Strength design method of large-scale non-uniformly reinforced cylindrical shell pressure-resistant structure

Abstract

The application provides a strength design method of a large non-uniformly reinforced cylindrical shell pressure-resistant structure, which comprises the following steps: (1) stress analysis is conducted on the reinforced cylindrical shell structure subjected to external hydrostatic pressure; (2) based on the elastic foundation beam theory, a cylindrical shell deflection curve expression containing unknown parameters is constructed; (3) according to the boundary conditions at the reinforcing ribs of each section of the cylindrical shell, the unknown parameters in the cylindrical shell deflection curve expression are solved to obtain a calculation formula of the cylindrical shell deflection curve, and the strength of the non-uniformly reinforced cylindrical shell pressure-resistant structure is calculated in combination with actual material parameters and structure parameters. The application has reasonable concept, breaks through the limitations of traditional methods, has a wider application range than traditional theoretical methods, can conveniently and quickly design the strength of the non-uniformly reinforced cylindrical shell structure, and is suitable for promotion and application.

Description

Technical Field

[0001] This invention relates to the field of underwater equipment manufacturing technology, specifically to a strength design method for a large non-uniformly reinforced cylindrical shell pressure-resistant structure. Background Technology

[0002] Stiffened cylindrical shell structures are widely used in large underwater equipment. With the development of the marine industry, higher demands are being placed on the optimized design of stiffened cylindrical shell structures. Uniform stiffener arrangements can no longer meet the service requirements of current underwater equipment. In practical engineering applications, stiffeners of different sizes or stiffnesses need to be arranged, and the spacing between stiffeners is no longer equal. Traditional strength theories for stiffened cylindrical shells assume that stiffeners are arranged with equal stiffness and equal spacing, which is not applicable to actual engineering structures, hindering the development of underwater equipment. Therefore, a new strength theory is urgently needed for non-uniformly stiffened cylindrical shells, which is of great significance for the structural design and optimization of underwater equipment. Summary of the Invention

[0003] In view of the technical problems existing in the background art, the present invention proposes a strength design method applicable to non-uniformly reinforced cylindrical shell structures. Its concept is reasonable, breaks through the limitations of traditional methods, has a wider range of applications than traditional theoretical methods, and can conveniently and quickly perform strength design on non-uniformly reinforced cylindrical shell structures, making it suitable for promotion and application.

[0004] To solve the above-mentioned technical problems, the present invention provides a strength design method for a large non-uniformly reinforced cylindrical shell pressure-resistant structure, characterized by comprising the following steps:

[0005] (1) Perform stress analysis on the reinforced cylindrical shell structure subjected to external hydrostatic pressure;

[0006] (2) Based on the theory of elastic foundation beams, construct the expression for the deflection curve of a cylindrical shell containing unknown parameters;

[0007] (3) Based on the boundary conditions at the stiffeners of each cylindrical shell, the unknown parameters in the deflection expression of the cylindrical shell are solved to obtain the calculation formula of the deflection curve of the cylindrical shell. Combined with the actual material parameters and structural parameters, the strength of the non-uniformly stiffened cylindrical shell pressure-resistant structure is calculated.

[0008] The strength design method for the large non-uniformly reinforced cylindrical shell pressure-resistant structure, wherein step (1) specifically involves: firstly constructing a geometrically simplified model of the non-uniformly reinforced cylindrical shell, which includes the cylindrical shell and n+1 circumferential reinforcing ribs of different sizes; then, performing a stress analysis on the cylindrical shell structure in the geometrically simplified model, considering a closed thin-walled cylindrical shell subjected to hydrostatic pressure; under the combined action of hydrostatic pressure and longitudinal pressure, the differential equation of the cylindrical shell is:

[0009]

[0010] In the above formula (1), w is the deflection of the cylindrical shell, p is the hydrostatic pressure acting on the outside of the cylindrical shell, E is the Young's modulus, μ is the Poisson's ratio, t is the thickness of the shell, R is the radius of the cylindrical shell, w⁗ and w″ respectively represent the fourth-order derivative and the second-order derivative of the deflection curve w, and the flexural rigidity of the cylindrical shell

[0011] The strength design method for the pressure-resistant structure of the large non-uniformly stiffened cylindrical shell, wherein the specific process of the step (2) is as follows:

[0012] n + 1 circumferential stiffeners divide the overall cylindrical shell into n segments of continuous cylindrical shells. According to the theory of elastic foundation beams, the differential equation in formula (1) is solved, and the expression of the deflection curve of the i-th segment of the cylindrical shell is obtained as:

[0013]

[0014] In the above formula (2), C i1 、C i2 、C i3 、C i4 are unknown parameters, w i is the deflection of the i-th segment of the cylindrical shell, t i is the thickness of the i-th segment of the cylindrical shell, is the flexural rigidity of the i-th segment of the cylindrical shell, R is the radius of the cylindrical shell, and p is the hydrostatic pressure acting on the outside of the cylindrical shell.

[0015] The strength design method for the pressure-resistant structure of the large non-uniformly stiffened cylindrical shell, wherein the specific process of the step (3) is as follows:

[0016] First, taking the center line of the leftmost stiffener of each segment of the cylindrical shell as the local coordinate origin, the boundary conditions at the first stiffener at the leftmost end of the cylindrical shell are:

[0017] D1w″1(0) = K1w′1(0) (3);

[0018]

[0019] In the above formulas (3)-(4), w′ and w‴ respectively represent the first-order derivative and the third-order derivative of the deflection curve w;

[0020] Among them, the continuity condition at the i-th (1 < i < n + 1) stiffener is:

[0021] w i-1 (l i-1 ) = w i (0) (5);

[0022] w′i-1 (l i-1 )=-w′ i (0) (6);

[0023] w″ i-1 (l i-1 )=w″ i (0) (7);

[0024] D i w″ i (0)=K i w′ i (0), D i-1 w″ i-1 (l i-1 )=-K i w′ i-1 (l i-1 (8);

[0025]

[0026] In equations (3)-(9) above, S i Let l be the area of ​​the i-th reinforcing rib; i K represents the length of the i-th cylindrical shell segment, i.e., the distance between the i-th and (i+1)-th reinforcing ribs; i It is the torsional stiffness at the elastic boundary, and its calculation formula is:

[0027] For the (n+1)th stiffener at the rightmost end of the cylindrical shell, the boundary conditions are:

[0028] D n w″ n (l n )=-K n+1 w′ n (l n (10);

[0029]

[0030] For a stiffened cylindrical shell with n segments, solve the equations (3) to (11) above to find the C value for each segment. i1 C i2 C i3 C i4 Substitute these values ​​into equation (1) above to obtain the deflection curve of each segment of the cylindrical shell.

[0031] The longitudinal stress on the i-th segment of the cylindrical shell is:

[0032]

[0033] The circumferential stress of the i-th segment of the cylindrical shell is:

[0034]

[0035] By adopting the above technical solution, the present invention has the following beneficial effects:

[0036] The strength design method for large non-uniformly stiffened cylindrical shell pressure structures proposed in this invention is reasonably conceived. Traditional theories assume that the cylindrical shell is a uniform structure with identical dimensions, stiffness, and constraint conditions and displacement deformation at the stiffeners. However, in actual structural design, the distribution of stiffeners is not uniform. This invention breaks through the limitations of traditional methods, enabling convenient and quick design of the strength of non-uniformly stiffened cylindrical shell structures. It has a wider range of applications than traditional theoretical methods and can be used for strength calculations of various complex non-uniformly stiffened cylindrical shell structures, making it suitable for promotion and application. Attached Figure Description

[0037] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0038] Figure 1 This is a simplified geometric model of the non-uniformly reinforced cylindrical shell involved in the strength design method of the large non-uniformly reinforced cylindrical shell pressure-resistant structure of the present invention.

[0039] Figure 2 This is a schematic diagram of the mechanical model of the cylindrical shell simplified as an elastic foundation beam involved in the strength design method of the large non-uniformly reinforced cylindrical shell pressure-resistant structure of the present invention.

[0040] Figure 3 This is a schematic diagram showing the cylindrical shell dimensions and calculation point locations involved in the strength design method of the large non-uniformly reinforced cylindrical shell pressure-resistant structure of the present invention. Detailed Implementation

[0041] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0042] The present invention will be further explained below with reference to specific embodiments.

[0043] like Figure 1As shown in the figure, this embodiment provides a strength design method for a large non-uniformly reinforced cylindrical shell pressure-resistant structure, which specifically includes the following steps:

[0044] S100. Stress analysis of a reinforced cylindrical shell structure subjected to external hydrostatic pressure.

[0045] First, construct a geometrically simplified model of the non-uniformly reinforced cylindrical shell (e.g.) Figure 1 As shown), the simplified geometric model includes a cylindrical shell and n+1 circumferential stiffeners of different sizes. Therefore, the overall cylindrical shell contains n continuous cylindrical shell segments. Several key parameters are considered, including material properties and the geometric properties of the stiffeners. In the simplified geometric model, the cylindrical shell is subjected to hydrostatic pressure. Then, a stress analysis is performed on the cylindrical shell structure in the simplified geometric model, considering a closed thin-walled cylindrical shell (thickness much smaller than the cylinder radius) subjected to hydrostatic pressure, such as... Figure 1 As shown; the differential equation for a cylindrical shell under the combined action of hydrostatic pressure and longitudinal pressure is:

[0046]

[0047] In equation (1) above, w is the deflection of the cylindrical shell, p is the hydrostatic pressure on the outside of the cylindrical shell, E is Young's modulus, μ is Poisson's ratio, t is the shell thickness, R is the radius of the cylindrical shell, w″″ and w″ represent the fourth and second derivatives of the deflection curve w, respectively, and the bending stiffness of the cylindrical shell.

[0048] S200. Based on the theory of elastic foundation beams, an expression for the deflection curve of a cylindrical shell containing unknown parameters is constructed; the specific process is as follows:

[0049] n+1 circumferential stiffeners divide the monolithic cylindrical shell into n continuous cylindrical shell segments (e.g., ... Figure 2 As shown), based on the theory of elastic foundation beams, solving the differential equation in equation (1) yields the expression for the deflection curve of the i-th segment of the cylindrical shell:

[0050]

[0051] In equation (2) above, C i1 C i2 C i3 C i4 For unknown parameters, w i Let t be the deflection of the i-th segment of the cylindrical shell. i Let be the thickness of the i-th cylindrical shell segment, and let be the bending stiffness of the i-th cylindrical shell segment. R is the radius of the cylindrical shell, and p is the hydrostatic pressure exerted on the outside of the cylindrical shell.

[0052] S300. Solve the unknown parameters in the flexure expression of the cylindrical shell according to the boundary conditions at each stiffener, and obtain the calculation formula for the deflection curve of the cylindrical shell. Combine the parameters of the actual materials (such as steel, titanium alloy, etc.) and the structural parameters to calculate the strength of the non-uniform stiffened cylindrical shell pressure-resistant structure. The specific process is as follows:

[0053] First, take the center line of the leftmost stiffener of each section of the cylindrical shell as the local coordinate origin. The boundary conditions at the leftmost first stiffener of the cylindrical shell are:

[0054] D1w1″(0) = K1w1′(0) (3);

[0055]

[0056] In the above formula, w′ and w″′ represent the first derivative and the third derivative of the deflection curve w respectively;

[0057] Among them, the continuity conditions at the i-th (1 < i < n + 1) stiffener are:

[0058] w i-1 (l i-1 ) = w i (0) (5);

[0059] w′ i-1 (l i-1 ) = -w′ i (0) (6);

[0060] w″ i-1 (l i-1 ) = w″ i (0) (7);

[0061] D i w″ i (0) = K i w′ i (0), D i-1 w″ i-1 (l i-1 ) = -K i w′ i-1 (l i-1 ) (8);[[ID=​​​​​​​​​​​​

[0064] For the (n+1)th stiffener at the rightmost end of the cylindrical shell, the boundary conditions are:

[0065] D n w″ n (l n )=-K n+1 w′ n (l n (10);

[0066]

[0067] For a stiffened cylindrical shell with n segments, solve the equations (3) to (11) above to find the C value for each segment. i1 C i2 C i3 C i4 Substitute these values ​​into equation (1) above to obtain the deflection curve of each segment of the cylindrical shell.

[0068] The longitudinal stress on the i-th segment of the cylindrical shell is:

[0069]

[0070] The circumferential stress of the i-th segment of the cylindrical shell is:

[0071]

[0072] Example:

[0073] Stress calculations were performed on a reinforced titanium alloy cylindrical shell based on the method of this invention. The cylindrical shell was subjected to a hydrostatic pressure of 15 MPa. The shell had a radius of 1000 mm, a length of 1050 mm, and a thickness of 20 mm. Thirteen circumferential ribs were distributed in the middle, with "T"-shaped cross-sections. The dimensions and spacing of the ribs were as follows. Figure 3 As shown. Young's modulus E = 115 GPa, Poisson's ratio μ = 0.35.

[0074] Calculate the selected position as follows Figure 3 As shown.

[0075] Table 1 shows a comparison between theoretical calculation results and numerical simulation results.

[0076] Table 1

[0077]

[0078]

[0079] This invention has a reasonable concept and breaks through the limitations of traditional methods. It has a wider range of applications than traditional theoretical methods and can conveniently and quickly perform strength design on non-uniformly reinforced cylindrical shell structures, making it suitable for promotion and application.

[0080] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A strength design method for a large, non-uniformly reinforced cylindrical shell pressure-resistant structure, characterized in that, Specifically, the following steps are included: (1) Perform stress analysis on the reinforced cylindrical shell structure subjected to hydrostatic pressure; the specific process is as follows: first, construct a geometrically simplified model of the non-uniform reinforced cylindrical shell, which includes the cylindrical shell and n +1 circumferential stiffener of different sizes; then, perform a stress analysis on the cylindrical shell structure in the geometrically simplified model, considering a closed thin-walled cylindrical shell subjected to hydrostatic pressure; the differential equation of the cylindrical shell under the combined action of hydrostatic pressure and longitudinal pressure is: （1）； In the above formula (1), w For the deflection of the cylindrical shell, p This refers to the hydrostatic pressure borne by the outside of the cylindrical shell. E For Young's modulus, μ Poisson's ratio t For shell thickness, R Where is the radius of the cylindrical shell. and Representing the torsion curves respectively w Find the fourth and second derivatives, and the bending stiffness of the cylindrical shell. ; (2) Based on the theory of elastic foundation beams, construct the expression for the deflection curve of a cylindrical shell containing unknown parameters; The specific process is as follows: n +1 circumferential reinforcing rib divides the integral cylindrical shell into n For a continuous cylindrical shell segment, based on the theory of elastic foundation beams, solving the differential equation in equation (1) yields the deflection curve expression for the i-th segment of the cylindrical shell: （2）； In the above formula (2), For unknown parameters, w i Let be the deflection of the i-th segment of the cylindrical shell. t i Let be the thickness of the i-th segment of the cylindrical shell. Let be the bending stiffness of the i-th cylindrical shell segment. R Where is the radius of the cylindrical shell. p The hydrostatic pressure borne by the outside of the cylindrical shell; (3) Based on the boundary conditions at the stiffeners of each cylindrical shell segment, the unknown parameters in the deflection curve expression of the cylindrical shell are solved to obtain the calculation formula for the deflection curve of the cylindrical shell. Combined with the actual material parameters and structural parameters, the strength of the non-uniformly stiffened cylindrical shell pressure-resistant structure is calculated; the specific process is as follows: First, taking the center line of the leftmost stiffener at the far left of each cylindrical shell segment as the local coordinate origin, the boundary conditions at the first stiffener at the far left of the cylindrical shell are as follows: （3）； （4）； In equations (3)-(4) above, and These represent taking the first and third derivatives with respect to the torsion curve w, respectively. Among them, the i (1< i < n +1) The continuity condition at the root stiffener is: （5）； （6）； （7）； （8）； （9）； In equations (3)-(9) above, S i Let l be the area of ​​the i-th reinforcing rib; i Let be the length of the i-th cylindrical shell segment, i.e., the length of the i-th reinforcing rib and the... i+1 Spacing between reinforcing ribs; K i It is the torsional stiffness at the elastic boundary, and its calculation formula is: ; For the rightmost end of the cylindrical shell n At the +1 reinforcing rib, the boundary conditions are: （10）； （11）； For those n For a reinforced cylindrical shell with segmental shells, solve the above equations (3) to (11) to find the solution for each segment of the shell. Substitute these values ​​into equation (1) above to obtain the deflection curve of each segment of the cylindrical shell. The longitudinal stress on the i-th segment of the cylindrical shell is: （12）； The circumferential stress of the i-th segment of the cylindrical shell is: （13）。

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