Numerical solution method, apparatus, equipment and storage medium for overpressure balloons

Abstract

This invention relates to the field of aerostat technology, providing a numerical solution method, apparatus, device, and storage medium for overpressure balloons. The method includes: obtaining constant parameters such as the target volume, overpressure, spherical surface density, and load capacity of the overpressure balloon to be solved; constructing a spherical generatrix-stress equation system based on the constant parameters; obtaining the initial values ​​and preset termination conditions of the generatrix-stress equation system; and iteratively solving the generatrix-stress equation system based on the initial values ​​and termination conditions to obtain the target parameters of the overpressure balloon. The numerical solution method for overpressure balloons provided by this invention, based on a spherical generatrix-stress equation system, transforms the shape parameters of the overpressure balloon into a numerical solution to a boundary value problem; when designing the shape of the overpressure balloon based on the solved target parameters, it considers the influence of the load on the stress distribution under bidirectional tension conditions, making the stress distribution of the overpressure balloon more reasonable compared to a spherical balloon.

Description

Technical Field

[0001] This invention relates to the field of airship technology, and in particular to a numerical solution method, apparatus, equipment and storage medium for overpressure balloons. Background Technology

[0002] High-altitude balloons, as a widely used type of high-altitude aerostat, have become a major tool for space science observation and technological development due to their advantages such as high flight altitude, low cost, short preparation time, and ease of flexible implementation. However, the operational capabilities and application range of high-altitude balloons are greatly limited because existing single zero-pressure balloon systems cannot achieve long-duration flights, single large overpressure balloon systems have limited environmental conditions for flight missions, and large overpressure balloon technology still needs improvement. Therefore, near-space tandem aerostat systems have emerged, which fully utilize the advantages of both zero-pressure and overpressure balloons and, through reasonable parameter design, solve the problems of short flight time and weak payload capacity of existing high-altitude balloons.

[0003] Near-space tandem aerostat systems primarily rely on overpressure balloons as "buoys" capable of withstanding significant pressure differentials. This allows them to maintain their shape under varying altitudes and temperatures, compensating for the limitations of the zero-pressure balloon serving as the main balloon. Therefore, the overpressure balloon, acting as a "buoy," is crucial in near-space tandem aerostat systems. Among existing smoothly spiraled overpressure balloons, a perfect sphere is the most commonly used shape, offering the largest volume-to-surface-area ratio and the lowest self-weight for the same buoyancy. However, when the pressure differential is constant, the membrane stress of a perfect sphere increases with balloon size, making it unsuitable for large overpressure balloons. Furthermore, considering the large pressure differential of overpressure balloons, the stress on the membrane is mainly caused by overpressure; therefore, existing overpressure balloon designs do not consider load conditions. However, in practical applications, the load on the bottom of the overpressure balloon can cause significant deformation of the sphere, resulting in severe stress concentration and weak areas in the membrane, affecting the rationality of stress distribution. Summary of the Invention

[0004] This invention provides a numerical solution method for overpressure balloons, which solves the technical problem that the load capacity is not considered in the design of spherical overpressure balloons in the prior art, affecting the rationality of stress distribution in overpressure balloons.

[0005] This invention provides a numerical solution method for overpressure balloons, comprising:

[0006] Obtain the constant parameters of the overpressure balloon to be solved; the constant parameters include the target volume, overpressure, surface density of the balloon membrane, and load capacity of the overpressure balloon.

[0007] Based on the constant parameters, construct the generatrix-stress equation system for the spherical shape corresponding to the overpressure balloon;

[0008] The initial values ​​and preset termination conditions of the busbar-stress equations are obtained. Based on the initial values ​​and the termination conditions, the busbar-stress equations are iteratively solved to obtain the target parameters of the overpressure balloon.

[0009] According to a numerical solution method for an overpressure balloon provided by the present invention, the termination condition includes a volume difference threshold, and the initial value includes the arc length of the generatrix of the overpressure balloon; the step of iteratively solving the generatrix-stress equations based on the initial value and the termination condition to obtain the target parameters of the overpressure balloon includes:

[0010] The first final value of the overpressure balloon is obtained by solving the generatrix-stress equations based on the initial values.

[0011] Determine the volume difference between the estimated volume of the overpressure balloon corresponding to the first final value and the target volume;

[0012] Determine whether the volume difference value is greater than the volume difference threshold in the termination condition;

[0013] If the volume difference value is greater than the volume difference threshold in the termination condition, then the preset arc length value is subtracted from the generatrix arc length in the initial value, and the step of solving the generatrix stress equations based on the initial value to obtain the first final value of the overpressure balloon is returned and executed; until the volume difference value is less than or equal to the volume difference threshold in the termination condition, the target parameters of the overpressure balloon are obtained according to the first final value.

[0014] According to the numerical solution method for an overpressure balloon provided by the present invention, the generatrix-stress equation system includes the radius of a first cross-sectional circle; the first cross-sectional circle is any cross-sectional circle along any point on the generatrix of the sphere and perpendicular to the axis of rotation of the sphere; the initial value also includes the bottom angle of the overpressure balloon, and the termination condition also includes a radius difference threshold.

[0015] According to the numerical solution method for an overpressure balloon provided by the present invention, after solving the generatrix-stress equations based on the initial values ​​to obtain the first final value of the overpressure balloon, the method further includes:

[0016] The radius of the second cross-sectional circle of the overpressure balloon is determined based on the first final value, and the radius difference between the second cross-sectional circle and the first cross-sectional circle is calculated; the height of the second cross-sectional circle in the overpressure balloon is the same as the height of the first cross-sectional circle in the sphere; the second cross-sectional circle is a cross-sectional circle along any point on the generatrix of the overpressure balloon and perpendicular to the axis of rotation of the overpressure balloon;

[0017] If the radius difference is greater than the radius difference threshold in the termination condition, or if the minimum radius of the second cross-section circle is less than 0, then the preset angle value is subtracted from the sphere bottom angle in the initial value, and the process returns to and executes the step of solving the generatrix-stress equation system based on the initial value to obtain the first final value of the overpressure balloon; until the radius difference is less than or equal to the radius difference threshold in the termination condition, and the minimum radius of the second cross-section circle is greater than or equal to 0, the step of determining whether the volume difference is greater than the volume difference threshold in the termination condition is executed.

[0018] According to the numerical solution method for an overpressure balloon provided by the present invention, the generatrix-stress equations are as follows:

[0019]

[0020] Where, σ m The meridional stress and σ of the overpressure balloon c Let be the circumferential stress of the overpressure balloon, r be the radius of the cross-sectional circle at any point along the generatrix of the sphere and perpendicular to the axis of rotation of the sphere; w = ρg, where ρ is the surface density of the spherical membrane of the overpressure balloon and g is the acceleration due to gravity; p be the overpressure of the overpressure balloon, s be the arc length of the generatrix of the overpressure balloon, z be the height of the sphere, A be the surface area of ​​the sphere, and V be the target volume of the overpressure balloon.

[0021] According to the numerical solution method for an overpressure balloon provided by the present invention, the circumferential stress of the overpressure balloon satisfies:

[0022]

[0023] n is a positive integer greater than 1, θ0 is the bottom angle of the overpressure balloon, and p max This indicates the maximum overpressure of the overpressure balloon.

[0024] According to the numerical solution method for an overpressure balloon provided by the present invention, the target parameter includes the generatrix shape of the overpressure balloon.

[0025] The present invention also provides a numerical solution apparatus for an overpressure balloon, comprising:

[0026] The parameter acquisition module is used to acquire the constant parameters of the overpressure balloon to be solved; the constant parameters include the target volume, overpressure, and surface density of the balloon.

[0027] The equation construction module is used to construct the generatrix-stress equation system corresponding to the right sphere of the overpressure balloon based on the constant parameters.

[0028] The numerical solution module is used to obtain the initial values ​​and preset termination conditions of the busbar-stress equation system, and to iteratively solve the busbar-stress equation system based on the initial values ​​and the termination conditions to obtain the target parameters of the overpressure balloon.

[0029] The present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the numerical solution method for the overpressure balloon as described above.

[0030] The present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the numerical solution method for overpressure balloons as described above.

[0031] The present invention also provides a computer program product, including a computer program that, when executed by a processor, implements the numerical solution method for overpressure balloons as described above.

[0032] The present invention provides a numerical solution method, apparatus, and storage medium for overpressure balloons. It acquires constant parameters such as the target volume, overpressure, spherical membrane density, and load capacity of the overpressure balloon to be solved, and constructs a set of generatrix-stress equations for a perfect sphere. Based on the acquired initial values ​​and termination conditions, the generatrix-stress equations are iteratively solved, transforming the solution for the shape parameters of the overpressure balloon into a numerical solution for a boundary value problem, thus obtaining the target parameters for the shape of the overpressure balloon that satisfy the conditions. When designing the shape of the overpressure balloon based on these target parameters, the bidirectional tensile load and boundary conditions of the overpressure balloon are considered, resulting in a more reasonable overall stress distribution under bidirectional tensile load conditions compared to a perfectly spherical overpressure balloon. Attached Figure Description

[0033] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0034] Figure 1 This is one of the flowcharts illustrating the numerical solution method for overpressure balloons provided by the present invention;

[0035] Figure 2 This is the second flowchart illustrating the numerical solution method for overpressure balloons provided by this invention.

[0036] Figure 3This is a schematic diagram of the numerical solution device for the overpressure balloon provided by the present invention;

[0037] Figure 4 This is a schematic diagram of the structure of the electronic device provided by the present invention. Detailed Implementation

[0038] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0039] The following is combined with Figures 1-2 The numerical solution method for the overpressure balloon of the present invention is described.

[0040] Reference Figure 1 , Figure 1 This is one of the flowcharts illustrating the numerical solution method for the overpressure balloon provided in the embodiments of this application, based on... Figure 1 The numerical solution method for overpressure balloons provided in this application includes:

[0041] Step 100: Obtain the constant parameters of the overpressure balloon to be solved; the constant parameters include the target volume, overpressure, surface density of the balloon membrane, and load capacity of the overpressure balloon.

[0042] Step 200: Construct the generatrix-stress equation set for the spherical shape corresponding to the overpressure balloon based on the constant parameters;

[0043] Step 300: Obtain the initial values ​​and preset termination conditions of the busbar-stress equation set; based on the initial values ​​and the termination conditions, iteratively solve the busbar-stress equation set to obtain the target parameters of the overpressure balloon.

[0044] In this embodiment, the numerical solution method for overpressure balloons is used to solve for the shape parameters of overpressure balloons under bidirectional tensile load conditions, especially for smoothly spiraled overpressure balloons. Based on the generatrix equation of a natural-shaped (i.e., a perfect spherical) balloon, an appropriate circumferential stress value is selected, transforming the generatrix equation into a first-order implicit nonlinear ordinary differential equation. Boundary value problems are solved according to initial and final conditions to obtain the target parameters required for overpressure balloon shape design. The overpressure balloon shape designed based on these target parameters, when used as the "buoy" overpressure balloon in a near-space tandem aerostat system, exhibits a more reasonable stress distribution compared to a perfect spherical overpressure balloon. Specifically, after using a perfect spherical overpressure balloon for system design to determine its relevant parameters, the shape is solved based on the perfect spherical overpressure balloon. The resulting balloon shape, while ensuring the balloon volume remains unchanged and without affecting the overall design parameters of the aerostat system, takes load conditions into account when designing the overpressure balloon shape. This makes the stress distribution at the bottom and top of the overpressure balloon more reasonable than that of a perfect spherical overpressure balloon, and more suitable for bidirectional tensile load scenarios.

[0045] Specifically, the constant parameters of the overpressure balloon to be solved are first obtained. These constant parameters are the basic design parameters that the overpressure balloon needs to possess, determined according to actual requirements. They can be specific values ​​or a range of values, which are not limited here. The obtained constant parameters include the target volume, overpressure, surface density of the balloon membrane, and payload capacity.

[0046] Referring to the numerical solution process for a naturally shaped balloon, the generatrix-stress equations for a completely rotationally symmetric balloon made solely of a thin film are used. Based on the obtained constant parameters, a generatrix-stress equation system for a perfectly spherical balloon corresponding to the overpressure balloon is constructed. The constructed generatrix-stress equation system is shown in Equation 1 below:

[0047]

[0048] In Formula 1, σ m The meridional stress and σ of the overpressure balloon c Let be the circumferential stress of the overpressure balloon, r be the radius of the cross-sectional circle at any point along the generatrix of the sphere and perpendicular to the axis of rotation of the sphere; w = ρg, where ρ is the surface density of the spherical membrane of the overpressure balloon and g is the acceleration due to gravity; p be the overpressure of the overpressure balloon, s be the arc length of the generatrix of the overpressure balloon, z be the height of the sphere, A be the surface area of ​​the sphere, and V be the target volume of the overpressure balloon.

[0049] The initial and termination conditions of the generatrix-stress equations are obtained. Based on these initial and termination conditions, the generatrix-stress equations are iteratively solved to obtain the target parameters of the overpressure balloon. The shape of the overpressure balloon is designed according to these target parameters, which, while satisfying the given basic design parameters, results in a more reasonable stress distribution at the top and bottom of the overpressure balloon under bidirectional tensile load conditions. It is known that when the circumferential stress value of the overpressure balloon is given, the equations in Formula 1 above become a first-order nonlinear implicit ordinary differential equation system. Given that at the bottom of the closed overpressure balloon, the radius of the circular cross-section perpendicular to the axis of rotation is r0 = 0, and at the top r1 = 0, assuming the arc length of the balloon generatrix is ​​s, and the volume of the overpressure balloon obtained from the series system design is V0, solving for the spherical shape is equivalent to finding the numerical solution to the boundary value problem of this differential equation system. Using the target-shooting method, it is transformed into an initial value problem, which can then be solved iteratively.

[0050] Specifically, the target parameters to be solved include the generatrix shape of the overpressure balloon. Considering that the numerical solution of the initial value problem requires a given solution accuracy as the termination condition for iteration, and that the stress singularity at the bottom r0 = 0 is unavoidable, in order to demonstrate the rationality of the stress distribution of the overpressure balloon with this shape compared to a perfectly spherical overpressure balloon without affecting the closure of the sphere corresponding to the numerical solution, r0 = Δr1 is set in the numerical solution. Δr1 is a small value that can be used as the solution error in the termination condition, and as the iteration termination condition for the bottom angle θ0. Furthermore, to ensure that the generatrix shape of a single sphere is solved, r > 0 needs to be maintained during the iteration process. The balloon volume remains basically unchanged relative to the given target volume (the error is less than ΔV, which is also a small value and can be used as the iteration termination condition for the generatrix arc length s of the overpressure balloon). Therefore, the numerical solution of the overpressure balloon generatrix shape can be obtained based on the generatrix-stress equation system.

[0051] Furthermore, the preset termination conditions include a volume difference threshold V. e The initial values ​​include the arc length of the generatrix of the overpressure balloon. Based on the given volume of the overpressure balloon, the generatrix-stress equations for a spherical shape are iteratively solved according to the set initial values ​​and termination conditions. This yields a generatrix shape for the overpressure balloon with a more reasonable stress distribution. Specifically, step 300, the iterative solution process of the generatrix-stress equations based on the initial values ​​and termination conditions, includes:

[0052] Step 301: Solve the generatrix-stress equations based on the initial values ​​to obtain the first final value of the overpressure balloon;

[0053] Step 302: Determine the volume difference between the estimated volume of the overpressure balloon corresponding to the first final value and the target volume;

[0054] Step 303: Determine whether the volume difference value is greater than the volume difference threshold in the termination condition;

[0055] Step 304: If the volume difference value is greater than the volume difference threshold in the termination condition, then subtract the preset arc length value from the generatrix arc length in the initial value, return and execute the step of solving the generatrix stress equation system based on the initial value to obtain the first final value of the overpressure balloon; until the volume difference value is less than or equal to the volume difference threshold in the termination condition, the target parameters of the overpressure balloon are obtained according to the first final value.

[0056] When solving the generatrix-stress equations, given the target volume of the overpressure balloon, the surface density of the spherical membrane, the overpressure amount, and the bottom load, the solution is obtained based on the initial values, yielding a first final value. The volume of the overpressure balloon corresponding to this first final value is compared with the given target volume to determine the volume difference ΔV. If this volume difference is less than or equal to the volume difference threshold V in the termination condition... e The first final value obtained is the target parameter that satisfies the condition; if the volume difference ΔV is greater than the volume difference threshold V e If the initial value is obtained by subtracting the preset arc length value Δs from the initial value, the new initial value is used. The busbar-stress equations are then solved again based on the new initial value until the volume difference ΔV meets the termination condition.

[0057] Furthermore, the generatrix-stress equations include the radius of the first cross-sectional circle, which is any cross-sectional circle along any point on the generatrix of the sphere and perpendicular to the axis of rotation of the sphere; the initial values ​​also include the bottom angle of the differential pressure balloon, and the preset termination condition also includes the radius difference threshold r. e After solving the generatrix-stress equations based on the initial values ​​to obtain the first final value, the process also includes:

[0058] Step 310: Determine the radius of the second cross-sectional circle of the overpressure balloon based on the first final value, and calculate the radius difference between the second cross-sectional circle and the first cross-sectional circle; the height of the second cross-sectional circle in the overpressure balloon is the same as the height of the first cross-sectional circle in the sphere; the second cross-sectional circle is a cross-sectional circle along any point on the generatrix of the overpressure balloon and perpendicular to the axis of rotation of the overpressure balloon;

[0059] Step 320: If the radius difference is greater than the radius difference threshold in the termination condition, or if the minimum radius of the second cross-sectional circle is less than 0, then subtract the preset angle value from the sphere bottom angle in the initial value, return and execute the step of solving the generatrix-stress equation system based on the initial value to obtain the first final value of the overpressure balloon; until the radius difference is less than or equal to the radius difference threshold in the termination condition, and the minimum radius of the second cross-sectional circle is greater than or equal to 0, execute the step of determining whether the volume difference is greater than the volume difference threshold in the termination condition.

[0060] After obtaining the first final value, the radius of the second cross-sectional circle of the overpressure balloon to be solved is determined based on the first final value, and the radius difference Δr between the second cross-sectional circle and the first cross-sectional circle is calculated. The second cross-sectional circle is a cross-sectional circle along any point on the generatrix of the overpressure balloon to be solved, and perpendicular to the axis of rotation of the overpressure balloon to be solved. Furthermore, the height of the second cross-sectional circle in the overpressure balloon to be solved is the same as the height of the first cross-sectional circle in the sphere. If the radius difference Δr between the second cross-sectional circle and the first cross-sectional circle is greater than the radius difference threshold r in the termination condition... e Or, the minimum radius r of the second cross-section circle. min If the initial value is 0, then the preset angle value Δθ is subtracted from the sphere bottom angle θ0 in the initial value, and this is used as the new initial value. The generatrix-stress equation is solved again based on the new initial value until the first final value satisfies the termination condition. Then, the volume difference value ΔV is checked to see if it is greater than the preset volume difference threshold V. e The steps.

[0061] It should be noted that the height of the cross-sectional circle in the overpressure balloon can be determined based on the distance between the cross-sectional circle and the vertex of the balloon's bottom; the bottom angle θ is the angle between the tangent of the generatrix and the rotation angle of the overpressure balloon at the intersection of the cross-sectional circle and the generatrix. Therefore, when the bottom angle changes, the height and radius of the cross-sectional circle will also change, thus altering the value of r.

[0062] Furthermore, the circumferential stress condition of the overpressure balloon should satisfy:

[0063]

[0064] In Formula 2, n is a positive integer greater than 1, θ0 is the bottom angle of the overpressure balloon, and p max This indicates the maximum overpressure of the overpressure balloon.

[0065] Reference Figure 2Another flowchart illustrating the numerical solution method for the overpressure balloon is shown. First, constant parameters such as the volume, surface density of the spherical membrane, overpressure, and bottom load of the overpressure balloon to be solved are obtained. Based on the obtained constant parameters, a set of generatrix-stress equations for a sphere is constructed. The generatrix-stress equations for the sphere are solved to determine the target parameters of the overpressure balloon to be solved.

[0066] The specific solution process includes: obtaining initial values, which include the generatrix arc length s of the overpressure balloon to be solved, the bottom angle θ0 of the balloon, and the circumferential stress value σ. c ; Obtain the preset termination condition r e V e The generatrix-stress equation is solved based on the initial values ​​to obtain the corresponding generatrix shape. Based on the volume of the overpressure balloon corresponding to this generatrix shape, the difference Δr between the radius of the cross-sectional circle at the same height (or the same bottom angle) as the spherical overpressure balloon is determined. It is then determined whether Δr is greater than r. e Or the minimum cross-sectional radius r of the corresponding overpressure balloon. min That is, whether the radius of the cross-sectional circle corresponding to the angle at the apex of the sphere's base is less than 0; if so, subtract the preset angle value Δθ from the sphere's base angle θ0 and solve again; until Δr is less than or equal to r. e , and r min When the value is greater than or equal to 0, determine whether the difference ΔV between the volume of the overpressure balloon and the given volume is greater than the preset volume difference threshold V. e If so, subtract the preset arc length value Δs from the initial value of the arc length s of the busbar, and then solve again; until ΔV is less than or equal to V. e Until then. When Δr is less than or equal to r e , and r min Greater than or equal to 0, and ΔV less than or equal to V e When the time is right, the spherical numerical solution of the overpressure balloon that meets the requirements can be obtained.

[0067] It is known that when the constant parameters such as the surface density of the spherical membrane, the overpressure inside and outside the balloon, and the load on the bottom of the sphere are different in the generatrix-stress equations, the spherical shape obtained by numerical solution may be different. These parameters, as input conditions for numerical solution of the spherical shape, can be determined and obtained according to the actual needs of the airship when designing a near-space tandem airship system.

[0068] In this embodiment, constant parameters of the overpressure balloon to be solved are obtained, including the balloon's load capacity. Based on these constant parameters, a generatrix-stress equation for a perfect sphere is constructed. By setting initial and termination conditions, the generatrix-stress equation is solved, transforming the solution of the overpressure balloon's generatrix-stress equation into a numerical solution of a boundary value problem, thus obtaining the target parameters for the overpressure balloon's shape. When designing the shape of the overpressure balloon based on the numerical values ​​of the solved target parameters, the influence of the load on the stress distribution under bidirectional tension conditions is considered. Therefore, compared to a perfect sphere, the solved overpressure balloon shape exhibits a more reasonable overall stress distribution under bidirectional tension conditions.

[0069] The numerical solution apparatus for overpressure balloons provided by the present invention will be described below. The numerical solution apparatus for overpressure balloons described below can be referred to in correspondence with the numerical solution method for overpressure balloons described above.

[0070] Reference Figure 3 The numerical solution apparatus for overpressure balloons provided by the present invention includes:

[0071] The parameter acquisition module 10 is used to acquire the constant parameters of the overpressure balloon to be solved; the constant parameters include the target volume, overpressure amount and surface density of the balloon.

[0072] Equation construction module 20 is used to construct the generatrix-stress equation set of the normal sphere corresponding to the overpressure balloon based on the constant parameters;

[0073] The numerical solution module 30 is used to obtain the initial values ​​and preset termination conditions of the busbar-stress equation system, and to iteratively solve the busbar-stress equation system based on the initial values ​​and the termination conditions to obtain the target parameters of the overpressure balloon.

[0074] In one embodiment, the termination condition includes a volume difference threshold, and the initial value includes the generatrix arc length of the overpressure balloon; the numerical solution module 30 is further configured to:

[0075] The first final value of the overpressure balloon is obtained by solving the generatrix-stress equations based on the initial values.

[0076] Determine the volume difference between the estimated volume of the overpressure balloon corresponding to the first final value and the target volume;

[0077] Determine whether the volume difference value is greater than the volume difference threshold in the termination condition;

[0078] If the volume difference value is greater than the volume difference threshold in the termination condition, then the preset arc length value is subtracted from the generatrix arc length in the initial value, and the step of solving the generatrix stress equations based on the initial value to obtain the first final value of the overpressure balloon is returned and executed; until the volume difference value is less than or equal to the volume difference threshold in the termination condition, the target parameters of the overpressure balloon are obtained according to the first final value.

[0079] In one embodiment, the generatrix-stress equations include the radius of a first cross-sectional circle; the first cross-sectional circle is any cross-sectional circle along any point on the generatrix of the sphere and perpendicular to the axis of rotation of the sphere; the initial value also includes the bottom angle of the overpressure balloon, and the termination condition also includes a radius difference threshold; the numerical solution module 30 is further used for:

[0080] The radius of the second cross-sectional circle of the overpressure balloon is determined based on the first final value, and the radius difference between the second cross-sectional circle and the first cross-sectional circle is calculated; the height of the second cross-sectional circle in the overpressure balloon is the same as the height of the first cross-sectional circle in the sphere; the second cross-sectional circle is a cross-sectional circle along any point on the generatrix of the overpressure balloon and perpendicular to the axis of rotation of the overpressure balloon;

[0081] If the radius difference is greater than the radius difference threshold in the termination condition, or if the minimum radius of the second cross-section circle is less than 0, then the preset angle value is subtracted from the sphere bottom angle in the initial value, and the process returns to and executes the step of solving the generatrix-stress equation system based on the initial value to obtain the first final value of the overpressure balloon; until the radius difference is less than or equal to the radius difference threshold in the termination condition, and the minimum radius of the second cross-section circle is greater than or equal to 0, the step of determining whether the volume difference is greater than the volume difference threshold in the termination condition is executed.

[0082] In one embodiment, the busbar-stress equations are:

[0083]

[0084] Where, σ m The meridional stress and σ of the overpressure balloon c Let be the circumferential stress of the overpressure balloon, r be the radius of the cross-sectional circle at any point along the generatrix of the sphere and perpendicular to the axis of rotation of the sphere; w = ρg, where ρ is the surface density of the spherical membrane of the overpressure balloon and g is the acceleration due to gravity; p be the overpressure of the overpressure balloon, s be the arc length of the generatrix of the overpressure balloon, z be the height of the sphere, A be the surface area of ​​the sphere, and V be the target volume of the overpressure balloon.

[0085] In one embodiment, the circumferential stress of the overpressure balloon satisfies:

[0086]

[0087] n is a positive integer greater than 1, θ0 is the bottom angle of the overpressure balloon, and p max This indicates the maximum overpressure of the overpressure balloon.

[0088] In one embodiment, the target parameter includes the generatrix shape of the overpressure balloon.

[0089] Figure 4 An example is a schematic diagram of the physical structure of an electronic device, such as... Figure 4 As shown, the electronic device may include: a processor 410, a communication interface 420, a memory 830, and a communication bus 440, wherein the processor 410, the communication interface 420, and the memory 430 communicate with each other through the communication bus 440. The processor 410 can call logical instructions in the memory 430 to execute a numerical solution method for the overpressure balloon, the method including:

[0090] Obtain the constant parameters of the overpressure balloon to be solved; the constant parameters include the target volume, overpressure, surface density of the balloon membrane, and load capacity of the overpressure balloon.

[0091] Based on the constant parameters, construct the generatrix-stress equation system for the spherical shape corresponding to the overpressure balloon;

[0092] The initial values ​​and preset termination conditions of the busbar-stress equations are obtained. Based on the initial values ​​and the termination conditions, the busbar-stress equations are iteratively solved to obtain the target parameters of the overpressure balloon.

[0093] Furthermore, the logical instructions in the aforementioned memory 430 can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, essentially, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0094] On the other hand, the present invention also provides a computer program product, the computer program product comprising a computer program that can be stored on a non-transitory computer-readable storage medium, wherein when the computer program is executed by a processor, the computer is able to execute the numerical solution method for the overpressure balloon provided by the above methods, the method comprising:

[0095] Obtain the constant parameters of the overpressure balloon to be solved; the constant parameters include the target volume, overpressure, surface density of the balloon membrane, and load capacity of the overpressure balloon.

[0096] Based on the constant parameters, construct the generatrix-stress equation system for the spherical shape corresponding to the overpressure balloon;

[0097] The initial values ​​and preset termination conditions of the busbar-stress equations are obtained. Based on the initial values ​​and the termination conditions, the busbar-stress equations are iteratively solved to obtain the target parameters of the overpressure balloon.

[0098] In another aspect, the present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the numerical solution method for the overpressure balloon provided by the methods described above, the method comprising:

[0099] Obtain the constant parameters of the overpressure balloon to be solved; the constant parameters include the target volume, overpressure, surface density of the balloon membrane, and load capacity of the overpressure balloon.

[0100] Based on the constant parameters, construct the generatrix-stress equation system for the spherical shape corresponding to the overpressure balloon;

[0101] The initial values ​​and preset termination conditions of the busbar-stress equations are obtained. Based on the initial values ​​and the termination conditions, the busbar-stress equations are iteratively solved to obtain the target parameters of the overpressure balloon.

[0102] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without any creative effort.

[0103] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0104] 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 of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A numerical solution method for overpressure balloons, characterized in that, include: Obtain the constant parameters of the overpressure balloon to be solved; the constant parameters include the target volume, overpressure, surface density of the balloon membrane, and load capacity of the overpressure balloon; Based on the constant parameters, construct the generatrix-stress equation system for the spherical shape corresponding to the overpressure balloon; The initial values ​​and preset termination conditions of the busbar-stress equations are obtained. Based on the initial values ​​and the termination conditions, the busbar-stress equations are iteratively solved to obtain the target parameters of the overpressure balloon. The termination condition includes a volume difference threshold, and the initial value includes the arc length of the generatrix of the overpressure balloon; the step of iteratively solving the generatrix-stress equations based on the initial value and the termination condition to obtain the target parameters of the overpressure balloon includes: The first final value of the overpressure balloon is obtained by solving the generatrix-stress equations based on the initial values. Determine the volume difference between the estimated volume of the overpressure balloon corresponding to the first final value and the target volume; Determine whether the volume difference value is greater than the volume difference threshold in the termination condition; If the volume difference value is greater than the volume difference threshold in the termination condition, then the preset arc length value is subtracted from the generatrix arc length in the initial value, and the step of solving the generatrix-stress equation system based on the initial value to obtain the first final value of the overpressure balloon is returned and executed; until the volume difference value is less than or equal to the volume difference threshold in the termination condition, the target parameters of the overpressure balloon are obtained according to the first final value.

2. The numerical solution method for the overpressure balloon according to claim 1, characterized in that, The generatrix-stress equation set includes the radius of the first cross-sectional circle; the first cross-sectional circle is any cross-sectional circle along any point on the generatrix of the sphere and perpendicular to the axis of rotation of the sphere; the initial value also includes the bottom angle of the overpressure balloon, and the termination condition also includes a radius difference threshold.

3. The numerical solution method for the overpressure balloon according to claim 2, characterized in that, After solving the generatrix-stress equations based on the initial values ​​to obtain the first final value of the overpressure balloon, the method further includes: The radius of the second cross-sectional circle of the overpressure balloon is determined based on the first final value, and the radius difference between the second cross-sectional circle and the first cross-sectional circle is calculated; the height of the second cross-sectional circle in the overpressure balloon is the same as the height of the first cross-sectional circle in the sphere; the second cross-sectional circle is a cross-sectional circle along any point on the generatrix of the overpressure balloon and perpendicular to the axis of rotation of the overpressure balloon; If the radius difference is greater than the radius difference threshold in the termination condition, or if the minimum radius of the second cross-section circle is less than 0, then the preset angle value is subtracted from the sphere bottom angle in the initial value, and the process returns to and executes the step of solving the generatrix-stress equation system based on the initial value to obtain the first final value of the overpressure balloon; until the radius difference is less than or equal to the radius difference threshold in the termination condition, and the minimum radius of the second cross-section circle is greater than or equal to 0, the step of determining whether the volume difference is greater than the volume difference threshold in the termination condition is executed.

4. The numerical solution method for the overpressure balloon according to claim 3, characterized in that, The busbar-stress equation set is as follows: ； in, The meridional stress of the overpressure balloon, The circumferential stress of the overpressure balloon, Let be the radius of the cross-sectional circle along any point on the generatrix of the sphere and perpendicular to the axis of rotation of the sphere; g, Let g be the surface density of the spherical membrane of the overpressure balloon, and g be the acceleration due to gravity. Let be the overpressure amount of the overpressure balloon, s be the generatrix arc length of the overpressure balloon, z be the height of the sphere, A be the surface area of ​​the sphere, and V be the target volume of the overpressure balloon.

5. The numerical solution method for the overpressure balloon according to claim 4, characterized in that, The circumferential stress of the overpressure balloon satisfies: ； n is a positive integer greater than 1. The angle of the bottom of the overpressure balloon, This indicates the maximum overpressure of the overpressure balloon.

6. The numerical solution method for the overpressure balloon according to claim 1, characterized in that, The target parameters include the generatrix shape of the overpressure balloon.

7. A numerical solution device for an overpressure balloon, characterized in that, The numerical solution method for overpressure balloons as described in claim 1 includes: The parameter acquisition module is used to acquire the constant parameters of the overpressure balloon to be solved; the constant parameters include the target volume, overpressure, and surface density of the balloon. The equation construction module is used to construct the generatrix-stress equation system corresponding to the right sphere of the overpressure balloon based on the constant parameters. The numerical solution module is used to obtain the initial values ​​and preset termination conditions of the busbar-stress equation system, and to iteratively solve the busbar-stress equation system based on the initial values ​​and the termination conditions to obtain the target parameters of the overpressure balloon.

8. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the numerical solution method for the overpressure balloon as described in any one of claims 1 to 6.

9. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the numerical solution method for the overpressure balloon as described in any one of claims 1 to 6.

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