CN108920797A - A kind of evaluation method of hemispherical pressure resistance end socket ultimate bearing capacity - Google Patents

Abstract

The invention discloses a method for estimating the ultimate bearing capacity of a hemispherical pressure-resistant head. 1. Setting the relevant parameters of the head, wherein the middle diameter r of the head, different thickness values t, and different yield strengths _σy ; 2. Research on the The influence of the head bearing capacity; define the influence of buckling strength on the ultimate bearing capacity of the head as the plastic attenuation factor k _p and solve it; 3. Obtain the nonlinear critical buckling load P _non of the perfect head: P _non = k _p P _{m ‑t} ; 4. Study the influence of geometric defects on the buckling load of the head, define the influence of geometric defects on the ultimate bearing capacity of the head as the geometric defect attenuation factor k _imp and solve it; 5. On the basis of k _p and k _imp , fit all the data with the formula, and solve the actual attenuation factor k _real , where k _real = k _p k _imp , and summarize the estimation formula of the ultimate bearing capacity P _real of the head: P _real = k _real P _m‑t ; 6. According to the relevant parameter values of the actual shell, they are substituted into the analytical formula to finally calculate the ultimate bearing capacity P _real of the head. The estimation method proposed by the present invention is more systematic and has a wider application range.

Description

A method for estimating the ultimate bearing capacity of a hemispherical pressure-resistant head

technical field

The invention belongs to the field of machinery, in particular to a method for estimating the ultimate bearing capacity of a hemispherical pressure-resistant head.

Background technique

As an essential part of the pressure vessel, the head is also widely used in deep-sea pressure-resistant submersibles, and its buckling pressure-resistant characteristics have an important impact on the pressure-resistant capability of the entire submersible. Most of the existing heads are hemispherical structures, and the accurate prediction of their ultimate bearing capacity has an important impact on the safety and economic performance of the submersible.

The Code for Classification and Construction of Diving Systems and Submersibles (CCS2013 for short) provides a method for predicting the ultimate bearing capacity of spherical shells. Among them, CCS means China Classification Society, hereinafter referred to as CCS. First, the numerical calculation prediction method, through the simulation calculation of the finite element software, introduces the first-order mode defect and elastic-plastic material properties to predict the ultimate load and buckling behavior of the spherical shell. Second, Chapter 16 of the code provides an empirical formula for predicting the ultimate bearing capacity of a pressure spherical shell:

Where: r _in is the inner diameter of the spherical shell, r _m is the middle diameter of the spherical shell, t is the thickness of the spherical shell, σ _y is the tensile strength of the material, δ is the defect amplitude, a, b, c, d, j, f, g , h is a constant coefficient; considering the material and geometric nonlinearity; it is used to predict the ultimate bearing capacity of the pressure-resistant spherical shell in the preliminary design stage of the pressure-resistant structure.

After years of research and summarization, finite element numerical calculations can predict the bearing capacity of spherical shells more accurately, but various model parameters need to be set during software calculations, and parameter deviations have a great impact on the results; and there is a lack of systematic research on the mechanism of shell instability and identification. At the same time, although the empirical formula provided by the classification society can accurately predict the bearing capacity of the pressure spherical shell under certain circumstances, it does not take into account the instability mechanism of the pressure structure. The formula does not involve relevant parameters of materials, such as yield Strength E, elastic modulus μ and yield strength σ _y , while the buckling behavior of spherical shells is often closely related to the buckling strength. Only the tensile strength of the material is involved in the formula, but the initial instability of the compressive structure often occurs in the linear elastic stage. Although the formula of the spherical shell structure can also be used for the hemispherical head, there are still some errors due to slightly different boundary conditions. Therefore, the prediction method of the ultimate bearing capacity of the head lacks a more systematic and widely used theoretical formula prediction method.

Contents of the invention

Purpose of the invention: Aiming at the problems existing in the prior art, the present invention provides a method for estimating the ultimate bearing capacity of a hemispherical pressure-resistant head that is more systematic and widely applicable.

Technical solution: In order to solve the above technical problems, the present invention provides a method for estimating the ultimate bearing capacity of a hemispherical pressure-resistant head, which is characterized in that it includes the following steps:

(1) Set the relevant parameters of the head, where the relevant parameters include the pitch diameter r of the head, different thickness values t and different yield strengths _σy ;

(2) Consider the impact on the bearing capacity of the head; define the influence of buckling strength on the ultimate bearing capacity of the head as the plastic attenuation factor k _p and solve it;

(3) Substituting the k _p obtained in step (2) and the empirical formula solution P _mt of the medium-thick shell to obtain the nonlinear critical buckling load P _non of the perfect head: P _non = k _p P _mt ;

(4) To study the influence law of geometric initial defects on the buckling load of the head, define the influence of buckling strength on the ultimate bearing capacity of the head as the geometric defect attenuation factor k _imp , and solve the geometric defect attenuation factor k _imp ;

(5) On the basis of k _p and k _imp , all the data are fitted with a formula to solve the actual attenuation factor k _real , where k _real = k _p k _imp , and the estimation formula of the ultimate bearing capacity P _real of the head is summarized: P _real = k _real P _mt ;

(6) According to the relevant parameter values of the actual shell, including the thickness value t, the yield strength σ _y , and the defect amplitude δ/r, they are substituted into the estimation formula of the inductive head ultimate bearing capacity P _real obtained in step (5), and finally Calculate the ultimate bearing capacity P _real of the head.

Further, the specific steps for setting the relevant parameters of the head in the step (1) are as follows: the middle diameter r of the head is set to 60mm, the thickness value t ranges from 0.24mm to 0.6mm, and is incremented by 0.06mm, and the selected A total of 7 thicknesses of 0.24mm, 0.30mm, 0.36mm, 0.42mm, 0.48mm, 0.54mm, and 0.60mm; the yield strength σ _y ranges from 180MPa to 230MPa, and the increment is 10MPa, taking 180MPa, 190MPa, 200MPa, 210MPa, 220MPa, There are 6 yield strengths of 230MPa.

Further, the specific steps for solving the plastic attenuation factor _kp in the step (2) are as follows:

(2.1) Calculate the linear buckling load P _mt of the perfect head of 42 models under 7 different thicknesses and 6 different yield strengths σ _y , the calculation empirical formula is: Among them, the elastic modulus E of the material is 193GPa, and the Poisson's ratio ν is 0.28;

(2.2) Set the material model as an ideal elastoplastic model, and the grid unit type as a fully integrated S4 unit; the boundary conditions of the head model are set according to CCS2013; a total of 7 different thicknesses and 6 different yield strengths σ _y 42 models were analyzed using the nonlinear arc length method to obtain the corresponding buckling load values;

(2.3) Define the influence of buckling strength on the ultimate bearing capacity of the head as the plastic attenuation factor k _p , calculate the plastic attenuation factor k _{p value of the above 42 models, and the plastic attenuation factor k p value} is the buckling load value obtained in the previous step The ratio of P mt to the empirical formula solution P _mt for thick shells in perfect geometry of the corresponding thickness;

(2.4) According to the plastic attenuation factor _kp values of the above 42 models, draw the relationship curve between the plastic attenuation factor _kp and the thickness-to-diameter ratio t/r under different yield strengths _σy ;

(2.5) by carrying out non-linear and linear regression analysis to step (2.4) gained relationship curve, fitting out formula Where k ₁ =1.22×10 ^-4 , k ₂ =-0.92.

Further, the specific steps for solving the geometric defect attenuation factor k _imp in the step (4) are as follows:

(4.1) The first-order modal defect is introduced as the initial defect, and the initial defect amplitude δ is selected from 5 types, which are 0.01mm, 0.02mm, 0.03mm, 0.04mm and 0.05mm; 6 different yield strengths σ _y , A total of 210 buckling load values under 7 different thicknesses and 5 different ratios of initial defect amplitude to head radius δ/r;

The first-order modal defect is the most dangerous defect form, and the prediction and calculation of the head bearing capacity considering the modal defect is the most conservative; therefore, the initial geometric defect is set as the modal defect. Through the linear buckling analysis of the finite element software, the buckling mode is obtained as the buckling mode of the head.

(4.2) Calculate the ratio of the above buckling load value to the corresponding nonlinear critical buckling load P _non of the perfect head to obtain 210 geometric defect attenuation factor k _imp values;

(4.3) According to different yield strengths σ _y , draw the relationship curves of the geometric defect attenuation factor k _imp with different thickness-to-diameter ratios t/r, and the ratio δ/r of different initial defect amplitudes to the radius of the head.

Further, in the step (5), the specific steps for inducing the ultimate bearing capacity P _real of the head are as follows:

(5.1) According to the formula k _real = k _p k _imp , 210 values of actual attenuation factor k _real are calculated;

(5.2) Combining the relationship curves of k _p and k _imp with different yield strengths σ _y , different thickness-to-diameter ratios t/r and the ratio δ/r of different initial defect amplitudes to the radius of the head, the formula of k _real is fitted :

(5.3) Import the fitted formula model and 210 groups of data into the MATLAB software, and obtain each parameter a1=5.3357 of the formula; a2=-3.3004; a3=-0.0142; a4=6.8721×10 ^-5 ; a5=0.8508; a6=-0.7433;

(5.4) Draw a numerical comparison chart based on the formula and all data.

Further, the specific steps for calculating the ultimate bearing capacity P _real of the head in the step (6) are as follows: According to the relevant thickness value t, yield strength σ _y , and defect amplitude δ/r of the actual head shell, substitute into the formula

in

, Calculate the ultimate bearing capacity P _real of the head.

Compared with the prior art, the present invention has the advantages of:

The present invention is based on the instability mechanism of the pressure-resistant head of the submersible (that is, the initial instability of the shell occurs in the linear elastic stage of the material, and the instability of the head is closely related to the yield strength of the material), and considers geometric parameters in detail (including the radius of the head, Wall thickness and defect amplitude) and material parameters (including elastic modulus, Poisson's ratio and yield strength), so that the estimated ultimate bearing capacity of the head is accurate and widely applicable.

The derivation process of the present invention can be used to summarize the estimation of the bearing capacity of the pressure vessel head of different materials.

Description of drawings

Fig. 1 is the relationship between the plastic attenuation factor _kp and the thickness-to-diameter ratio t/r based on different buckling strengths _σy in specific embodiments;

Fig. 2 is the relationship between the geometric defect attenuation factor k _imp and the thickness-to-diameter ratio t/r under different defect amplitudes and yield strengths σ _y in specific embodiments;

Fig. 3 is the comparison figure between Matlab fitting formula and actual data in the specific embodiment.

Detailed ways

The present invention will be further explained below in conjunction with the accompanying drawings and specific embodiments.

The present invention provides a method for estimating the ultimate bearing capacity of a hemispherical pressure-resistant head:

Step 1: Set the relevant parameters of the head, where the middle diameter r of the head is set to 60mm, the thickness value t ranges from 0.24mm to 0.6mm, and is incremented by 0.06mm, and a total of 0.24mm, 0.30mm, 0.36mm, 0.42mm, 0.48mm, 0.54mm, 0.60mm 7 kinds of thickness; yield strength σ _y ranges from 180MPa to 230MPa, the increment is 10MPa, 180MPa, 190MPa, 200MPa, 210MPa, 220MPa, 230MPa total 6 kinds of yield strength;

Step 2: Study the influence of material yield strength on the bearing capacity of the head; define the influence of the buckling strength on the ultimate bearing capacity of the head as the plastic attenuation factor, and solve the plastic attenuation factor k _p :

a. Calculate the linear buckling load P _mt of the perfect head of 42 models under 7 different thicknesses and 6 different yield strengths σ _y , the calculation empirical formula is: Among them, the elastic modulus E of the material is 193GPa, and the Poisson's ratio ν is 0.28;

b. Set the material model as an ideal elastoplastic model, and the grid unit type is a fully integrated S4 unit; the boundary conditions of the head model are set according to CCS2013; a total of 42 under 7 different thicknesses and 6 different yield strengths σ _y Each model is analyzed by the finite element software ABAQUS and the nonlinear arc length method to obtain the corresponding buckling load value;

c. Define the influence of buckling strength on the ultimate bearing capacity of the head as the plastic attenuation factor k _p , calculate the plastic attenuation factor k _{p value of the above 42 models, and the plastic attenuation factor k p value} is the same as the buckling load value obtained in the previous step The ratio of the empirical formula solution P _mt for thick shells in perfect geometry with corresponding thicknesses;

d. According to the plastic attenuation factor k _p value of the above 42 models, draw the relationship curve between the plastic attenuation factor k _p and the thickness-to-diameter ratio t/r under different yield strength σ _y , as shown in Figure 1;

e. By performing nonlinear and linear regression analysis on the relationship curve obtained in the previous step, the formula is fitted Where k ₁ =1.22×10 ^-4 , k ₂ =-0.92;

Step 3: The nonlinear critical buckling load P _non of the perfect head is obtained by the product of the plastic attenuation factor k _p and the solution P _mt of the empirical formula for medium-thick shells: P _non = k _p P _mt .

Step 4: Study the influence of geometrical initial defects on the buckling load of the head, define the effect of buckling strength on the ultimate bearing capacity of the head as the geometric defect attenuation factor k _imp , and solve the geometric defect attenuation factor k _imp :

a. The first-order modal defect is introduced as the initial defect, and the initial defect amplitude δ is 5 types, which are 0.01mm, 0.02mm, 0.03mm, 0.04mm and 0.05mm; 6 different yield strengths are calculated by the analysis software ABAQUS A total of 210 buckling load values under σ _y , 7 different thicknesses, and 5 different ratios of initial flaw amplitude to head radius δ/r;

b. Calculate the ratio of the above buckling load value to the corresponding perfect head nonlinear critical buckling load P _non to obtain 210 geometric defect attenuation factor k _imp values;

c. According to different yield strengths _σy , draw the relationship curves of the geometric defect attenuation factor k _imp and different thickness-to-diameter ratios t/r, and the ratio δ/r of different initial defect amplitudes to the radius of the head, as shown in Figure 2. In the figure, a is the situation where the yield strength is 180MPa; b is the situation where the yield strength is 190MPa; c is the situation where the yield strength is 200MPa; d is the situation where the yield strength is 210MPa; e is the situation where the yield strength is 220MPa; The case where the strength is 230MPa;

It can be seen in Fig. 2 that the sensitivity of the critical buckling load of the head to geometric defects increases with the increase of defect size and yield strength and the decrease of wall thickness. Among the three, the yield strength has the least influence. Under the condition that the yield strength and defect size remain unchanged, the relationship between the geometric defect attenuation factor k _imp and the thickness-to-diameter ratio t/r can be approximately divided into two linear segments. The first segment is in the range of (0.004<t/r<0.007), and the relationship between the two forms a linear relationship with a higher slope. The second segment is in the range of (0.007<t/r<0.010), and the relationship between the two forms a linear relationship with a low slope. relationship, this tendency is attributed to the nonlinearity of the material.

Step 5: Combined with the above analysis, import all 210 sets of data into MATLAB for formula fitting, and solve the actual attenuation factor k _real , where k _real = k _p k _imp , the estimation formula of the ultimate bearing capacity P _real of the head: P _real = k _real P _mt .

a. According to the formula k _real = k _p k _imp , 210 values of actual attenuation factor k _real are calculated;

b. Combining k _p and k _imp with different yield strengths σ _y , different thickness-to-diameter ratios t/r and different ratios of initial defect amplitudes to head radius δ/r, the formula for k _real is fitted:

c. Import the fitted formula model and 210 groups of data into the MATLAB software, and fit each parameter a1=5.3357 of the formula; a2=-3.3004; a3=-0.0142; a4=6.8721×10 ^-5 ; a5=0.8508; a6=-0.7433.

d. Draw a numerical comparison chart based on the formula and all actual data, as shown in Figure 3, the solid line is the formula curve, and the dots are the data values. As shown in Figure 3, it can be seen that the data calculated by the formula has the same trend as the actual data, and the error is within 4%.

Step 6: Substituting the relevant thickness value t, yield strength σ _y , and defect amplitude δ/r of the actual head shell into the analytical formula to finally calculate the required ultimate bearing capacity P _real of the head.

In order to verify the analytical formula of the present invention, five scale models of hemispherical heads were manufactured, and measurements and crush tests were carried out. The test models are named 1#, 2#, 3#, 4# and 5# respectively. Meanwhile, the corresponding material parameters were obtained by uniaxial tensile tests. These test heads had a nominal radius of 60 mm and were made of 304 stainless steel with a yield strength of 205 MPa. The thickness, actual radius and out-of-roundness (OOR) of the head are accurately measured through corresponding tests and are listed in columns 2, 3 and 4 of Table 1. After the geometric parameters are measured, the hydraulic test is carried out in the pressure chamber, and the measured ultimate bearing capacity P _test is listed in column 5 of Table 1.

Table 1 The measurement and test results of the head model, and the predicted bearing capacity P _real according to the analytical formula.

t _ave (mm) r _ave /mm OOR P _test (MPa) P _real (MPa) P _real /P _test 1# 0.432 58.84 0.037 2.707 2.616 0.966 2# 0.422 58.77 0.038 2.482 2.527 1.018 3# 0.423 58.99 0.038 2.593 2.527 0.975 4# 0.406 58.77 0.039 2.493 2.397 0.961 5# 0.416 58.75 0.035 2.360 2.518 1.067

According to the relevant data of measurement, according to the analytical formula of the present invention, carry out the prediction of head bearing capacity, the result is listed in the 5th row of table 1; In the table, the ratio of analytical formula gained result and test result in the last column parentheses, change Range 0.961-1.067. It can be seen that this analytical formula can accurately predict the failure pressure of the head.

The thickness value is not limited to the value mentioned in step 1, and no less than 8 values can be used scattered within the commonly used range. The yield strength is not limited to the value mentioned in step 1, and the yield strength can be scattered and collected no less than 4 values within the corresponding range. value, so as to calculate the estimation formula.

Due to the different elastic modulus E and Poisson's ratio of different materials, the fitting parameters of each formula will be different, but the final estimation mathematical model can still be obtained by referring to the steps of this estimation method.

Heads with different pitch diameters can also use the steps of this estimation method to obtain the final estimation mathematical model.

The above-mentioned embodiment only illustrates the principle of the present invention and its effect, and the embodiment of partial use, but is not intended to limit the present invention; It should be pointed out that for those of ordinary skill in the art, without departing from the Under the premise of creating ideas, some modifications and improvements can also be made, which all belong to the protection scope of the present invention.

Claims (6)

1. a kind of evaluation method of hemispherical pressure resistance end socket ultimate bearing capacity, which is characterized in that include the following steps：

(1) end socket relevant parameter is set, wherein relevant parameter includes central diameter r, the different-thickness value t and difference yield strength of end socket σ_y；

(2) consider the influence to end socket bearing capacity；Influence by buckling strength to end socket ultimate bearing capacity is defined as anelastic attenuation Factor k_pAnd it solves；

(3) k that will be acquired in step (2)_pWith the empirical equation solution P of middle thick shell_m-tIt is non-linear critical in the wrong that substitution acquires perfect end socket Qu ZaiheP_non：P_non=k_pP_m-t；

(4) geometry initial imperfection is studied to the affecting laws of end socket buckling load, by buckling strength to end socket ultimate bearing capacity Influence is defined as geometrical defect decay factor k_imp, solve geometrical defect decay factor k_imp；

(5) in k_pAnd k_impOn the basis of, all data are subjected to formula fitting, solve actual attenuation factor k_real, wherein k_real=k_pk_imp, conclude end socket ultimate bearing capacity P_realEstimation formula：

P_real=k_realP_m-t；

It (6) include thickness value t, yield strength σ according to the related parameter values of practical shell_y, defect amplitudes δ/r, substitute into step (5) In the conclusion end socket ultimate bearing capacity P that obtains_realEstimation formula, it is final to calculate end socket ultimate bearing capacity P_real。

2. a kind of evaluation method of hemispherical pressure resistance end socket ultimate bearing capacity according to claim 1, which is characterized in that institute Stating setting end socket relevant parameter in step (1), specific step is as follows：The central diameter r of end socket is set as 60mm, thickness value t range from 0.24mm to 0.6mm, carried out with 0.06mm it is incremental, choose total 0.24mm, 0.30mm, 0.36mm, 0.42mm, 0.48mm, 0.54mm, 0.60mm7 kind thickness；Yield strength σ_yRange is from 180MPa to 230MPa, increment 10MPa, take 180MPa, 190MPa, 200MPa, 210MPa, 220MPa, 230MPa totally 6 kinds of yield strengths.

3. a kind of evaluation method of hemispherical pressure resistance end socket ultimate bearing capacity according to claim 2, which is characterized in that institute It states and solves anelastic attenuation factor k in step (2)_pSpecific step is as follows：

(2.1) 7 kinds of different-thickness, 6 kinds of different yield strength σ are calculated_yUnder the perfect end socket of totally 42 models linear buckling load P_m-t, calculating empirical equation is：Wherein the elastic modulus E of material is 193GPa, and Poisson's ratio ν is 0.28；

(2.2) material model is set as ideal elastoplastic model, and grid cell type is the S4 unit of complete integral；End socket model Boundary condition be configured according to CCS2013；To 7 kinds of different-thickness, 6 kinds of different yield strength σ_yUnder totally 42 models, adopt Carry out analysis with non-linear arc regular way and obtains corresponding buckling load value；

(2.3) influence by buckling strength to end socket ultimate bearing capacity is defined as anelastic attenuation factor k_p, calculate above-mentioned 42 models Anelastic attenuation factor k_pValue, anelastic attenuation factor k_pValue is the perfect geometry of buckling load value and respective thickness that upper step obtains The empirical equation solution P of middle thickness shell_m-tRatio；

(2.4) according to the anelastic attenuation factor k of above-mentioned 42 models_pValue, draws different yield strength σ_yLower anelastic attenuation factor k_p With the graph of relation of radius-thickness ratio t/r；

(2.5) as carrying out non-linear and linear regression analysis to graph of relation obtained by step (2.4), formula is fittedWherein k₁=1.22 × 10^-4,k₂=-0.92.

4. a kind of evaluation method of hemispherical pressure resistance end socket ultimate bearing capacity according to claim 3, which is characterized in that institute It states and solves geometrical defect decay factor k in step (4)_impSpecific step is as follows：

(4.1) first-order modal defect is introduced as initial imperfection, initial imperfection amplitude δ takes 5 kinds, respectively 0.01mm, 0.02mm, 0.03mm, 0.04mm and 0.05mm；Calculate 6 kinds of different yield strength σ_y, 7 kinds of different-thickness, 5 kinds of differences it is initial Totally 210 kinds of buckling load values under ratio delta/r of defect amplitudes and end socket radius；

(4.2) above-mentioned buckling load value and the non-linear Critical Buckling Load P of corresponding perfect end socket are calculated_nonRatio obtain 210 A geometrical defect decay factor k_impNumerical value；

(4.3) according to different yield strength σ_yGeometrical defect decay factor k is drawn respectively_impIt is initial from different radius-thickness ratio t/r, difference Ratio delta/r graph of relation of defect amplitudes and end socket radius.

5. a kind of evaluation method of hemispherical pressure resistance end socket ultimate bearing capacity according to claim 4, which is characterized in that institute It states and obtains conclusion end socket ultimate bearing capacity P in step (5)_realSpecific step is as follows：

(5.1) according to formula k_real=k_pk_imp, 210 actual attenuation factor k are calculated_realNumerical value；

(5.2) k is combined_pAnd k_impFrom different yield strength σ_y, difference radius-thickness ratio t/r and different initial imperfection amplitude and end socket radius Ratio delta/r graph of relation, fit k_realFormula：

(5.3) formula model of fitting and 210 groups of data are imported in MATLAB software, obtains the parameters a1=of formula 5.3357；A2=-3.3004；A3=-0.0142；A4=6.8721 × 10^-5；A5=0.8508；A6=-0.7433；

(5.4) numerical value comparison diagram is drawn according to formula and all data.

6. a kind of evaluation method of hemispherical pressure resistance end socket ultimate bearing capacity according to claim 5, which is characterized in that institute It states and calculates end socket ultimate bearing capacity P in step (6)_realSpecific step is as follows：According to the related thick angle value of practical end socket shell T, yield strength σ_y, defect amplitudes δ/r, substitute into formula

Wherein

,

Calculate end socket ultimate bearing capacity P_real。