CN112699464B - Single-stringer short plate bearing capacity calculation method - Google Patents
Single-stringer short plate bearing capacity calculation method Download PDFInfo
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Abstract
The invention discloses a method for calculating the bearing capacity of a single long purlin short slab, which comprises the following steps: acquiring the skin thickness and the section area of the single long purlin short slab to be calculated, and calculating the pressure loss strength of the single long purlin short slab; calculating the compressive stress of the single long purlin short slab based on the length, the inertia moment and the area of the section and the pressure loss strength of the single long purlin short slab; under the condition that the single long purlin short plate bears uniform axial compression load, calculating the local buckling stress of the skin of the single long purlin short plate; under the condition that one side of the single long truss short plate is in a free state, calculating the effective width of the single long truss short plate skin by using the pressure loss strength, and calculating the effective area of the single long truss short plate skin based on the effective width; and calculating the failure load of the single long truss short plate on the basis of fully analyzing the failure mode and failure mechanism of the stiffened short plate. The method can accurately calculate the real bearing capacity of the single long truss short plate, and effectively solves the problems of complex calculation process and large calculation error of the existing method.
Description
Technical Field
The invention belongs to the technical field of aviation design, and particularly relates to a method for calculating the bearing capacity of a single long truss short plate, which provides a data base for the design of a stiffened wall plate of an airplane wing.
Background
The reinforced short plate becomes a basic element of an airplane structure with high specific strength and high structural efficiency, and is applied to main bearing structures such as wing boxes, airframes, empennage boxes and the like. In the service process of the airplane, the reinforced short plate is often subjected to axial compression load, and the ultimate bearing capacity after buckling is the key point concerned by airplane design. In order to give full play to the bearing capacity of the structure, the short reinforced plate is allowed to be designed according to the backward bending. For structural strength designers of airplanes, how to accurately predict the post-buckling response and the failure mode of the reinforced short slab under the condition of compressive load is a problem worthy of deep exploration.
The column curve of the pressed reinforced flat plate is divided into a short column destroyed by local instability of a reinforced short plate, a medium-length column destroyed by a mixed mode of local instability of a reinforced plate and bending instability and a long column destroyed by elastic bending instability according to different slenderness ratios. The scholars in China carry out numerical simulation, engineering method calculation and experimental research on the pressure loss stress of the section bar/single stringer and provide related comparison results and conclusions. The calculation of the pressure loss load/stress used for designing the stiffened wall panel needs to meet the following preconditions: one is that the ribs and the free edge of the skin are stable, i.e. each element has a small slenderness ratio. Secondly, the stable profile is not easy to generate local buckling and the whole profile can achieve plastic yield. The skin free edge is prone to be unstable in a too early manner without paying attention to the above preconditions, and the obtained pressure loss load is not true. And under the action of uniform compression load, the stress distribution of the skin and the ribs is uniform before the skin reaches the buckling strength, the skin at two sides of the ribs buckles along with the increase of the load, the skin cannot bear the stress larger than the buckling stress, and the skin is elastically supported by the ribs and is free at one side. The skin is destabilized, but the ribs can withstand higher stresses until failure. Foreign scholars have conducted intensive research on single stringer compression. Chiara Bisagni performed tests for the presence or absence of delamination using single stringer compression test pieces representing multi-stringer wallboard structures, predicting post-buckling response and the progression of damage from onset to collapse using finite element models based on shell elements including interlaminar damage. Lynch carries out finite element simulation on the post-buckling behavior of the single long-truss riveting reinforced short slab under the compression load, and compares the post-buckling behavior with test and theoretical data, and the errors of buckling and breaking loads and test values are within 2.5%. Patnailk obtains the conclusion that the initial buckling load and the breaking load of an FSW plate are both higher than those of a traditional riveting plate through a comparative compression test of the aluminum alloy 7075-T6 stiffened plate single stringer FSW plate and the traditional riveting plate. Bisagni C adopts a hat-shaped single stringer to research buckling response of the stiffened plate after numerical simulation, and the analysis result is well matched with the test and the failure mode is consistent. Vescovini establishes a rapid parameterized finite element model to predict post buckling response, failure modes and damage tolerance of the single stringer stiffened plate, and scans a Global model by using a detailed local model through a Global/local method to determine the damage tolerance of the most critical position. In the research, ABQUS is mostly used for carrying out numerical simulation to obtain a load-displacement curve, and a buckling balance path behind the load-displacement curve is not solved; in addition, the methods are results obtained based on finite element software simulation, but the finite element methods are difficult and complex in process no matter modeling, design solving strategies and the like; the finite element method loses the test result or the reference of the engineering calculation method, and the finite element result is difficult to evaluate; the existing engineering calculation method comprises the following steps: for example, the plate element method and the like, the method calculates the pressure loss stress which causes the premature instability of the free edge of the single long-truss short plate skin, and the obtained pressure loss stress is not true, and the obtained ultimate bearing capacity is not true, so that the error between the calculation result and the actual condition is larger.
For the above reasons, the finite element calculation method cannot well meet the requirements of engineering applications.
Disclosure of Invention
The invention aims to provide a method for calculating the bearing capacity of a single long truss short plate, which considers the failure mechanism of a stiffened short plate, can accurately calculate the real bearing capacity of the single long truss short plate and effectively solves the problems of complex calculation process and large calculation error of the conventional method.
In order to realize the task, the invention adopts the following technical scheme:
a method for calculating the bearing capacity of a single long truss short plate comprises the following steps:
acquiring skin thickness and section area of the single long truss short slab to be calculated, and calculating the pressure loss strength of the single long truss short slab;
calculating the compressive stress of the single long truss short plate based on the length, the moment of inertia and the area of the section of the single long truss short plate and the pressure loss strength;
under the condition that the single long purlin short plate bears uniform axial compression load, calculating the local buckling stress of the skin of the single long purlin short plate;
under the condition that one side of the single long-truss short slab is in a free state, calculating the effective width of the skin of the single long-truss short slab by using the pressure loss strength, and calculating the effective area of the skin of the single long-truss short slab based on the effective width;
on the basis of fully analyzing the failure mode and failure mechanism of the stiffened short plate, calculating the failure load of the single long truss short plate based on the pressure loss strength, the compressive stress, the local buckling stress of the skin and the effective area of the skin.
Further, the pressure loss strength is calculated by the following formula:
in the above formula, σ 0.2 To give a flexionA service limit; a is the section area of the single long purlin short slab; delta is the skin thickness; e is the modulus of elasticity and g is the number of cuts plus the number of flanges.
Further, the compressive stress of the single stringer short plate is calculated according to the following formula:
in the above-mentioned formula, the compound has the following structure,
l is the length of the single long purlin short slab, C is the end support coefficient,
i and A are respectively the inertia moment and the area of the section of the short reinforced plate.
Further, the local buckling stress of the single stringer short slab skin is calculated according to the formula:
in the formula: b is the width of the loading edge during loading; k is a radical of c Is the coefficient of compressive critical stress, mu e Is the elastic poisson's ratio of the material.
Further, the effective width calculation formula is:
further, the effective area of the skin is A (eff) ＝δ×W 1 Where δ is the skin thickness.
Further, the formula for calculating the failure load of the single long truss short plate is as follows:
P ult ＝A (str) σ ult(str) +A (eff) σ ult(sk) +(A (sk) -A (eff) )σ b(sk)
wherein, P ult Is a failure load; a. The (str) Is the cross-sectional area of the single long purlin short slab; sigma ult(str) The pressure loss strength; a. The (eff) Is the effective area of the skin; sigma b(sk) Is the local buckling stress of the skin; a. The (sk) Is the skin cross-sectional area; sigma ult(sk) Is the skin compressive stress.
Further, the value of the cutting number plus the flange number g is 12.75, the value of the end support coefficient C is 1.0, and the compression critical stress coefficient k is c Is 3.65.
Compared with the prior art, the invention has the following technical characteristics:
1. on the basis of fully analyzing failure modes and failure mechanisms of the reinforced short slab, a relatively complex calculation formula of the bearing capacity of the single-stringer short slab is provided; the calculation formula of the effective width of the skin under the free state is used for calculating the bearing capacity of the single long truss short plate, so that the effective width is introduced, and the calculation of the bearing capacity is more accurate; by adopting an engineering calculation method considering the failure mechanism of the short reinforced plate, the relative error with the test is less than 5 percent, and the engineering design requirement is basically met.
2. The improvement of the calculation precision of the bearing capacity of the single long purlin short slab calculated by the method has important significance for the engineering design, the bearing capacity of the structure is fully exerted, the single long purlin short slab is allowed to be designed according to the post bending, and the weight of the structure is further reduced.
Drawings
FIG. 1 is a schematic sectional parameter view of a test piece used in the examples;
FIG. 2 shows example 1 # The failure morphology of the test piece;
FIG. 3 shows example 2 # The failure appearance of the test piece;
FIG. 4 shows example 3 # The failure morphology of the test piece;
FIG. 5 shows example 4 # The failure morphology of the test piece;
FIG. 6 shows example 5 # And (4) failure morphology of the test piece.
Detailed Description
The semi-theoretical and semi-empirical engineering calculation method is widely applied to the field of aviation due to the fact that the method is convenient to use and simple in calculation. The calculation of the bearing capacity of the short reinforced plate usually adopts engineering analysis methods such as a plate element method and the like, the calculation formula of the method is simple, but the bearing capacity and the test error of the short reinforced plate obtained by calculation are large.
In order to be suitable for practical engineering application, the invention provides a method for calculating the bearing capacity of a single long truss short plate, which comprises the following steps of:
step 1, obtaining the skin thickness and the section area of the single long truss short slab to be calculated, and calculating the pressure loss strength of the single long truss short slab.
When the length of the single long purlin short plate is short (the ratio of the length to the rotation radius L/rho is less than 20), after the section is locally unstable, the section can bear larger load, until the section is damaged (wrinkled and broken), the axis of the section still keeps a straight line, the damage form is called pressure loss, and the corresponding damage stress is called pressure loss strength; in this embodiment, the pressure loss strength is calculated by the following formula:
in the above formula, σ 0.2 Is the yield limit; a is the section area of the single long purlin short slab; delta is the skin thickness; e is the modulus of elasticity and g is the number of cuts plus the number of flanges, g being chosen to be 12.75 in this example.
Step 2, calculating the compressive stress of the single long truss short plate based on the length, the moment of inertia and the area of the section of the single long truss short plate and the pressure loss strength, wherein the formula is as follows:
in the above formula, the first and second carbon atoms are,
l is the length of the single stringer short slab, C is the endSupport factor, taken as 1.0 in this example;
i and A are respectively the inertia moment and the area of the section of the reinforced short plate.
Step 3, calculating the local buckling stress of the skin of the single long-truss short slab under the condition that the single long-truss short slab bears the uniform axial compression load, wherein the formula is as follows:
in the formula: b is the width of the loading edge during loading; k is a radical of formula c 3.65 is freely taken from one side of the three-side simple support as a compression critical stress coefficient; mu.s e Is the elastic poisson's ratio of the material.
Step 4, calculating the effective width of the skin of the single long-truss short slab by using the pressure loss strength under the condition that one side of the single long-truss short slab is in a free state, and calculating the effective area of the skin of the single long-truss short slab based on the effective width; wherein:
the effective width calculation formula is:
effective area of skin is A (eff) ＝δ×W 1 Where δ is the skin thickness.
And 5, on the basis of fully analyzing the failure mode and failure mechanism of the reinforced short slab, establishing the following bearing capacity calculation formula to calculate the failure load of the single-stringer short slab based on the pressure loss strength, the compressive stress, the local buckling stress of the skin and the effective area of the skin:
P ult ＝A (str) σ ult(str) +A (eff) σ ult(sk) +(A (sk) -A (eff) )σ b(sk)
wherein, P ult Is a failure load; a. The (str) Is the cross-sectional area of the single long purlin short slab; sigma ult(str) The pressure loss strength; a. The (eff) Is the effective area of the skin; sigma b(sk) Is the local buckling stress of the skin; a. The (sk) Is the cross-sectional area of the skin; sigma ult(sk) Is the skin compressive stress.
Experimental part:
single stringer compression test pieces were designed to study post-buckling characteristics by numerical simulation. The total width of the test piece is 150mm, the length and the section parameters of the test piece are designed according to the slenderness ratio of the test piece which is far less than 20, and the length of the test piece is 100mm. The test piece is shown in FIG. 1 in cross section. Specific profile parameters are shown in table 1.
TABLE 1 test piece section parameters
The test piece is made of an aluminum alloy 7150-T7751 prestretched thick plate with 76.2mm of wool, and the material performance parameters are as follows: the compressive elastic modulus Ec =73723MPa, the breaking strength σ b =565MPa, and the compressive yield strength σ 0.2c =530mpa.
The section stress of the linear region of the reinforced short plate test piece before buckling is uniformly distributed, and the skin can uniformly bear the compression load. And (3) buckling of the skin begins to occur along with the increase of the load, the skin enters a nonlinear post-buckling area, the load continues to increase, the stringer and the skin in the effective width continue to bear, when the ultimate bearing capacity is reached, the load reaches a peak value, and then the reinforced short plate enters a post-collapse area. The reinforced short plate test piece generates obvious local instability phenomenon in the continuous loading process, and the tearing and separation phenomenon of the stringer and the skin partially occurs, so that the reinforced short plate test piece is regarded as damaged even if no sound is generated until the reinforced short plate test piece cannot be continuously loaded. The breaking load and the average value of the test pieces are shown in table 2, and the relevant test pieces used in the test are shown in fig. 2 to 6.
TABLE 2 destructive load test results
The bearing capacity of the reinforced short plate can be calculated to be 354.67kN by the method.
As can be seen, the relative error between the test value 370kN and the engineering calculation method of the invention is 4.14%, and the requirements of engineering application are met.
Experiments using the current methodology are as follows:
compression tests of thin-wall section profiles show that when the length of the profile is short, the profile can bear large load after local instability of the profile until damage occurs. Such a failure caused by local buckling is called a pressure loss strength, and the corresponding stress is a pressure loss stress. As the profile load increases, the deformation of the plate portion increases and the increased load is carried by the stiffer corner regions until the stress increases to a sufficiently high value to cause failure. At present, the compressive stress of the profile is generally calculated by a semi-empirical method based on a large number of tests.
The plate element method is a semi-empirical method for calculating the pressure loss stress of the section of the profile. The calculation steps are as follows:
1) Dividing the section of the profile into a plurality of plate elements (plate elements with one free end or without the free end);
2) Calculating the pressure loss stress of each plate element;
3) The pressure loss stress of the entire section is calculated.
The allowable pressure loss stress of the entire section is calculated by the weighted average of the pressure loss stresses of the individual plate elements:
in the formula:
b i -the width of the ith plate element;
δ i -the thickness of the ith plate element;
σ fi -the pressure loss stress of the ith plate element, the cut-off value being taken as σ 0.2 ；
N is the total number of plate elements forming the section.
The bearing capacity of the reinforced short plate can be calculated to be 269kN by a plate element method.
Through the actual experimental data in table 2, it can be seen that the relative error between the test value and the engineering calculation method "plate element method" is 27.2%, and the engineering application requirements cannot be met.
The above embodiments are only used for illustrating the technical solutions of the present application, and not for limiting the same; although the present application has been described in detail with reference to the foregoing embodiments, it should be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equally replaced; such modifications and substitutions do not substantially depart from the spirit and scope of the embodiments of the present application, and are intended to be included within the scope of the present application.
Claims (2)
1. A method for calculating the bearing capacity of a single long truss short plate is characterized by comprising the following steps:
acquiring skin thickness and section area of the single long truss short slab to be calculated, and calculating the pressure loss strength of the single long truss short slab;
calculating the compressive stress of the single long truss short plate based on the length, the moment of inertia and the area of the section of the single long truss short plate and the pressure loss strength;
under the condition that the single long truss short plate bears uniform axial compression load, calculating the local buckling stress of the skin of the single long truss short plate;
under the condition that one side of the single long truss short plate is in a free state, calculating the effective width of the single long truss short plate skin by using the pressure loss strength, and calculating the effective area of the single long truss short plate skin based on the effective width;
on the basis of fully analyzing the failure mode and failure mechanism of the stiffened short plate, calculating the failure load of the single long truss short plate based on the pressure loss strength, the compressive stress, the local buckling stress of the skin and the effective area of the skin;
the pressure loss strength is calculated according to the following formula:
in the above formula, σ 0.2 Is the yield limit; a is the section area of the single long purlin short slab; delta is the skin thickness; e is the elastic modulus, g is the number of cuts plus the number of flanges;
the compressive stress of the single long truss short plate is calculated according to the following formula:
in the above formula, the first and second carbon atoms are,
l is the length of the single long purlin short slab, C is the end support coefficient,
i and A are respectively the inertia moment and the area of the section of the short reinforced plate;
the local buckling stress of the single long truss short plate skin is calculated according to the formula:
in the formula: b is the width of the loading edge during loading; k is a radical of c Is the coefficient of compressive critical stress, mu e Is the elastic poisson's ratio of the material;
the effective width calculation formula is as follows:
the effective area of the skin is A (eff) ＝δ×W 1 Wherein δ is the skin thickness;
the formula adopted for calculating the failure load of the single long truss short plate is as follows:
P ult ＝A (str) σ ult(str) +A (eff) σ ult(sk) +(A (sk) -A (eff) )σ b(sk)
wherein, P ult Is a failure load; a. The (str) Is the cross-sectional area of the single long purlin short slab; sigma ult(str) The pressure loss strength; a. The (eff) Is the effective area of the skin; sigma b(sk) Is the local buckling stress of the skin; a. The (sk) Is the cross-sectional area of the skin; sigma ult(sk) Is the skin compressive stress.
2. The method of claim 1, wherein the number of cuts plus the number of flanges g is 12.75, the end support coefficient C is 1.0, and the compression critical stress coefficient k is 1 c Is 3.65.
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Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN103870613A (en) * | 2012-12-10 | 2014-06-18 | 中国飞机强度研究所 | Calculation method of bearing capacity of reinforced wall plate |
| CN111143941A (en) * | 2019-12-24 | 2020-05-12 | 中国航空工业集团公司西安飞机设计研究所 | Method for calculating axial compression bearing capacity of composite material reinforced wall plate |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103870613A (en) * | 2012-12-10 | 2014-06-18 | 中国飞机强度研究所 | Calculation method of bearing capacity of reinforced wall plate |
| CN111143941A (en) * | 2019-12-24 | 2020-05-12 | 中国航空工业集团公司西安飞机设计研究所 | Method for calculating axial compression bearing capacity of composite material reinforced wall plate |
Non-Patent Citations (1)
| Title |
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| 民机复合材料帽型长桁压缩承载力分析与试验;张绪等;《材料导报》;20191125;全文 * |
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