CN112307660A - Method for calculating modulus-free bulging numerical value of cylindrical shell of submersible - Google Patents
Method for calculating modulus-free bulging numerical value of cylindrical shell of submersible Download PDFInfo
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- 238000006073 displacement reaction Methods 0.000 claims description 6
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Abstract
The invention discloses a method for calculating a modulus-free bulging numerical value of a cylindrical shell of a submersible, which comprises the following steps: establishing a cylindrical shell bus geometric model; establishing a cylindrical shell bus grid unit model; defining the elastic-plastic material parameters of the cylindrical shell parent metal; defining the section parameters of the cylindrical shell unit model; defining the maximum bulging load and equivalent boundary conditions of the cylindrical shell unit model; performing nonlinear solving calculation by adopting a Newton iteration method; and extracting the change history of the cylindrical shell dieless free bulging parameters along with the bulging amount. The invention solves the problems and defects in the prior art and provides a theoretical tool for the design and optimization of the technological parameters of the cylindrical shell dieless free bulging of the submersible.
Description
Technical Field
The invention belongs to the technical field of plate shell plastic processing, and particularly relates to a cylindrical shell die-free bulging process.
Background
The submersible is important equipment for ocean exploration and development, the pressure-resistant shell is a key component and a buoyancy unit of the submersible, and the pressure-resistant shell can ensure that internal equipment is not damaged and workers are safe in the submerging process of the submersible and simultaneously provides positive buoyancy. The cylindrical shell is a basic pressure-bearing unit of the pressure-bearing shell and has the advantages of high space utilization rate, good hydrodynamic characteristics, convenience in design and calculation and the like.
However, the ultimate bearing capacity of the cylindrical shell is very sensitive to initial geometric defects, resulting in reduced safety. Through exerting interior pressure to the cylinder shell, carry out the cylinder shell and do not have the mould and freely expand shape, can eliminate too big initial geometry defect, increase material yield strength, balance the mechanical properties everywhere of casing, and then improve the ultimate bearing capacity of cylinder shell, improve the casing security, also increased the inner space simultaneously. However, the industry still lacks a computational analysis means related to the cylindrical shell dieless free bulging process.
Disclosure of Invention
In order to solve the technical problems mentioned in the background technology, the invention provides a method for calculating a modulus-free bulging numerical value of a cylindrical shell of a submersible.
In order to achieve the technical purpose, the technical scheme of the invention is as follows:
a modulus-free bulging numerical calculation method for a submersible cylindrical shell comprises the following steps:
(1) establishing a cylindrical shell bus geometric model;
(2) establishing a cylindrical shell bus grid unit model;
(3) defining the elastic-plastic material parameters of the cylindrical shell parent metal;
(4) defining the section parameters of the cylindrical shell unit model;
(5) defining the maximum bulging load and equivalent boundary conditions of the cylindrical shell unit model;
(6) performing nonlinear solving calculation by adopting a Newton iteration method;
(7) and extracting the change history of the cylindrical shell dieless free bulging parameters along with the bulging amount.
Further, in the step (1)The method adopts a one-dimensional axisymmetric straight line for modeling, and the coordinates of two end points of the straight line are respectively (r)00) and (r)02 l); wherein r is0The outer radius of the cylindrical shell is defined, and 2l is the height of the cylindrical shell.
Further, in the step (2), a cylindrical shell bus grid unit model is established, the unit type is selected to be a linear axisymmetric shell unit, and the number of grids is odd; determining that the size of the grid is smaller than the height 2l of the cylindrical shell and the excircle radius r of the cylindrical shell through the analysis of the convergence of the grid0The grid type employs a fully integrated unit.
Further, in the step (3), the elastic-plastic material parameters include elastic material parameters and plastic material parameters, the elastic material parameters include an elastic modulus and a poisson ratio of the parent metal, and the plastic material parameters include a yield strength and a strength coefficient of the parent metal; the elastic material parameter and the plastic material parameter are measured by a uniaxial tensile test of a standard sample.
Further, in step (4), the cylindrical shell element midplane is set to be the outer surface of the cylindrical shell, the cylindrical shell element thickness is set to be the initial thickness, and the elasto-plastic material parameters determined in step (3) are assigned to the cylindrical shell element.
Further, in the step (5), the maximum bulging load p is defined on the inner surface of the cylindrical shell, all degrees of freedom are fixed on one end of the cylindrical shell, the axial moving degree of freedom is released on the other end of the cylindrical shell, other degrees of freedom are restrained, and an axial equivalent load is applied
Wherein r is0Is the outer circle radius of the cylindrical shell.
Further, in step (6), the initial load increment is less than one thousandth of the maximum bulging load, the maximum load increment is not more than two percent of the maximum bulging load, the minimum load increment is less than one thousandth of the maximum bulging load, and the maximum allowable increment step number is at least 5000.
Further, in the step (7), the cylindrical shell die-free bulging parameters comprise height, thickness, stress, strain and bulging pressure.
Further, extracting a change process of the vertical displacement of the upper end point of the cylindrical shell along with the bulging amount, namely a height-bulging amount curve; extracting the change course of the thickness of the midpoint of the cylindrical shell along with the bulging amount, namely a thickness-bulging amount curve; extracting the equivalent strain and equivalent stress change history along with the bulging amount of the middle point of the cylindrical shell, namely an equivalent strain-bulging amount curve and an equivalent stress-bulging amount curve; and extracting the horizontal displacement history of the midpoint of the cylindrical shell along with the change of the bulging pressure, namely a bulging pressure-bulging amount curve.
Further, in the step (7), the variation history of each parameter with the amount of bulging at different bulging pressures is extracted.
Adopt the beneficial effect that above-mentioned technical scheme brought:
the invention adopts an axial symmetry shell unit model, removes circular thick plate end sockets at two end parts of the cylindrical shell, and replaces the axial symmetry shell unit model with equivalent axial load and equivalent boundary conditions, thereby avoiding the problem of discontinuous boundary caused by too large thickness difference of the plate shell when the circular thick plate is directly modeled, ensuring easy convergence of calculation, simultaneously reducing the effective degree of freedom of a numerical model, improving the calculation efficiency and precision, and providing a theoretical tool for the design and optimization of the dieless free bulging process parameters of the cylindrical shell of the submersible.
Drawings
FIG. 1 is an overall flow chart of the present invention;
FIG. 2 is a schematic view of the cylindrical shell dieless free bulging structure of the present invention;
FIG. 3 is a schematic view of a cylindrical shell busbar geometry model of the present invention;
FIG. 4 is a schematic diagram of a cylindrical shell bus grid cell model of the present invention;
FIG. 5 is a schematic diagram of equivalent boundary conditions for a cylindrical shell bus bar in accordance with the present invention;
FIG. 6 is a diagram showing the relation between the cylindrical shell dieless free bulging height 2l and the bulging amount h;
FIG. 7 is a diagram showing the relation between the cylindrical shell dieless free bulging pressure p and the bulging amount h according to the present invention;
FIG. 8 is a diagram showing the relation between strain epsilon and bulging amount h in the cylindrical shell dieless free bulging middle point;
FIG. 9 is a diagram showing the relationship between the midpoint stress σ and the bulging amount h in the cylindrical shell dieless free bulging according to the present invention;
FIG. 10 is a diagram showing the relation between the thickness t of the middle point of the cylindrical shell dieless free bulging and the bulging amount h;
fig. 11 is a schematic diagram of the cylindrical shell dieless free bulging pressurization of the present invention.
Detailed Description
The technical scheme of the invention is explained in detail in the following with the accompanying drawings.
The invention is further elaborated according to the flow chart of the numerical calculation method of the cylindrical shell dieless free bulging shown in figure 1. The dimensional parameters of the cylindrical shell of the embodiment are shown in table 1, the shell bulging structure is shown in fig. 2, the shell material is stainless steel, and the material parameters are shown in table 2. The specific implementation process is realized by adopting general commercial Computer Aided Engineering (CAE) software ABAQUS, and the correctness of the numerical method is verified through the bulging test of three object cylindrical shells.
TABLE 1 nominal dimensions of cylindrical shells
| Parameter(s) | Value (mm) |
| Size of cylindrical shell | |
| Outer radius (r)0) | 51 |
| Height (2l) | 100 |
| Initial thickness (t)0) | 0.9 |
| Size of thick plate | |
| Radius (r)0) | 51 |
| Thickness (T) | 16 |
TABLE 2 elasto-plastic parameters of three standard stainless steel material samples
| Material sample | σy(MPa) | E1(GPa) | E(GPa) | μ |
| C1 | 288.5 | 1310.6 | 214.4 | 0.27 |
| C2 | 286.2 | 1307.2 | 208.1 | 0.28 |
| C3 | 279.1 | 1298.1 | 195.5 | 0.29 |
| average | 284.6 | 1305.3 | 206.0 | 0.28 |
σyYield strength; e1-intensity factor; e ═ elastic modulus; mu-Poisson's ratio
The method comprises the first step (S1) of establishing a cylindrical shell bus geometric model, and modeling by adopting a one-dimensional axisymmetric straight line, wherein coordinates of two end points of the straight line are respectively (r)0，0)、(r02 l). Wherein r is0The outer radius of the cylindrical shell is defined, and 2l is the height of the cylindrical shell.
The specific operation is as follows:
in the commercial software ABAQUS/Part module, the column-shell height 2l of 100mm and the outer circle radius r are established in the form of axisymmetric, deformable, shell elements0A 51mm geometric model, as shown in figure 3.
Secondly (S2), establishing a cylindrical shell bus grid unit model, selecting the unit type as a linear axisymmetric shell unit, wherein the number of grids must be odd number to ensure that the geometric and physical parameters of the dangerous points are extracted; and the mesh size is determined to be smaller than the height 2l and the radius r through mesh convergence analysis0The ratio and the grid type adopt a complete integral unit to ensure the calculation accuracy.
The specific operation is as follows:
in a commercial software ABAQUS/Mesh module, a unit type is selected as a 2-node linear axisymmetric thin-shell/thick-shell unit (SAX1), and the generatrix determined in the first step is subjected to grid division to finally determine 100 grids and 101 nodes. As shown in fig. 4.
And step three (S3), defining the elastic-plastic material parameters of the cylindrical shell parent metal, wherein the specific elastic-plastic material parameters are measured according to a uniaxial tensile test of ISO 6892-1 standard and comprise elastic modulus, Poisson' S ratio, buckling strength, hardening parameters and the like.
The specific operation is as follows:
in the commercial software ABAQUS/Property module, the elastic parameters of the stainless steel parent material are input, wherein the Young modulus is 206GPa, and the Poisson ratio is 0.28. The plastic parameter is the stress sigma of the parent metal solved according to the plastic equation (1-1)eq-strain value εeqAnd input into software, wherein the yield strength sigmay284.6MPa and the strength coefficient E1Is 1305.3. These parameters were measured by uniaxial tensile testing of 3 standard specimens.
σeq＝σy+E1εeq (1-1)
A fourth step (S4) of defining the cylindrical shell element model section parameters, setting the shell element middle surface as the outer surface of the cylindrical shell and the shell element thickness as the initial thickness (t)0) And assigning the material parameters determined in the third step to the shell element.
The specific operation is as follows:
and (3) establishing a continuous and uniform shell section in a commercial software ABAQUS/Property module, setting the thickness to be 0.9mm, selecting 5 integrating points in the thickness direction, selecting the material parameters determined in the third step, selecting the unit model determined in the second step, and setting the middle surface of the shell unit as the outer surface of the cylindrical shell.
The fifth step (S5) is that the maximum bulging load and the equivalent boundary condition of the cylindrical shell unit model are defined, the maximum bulging load p is defined on the inner surface of the cylindrical shell, all degrees of freedom are fixed on one end of the cylindrical shell, the axial movement degree of freedom is released on the other end of the cylindrical shell, other degrees of freedom are restrained, and the axial equivalent load is applied, wherein the equivalent load is a thick plate sealPressure on the head
The specific operation is as follows:
in the commercial software ABAQUS/Load module, the maximum bulging Load p is defined as 20Mpa on the inner surface inside the cylindrical shell, and the freedom of positioning is provided at the lower end of the cylindrical shell unit model: u1 ═ U2 ═ UR3 ═ 0; the upper end defines the degree of freedom: u1 UR 30 while applying an equivalent load
As shown in fig. 5.
And sixthly (S6), performing nonlinear solution calculation by adopting a Newton iteration method, wherein the initial load increment is less than one thousandth of the maximum bulging load, the maximum load increment is not higher than two percent of the maximum bulging load, the minimum load increment is less than one ten thousandth of the maximum bulging load, and the maximum allowable increment step number is at least 5000 steps.
The specific operation is as follows:
in a commercial software ABAQUS/Step module, a static and general implicit analysis Step is defined, a nonlinear option is started, the initial load increment is set to be 0.002, the maximum load increment is set to be 0.02, and the minimum load increment is set to be 10-50The maximum allowable number of incremental steps is set to 10000 steps. And then establishing an analysis task in an ABAQUS/Job module, and submitting solution calculation.
The seventh step (S7), extracting the cylindrical shell die-free bulging parameters under different bulging pressures, specifically comprising: the length, thickness, stress, strain and bulging pressure are changed along with the parameters of bulging quantity.
The specific operation is as follows:
in the commercial software ABAQUS/Visualization module, the vertical displacement variation history with the swelling capacity of the upper end point of the cylindrical shell, i.e., the height-swelling capacity curve, was extracted, as shown in FIG. 6.
In the commercial software ABAQUS/Visualization module, the horizontal displacement history of the midpoint of the cylindrical shell along with the change of the bulging pressure, i.e., the bulging pressure-bulging amount curve, is extracted, as shown in FIG. 7.
In a commercial software ABAQUS/Visualization module, the equivalent strain and equivalent stress change history along with the bulging capacity of the cylindrical shell, namely an equivalent strain-bulging capacity curve (figure 8) and an equivalent stress-bulging capacity curve (figure 9), are extracted.
In the commercial software ABAQUS/Visualization module, the variation history of the point thickness with the amount of bulging in the cylindrical shell, i.e., the thickness-amount-of-bulging curve, was extracted as shown in FIG. 10.
To verify the correctness of the above numerical calculation method, three stainless steel cylindrical shells were machined according to the parameters of table 1, and bulging pressures of 8.5MPa, 10.5MPa, and 12MPa were applied, respectively, as shown in fig. 11. Measuring bulging amount and height data under three bulging pressures by using a three-dimensional scanner, wherein the bulging amount and the height data are respectively shown in figures 6 and 7; wall thickness data were measured using a non-destructive thickness gauge at three bulging pressures, as shown in fig. 10. As can be seen from fig. 6, 7 and 10, the numerical results and the test results have good consistency, which proves the correctness of the method of the present invention.
The embodiments are only for illustrating the technical idea of the present invention, and the technical idea of the present invention is not limited thereto, and any modifications made on the basis of the technical scheme according to the technical idea of the present invention fall within the scope of the present invention.
Claims (10)
1. A modulus-free bulging numerical calculation method for a submersible cylindrical shell is characterized by comprising the following steps:
(1) establishing a cylindrical shell bus geometric model;
(2) establishing a cylindrical shell bus grid unit model;
(3) defining the elastic-plastic material parameters of the cylindrical shell parent metal;
(4) defining the section parameters of the cylindrical shell unit model;
(5) defining the maximum bulging load and equivalent boundary conditions of the cylindrical shell unit model;
(6) performing nonlinear solving calculation by adopting a Newton iteration method;
(7) and extracting the change history of the cylindrical shell dieless free bulging parameters along with the bulging amount.
2. The submersible cylindrical shell modulus-free bulging numerical calculation method according to claim 1, wherein in the step (1), a one-dimensional axisymmetric straight line is used for modeling, and coordinates of two end points of the straight line are respectively (r)00) and (r)02 l); wherein r is0The outer radius of the cylindrical shell is defined, and 2l is the height of the cylindrical shell.
3. The submersible cylindrical shell mould-free bulging numerical calculation method according to claim 1, wherein in the step (2), a cylindrical shell bus grid unit model is established, the unit type is selected to be a linear axisymmetric shell unit, and the number of grids is odd; determining that the size of the grid is smaller than the height 2l of the cylindrical shell and the excircle radius r of the cylindrical shell through the analysis of the convergence of the grid0The grid type employs a fully integrated unit.
4. The submersible cylindrical shell modulus-free bulging numerical calculation method according to claim 1, wherein in the step (3), the elastic-plastic material parameters comprise elastic material parameters and plastic material parameters, the elastic material parameters comprise an elastic modulus and a poisson's ratio of the parent metal, and the plastic material parameters comprise a yield strength and a strength coefficient of the parent metal; the elastic material parameter and the plastic material parameter are measured by a uniaxial tensile test of a standard sample.
5. The submersible cylindrical shell mold-less free bulging numerical calculation method according to claim 1, wherein in the step (4), the cylindrical shell unit midplane is set to an outer surface of the cylindrical shell, the cylindrical shell unit thickness is set to an initial thickness, and the elastoplastic material parameter determined in the step (3) is given to the cylindrical shell unit.
6. The submersible cylindrical shell modeless free bulging numerical calculation method of claim 1, wherein in step (5), a maximum bulging load p is defined on the inner surface of the cylindrical shell, all degrees of freedom are fixed to one end of the cylindrical shell, and axial movement degrees of freedom are released to the other end of the cylindrical shell, and other self-expansion forces are restrainedDegree of freedom, and applying an axial equivalent load
Wherein r is0Is the outer circle radius of the cylindrical shell.
7. The method for calculating the modeless free bulging numerical value of a submersible cylindrical shell according to claim 1, wherein in step (6), the initial load increment is less than one thousandth of the maximum bulging load, the maximum load increment is not more than two percent of the maximum bulging load, the minimum load increment is less than one thousandth of the maximum bulging load, and the maximum allowable increment step number is at least 5000.
8. The submersible cylindrical shell modulus-free bulging numerical calculation method according to claim 1, wherein in step (7), the cylindrical shell modulus-free bulging parameters include height, thickness, stress, strain and bulging pressure.
9. The submersible cylindrical shell modulus-free bulging numerical calculation method according to claim 8, wherein a vertical displacement variation history along with a bulging amount of a cylindrical shell, namely a height-bulging amount curve, is extracted from an upper end point of the cylindrical shell; extracting the change course of the thickness of the midpoint of the cylindrical shell along with the bulging amount, namely a thickness-bulging amount curve; extracting the equivalent strain and equivalent stress change history along with the bulging amount of the middle point of the cylindrical shell, namely an equivalent strain-bulging amount curve and an equivalent stress-bulging amount curve; and extracting the horizontal displacement history of the midpoint of the cylindrical shell along with the change of the bulging pressure, namely a bulging pressure-bulging amount curve.
10. The submersible cylindrical shell modulus-free bulging numerical calculation method according to claim 1, wherein in the step (7), the variation history of each parameter with the bulging amount under different bulging pressures is extracted.
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