention employing split flange I-Liang Moxing as a numerical analysis of an elastic bounding plate.
Detailed Description
The present invention is described in further detail below with reference to the drawings to enable those skilled in the art to practice the invention by referring to the description.
Based on a unified algorithm of the ultimate bearing capacity of the elastic boundary plate, the ultimate bearing capacity when the local buckling range of the plate steel structure reaches the ultimate state can be calculated through the unified algorithm according to the elastic buckling stress of the local plate, and the integral ultimate bearing capacity of the elastic boundary plate is obtained through analyzing the bearing capacity improvement coefficient of the least favorable plate.
The buckling stress in the effective width formula is equivalent to buckling stress of any elastic boundary plate, so that the unified algorithm of the limit bearing capacity of the elastic boundary plate can be regarded as a unified formula of the limit bearing capacity of the effective width formula generalized to the plate steel structure under the action of the load in the vertical section.
Specifically, the invention comprises the following three steps:
1. initial condition setting for plate steel structure
The sheet steel structure is considered as a collection of elastic border plates.
With elastic boundary plates under a complex set of loads (sigma) x 、σ y And τ) the equivalent buckling stress of its elastic boundary plate when buckling occurs
Figure GDA0004140940850000041
Is the formula one:
Figure GDA0004140940850000042
；
wherein the vertical section stress of the elastic boundary plate in the x or y direction is sigma x 、σ y Shear stress is tau;
the parameters marked with the sign of #, are parameters of the elastic boundary plate, and the parameters marked with the right subscript as e indicate equivalent stress.
Let sigma be x 、σ y Equal proportion of tau is increased by lambda times until the elastic boundary plate reaches the bearing capacity limit state, then the elastic boundary plate is loaded in complex (lambda sigma x 、λσ y And λτ) to reach the ultimate bearing capacity state, the equivalent ultimate bearing capacity thereof
Figure GDA0004140940850000051
Can be expressed as equation two:
Figure GDA0004140940850000052
。
2. fitting to obtain ultimate bearing capacity formula of plate steel structure
According to the unified algorithm description of the ultimate bearing capacity of the elastic boundary plate, the ultimate bearing capacity formula of the ideal compression simple support plate after buckling can be expressed as a formula III:
Figure GDA0004140940850000053
；
wherein C is i Constant, i=1, 2,3, σ u Is the ultimate stress, sigma y Is of yield strength, sigma cr Is buckling stress;
it should be noted that under a large number of practical experience, due to
Figure GDA0004140940850000054
An item does not describe a true data curve well, so it is often omitted.
Referring to the ultimate bearing capacity formula of the pressure receiving plate, the ultimate bearing capacity formula of the steel plate structure can be directly assumed as the following formula four:
Figure GDA0004140940850000055
wherein C is i Is a constant (i=1, 2) independent of boundary conditions.
3. Fitting and solving undetermined constant C by utilizing actual measured value of ultimate bearing capacity of steel plate structure
The fourth formula is a generalized effective width formula, and is applied to the ultimate bearing capacity analysis of the plate steel structure, and is also called an ultimate bearing capacity unified formula of the plate steel structure. Fitting and solving a undetermined constant C according to the actual measured value of the ultimate bearing capacity of the steel plate structure to obtain
Figure GDA0004140940850000061
Due to the numerical fitting formula five
Figure GDA0004140940850000062
The value may exceed sigma y For the purpose of design safety, when
Figure GDA0004140940850000063
In the case of taking->
Figure GDA0004140940850000064
The unified algorithm of the limit bearing capacity of the elastic boundary plate disclosed by the invention comprises the following specific steps of:
step one, analyzing and obtaining the ultimate bearing capacity and ultimate vector corresponding to the pressed local plate by adopting a successive approximation method based on the elastic buckling stress of the pressed local plate;
step two, fitting to obtain a limit bearing capacity formula of the pressed local plate based on the limit bearing capacity and the limit vector corresponding to the pressed local plate obtained in the step one;
and step three, the ultimate bearing capacity formula in the step two is popularized to the plate steel structures under other different boundary conditions, so that a unified formula of the ultimate bearing capacity of the elastic boundary plate is obtained, and the integral ultimate bearing capacity of the elastic boundary plate is obtained.
Examples:
the method comprises the steps of adopting a split flange I-beam model to carry out numerical analysis on an elastic boundary plate, wherein a calculation model is shown in figure 1, a comparison method is a Monte Carlo random finite element method mentioned in the background art of the invention, firstly, bending analysis is carried out after the stiffness ratio of a flange is 3-way spring, so as to obtain bending equivalent stress dxyl of the rectangular plate, then, ultimate bearing capacity analysis is carried out, so as to obtain equivalent ultimate bearing capacity dxyl1, and finally, the calculation accuracy ys1 of a unified formula of the ultimate bearing capacity of the steel plate structure is obtained through the comparison analysis. The calculated structure is shown in tables 1-2:
Figure GDA0004140940850000065
/>
Figure GDA0004140940850000071
TABLE 1 calculation accuracy analysis of a calculation model when it is pressed unidirectionally
Figure GDA0004140940850000072
Calculating accuracy analysis of the calculation model under the action of complex load in table 2, wherein L in table 1 and table 2 is the length of a component; t is the thickness of the component, b f Is the length of the flange, t f As the thickness of the flange is the thickness, the calculation accuracy of the calculation model compression limit bearing capacity analysis by adopting a unified formula is 0.9-1.1 under most conditions, so that the calculation accuracy of engineering calculation is met, the limit of the calculation model in the aspect of use scene is broken when the bearing capacity of the plate steel structure is calculated, the influence of air flow on the metal plate steel in each flow area in the process of reentry of an aerospace vehicle from outer space can be reliably simulated, and the defect of inaccurate structural elastoplastic analysis prediction caused by the Monte Carlo random finite element method in the pneumatic environment of the near-continuous sliding transition flow area is particularly overcome.
The above is merely illustrative of a preferred embodiment, but is not limited thereto. In practicing the present invention, appropriate substitutions and/or modifications may be made according to the needs of the user.
The number of equipment and the scale of processing described herein are intended to simplify the description of the present invention. Applications, modifications and variations of the present invention will be readily apparent to those skilled in the art.
Although embodiments of the invention have been disclosed above, they are not limited to the use listed in the specification and embodiments. It can be applied to various fields suitable for the present invention. Additional modifications will readily occur to those skilled in the art. Therefore, the invention is not to be limited to the specific details and illustrations shown and described herein, without departing from the general concepts defined in the claims and their equivalents.

Claims (1)

1. A method of analyzing the load bearing capacity of a sheet steel structure, comprising:
step one, setting a plate steel structure as a set of a series of elastic boundary plates, and finishing the initial condition setting of the plate steel structure;
fitting based on a unified algorithm of the ultimate bearing capacity of the elastic boundary plate to obtain an ultimate bearing capacity formula of the plate steel structure;
fitting and solving a coefficient C to be determined by utilizing a real measured value of the ultimate bearing capacity of the plate steel structure, and completing the analysis of the bearing capacity of the plate steel structure;
in step one, the initial condition setting of the sheet steel structure is configured to include:
with elastic boundary plates under a complex set of loads (sigma) x 、σ y And τ) the equivalent buckling stress of its elastic boundary plate when buckling occurs
Figure FDA0004140940840000011
Is the formula one:
Figure FDA0004140940840000012
；
wherein the vertical section stress of the elastic boundary plate in the x or y direction is sigma x 、σ y Shear stress is tau;
let sigma be x 、σ y Equal proportion of tau is increased by lambda times until the elastic boundary plate reaches the bearing capacity limit state, then the elastic boundary plate is loaded in complex (lambda sigma x 、λσ y And λτ) to reach the ultimate bearing capacity state, the equivalent ultimate bearing capacity thereof
Figure FDA0004140940840000013
Expressed as equation two:
Figure FDA0004140940840000014
the method comprises the steps of carrying out a first treatment on the surface of the The ultimate bearing capacity formula of the elastic boundary plate in the unified algorithm is expressed as formula three:
Figure FDA0004140940840000015
；
wherein C is i Constant, i=1, 2,3, σ u Is the ultimate stress, sigma y Is of yield strength, sigma cr Is buckling stress;
in the third formula
Figure FDA0004140940840000021
The term cannot describe the true data curve, so the ultimate bearing capacity formula IV of the plate steel structure is obtained based on the formula III assumption:
Figure FDA0004140940840000022
the method comprises the steps of carrying out a first treatment on the surface of the In the third step, a pending constant C in a plate steel structure ultimate bearing capacity formula is obtained through fitting according to a plate steel structure ultimate bearing capacity real measurement value, the pending constant C is used as a plate steel structure ultimate bearing capacity formula to be used as a generalized effective width formula, and the pending constant C is applied to ultimate bearing capacity analysis of a plate steel structure to obtain an ultimate bearing capacity unified formula five of the plate steel structure:
Figure FDA0004140940840000023
wherein when
Figure FDA0004140940840000024
In the case of taking->
Figure FDA0004140940840000025
/>
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Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN110287637A (en) * 2019-07-03 2019-09-27 西南交通大学 A kind of elastic-plastic buckling bearing capacity computation method
CN112084555A (en) * 2020-08-11 2020-12-15 重庆瑜煌电力设备制造有限公司 Method for calculating bearing capacity of ring plate of circumferential stiffening rib true test data node of steel pipe tower
CN113515801A (en) * 2021-07-23 2021-10-19 中国电力工程顾问集团中南电力设计院有限公司 Method for calculating bearing capacity of K-shaped steel pipe penetration welding joint with stiffening rib

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Publication number Priority date Publication date Assignee Title
JP5582410B2 (en) * 2011-01-11 2014-09-03 株式会社リコー Fixing apparatus and image forming apparatus
WO2016187482A1 (en) * 2015-05-19 2016-11-24 Georgia Tech Research Corporation Self-consolidating concrete construction with self-roughening properties

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN110287637A (en) * 2019-07-03 2019-09-27 西南交通大学 A kind of elastic-plastic buckling bearing capacity computation method
CN112084555A (en) * 2020-08-11 2020-12-15 重庆瑜煌电力设备制造有限公司 Method for calculating bearing capacity of ring plate of circumferential stiffening rib true test data node of steel pipe tower
CN113515801A (en) * 2021-07-23 2021-10-19 中国电力工程顾问集团中南电力设计院有限公司 Method for calculating bearing capacity of K-shaped steel pipe penetration welding joint with stiffening rib

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康孝先等.初始缺陷对板钢结构极限承载力的影响分析.《工程力学》.2009,第105-110页. *

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