Design method of elastic ring bubble-shaped buckling structure under double-ring constraint
By establishing differential equation systems and energy functional models, the critical strain of the elastic ring bubble buckling structure under double ring constraints is accurately predicted, which solves the problem that cannot be accurately analyzed in the existing technology, and realizes the stability design and application of the bubble buckling structure.
Patent Information
- Application Number
- CN202310586138.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2023-05-23
- Publication Date
- 2025-07-25
AI Technical Summary
The prior art cannot accurately analyze the evolution process of elastic ring bubble buckling structure under double ring constraints, resulting in the inability to determine its critical strain, which limits its application in the engineering field.
By establishing differential equation systems and boundary conditions, the buckling structure of the elastic ring is calculated, the critical perimeter ratios λ1, λ2, and λ3 are determined, and combined with the energy functional model, the generation of the bubbly buckling structure and the critical strain at the end are accurately predicted.
It provides a design method for accurately predicting the blister buckling structure of elastic rings, determines the conditions for its stable existence, is suitable for application design under the constraints of double rings of different sizes, calculates the inclination angle, curvature and internal force at any position, and is widely used in equipment such as peristaltic pumps.
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Figure CN120372836A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of mechanical structure design, and particularly relates to a design method for an elastic circular ring water bubble-shaped buckling structure under double circular ring constraints. Background Art
[0002] The buckling structure of an elastic circular ring is widely used in fields such as architecture and medical equipment. Among them, the water bubble-shaped buckling structure under double circular ring constraints is more stable than the traditional single-sided constraint and has no noise during the movement process. Therefore, it is suitable for applications in devices with obvious disturbances such as peristaltic pumps and rotary drives. However, due to the characteristics of large displacement and nonlinearity of the flexible material under load deformation, the current analysis methods for such buckling structures are mainly limited to experiments and finite element simulations. Among them, experiments cannot obtain complex information such as stress, strain, and curvature of the entire elastic circular ring. In the finite element analysis, the evolution of the buckling structure is a smooth transition, so the conditions for the stable existence of the water bubble-shaped buckling structure cannot be defined. At present, no work provides an accurate analysis and design for the evolution process of the elastic circular ring buckling structure under double circular ring constraints. However, when applying the water bubble-shaped buckling structure under double circular ring constraints to the engineering field, it is necessary to determine the critical strain of this buckling structure. Summary of the Invention
[0003] The purpose of the present invention is to provide a design method for an elastic circular ring water bubble-shaped buckling structure under double circular ring constraints, which is beneficial to accurately predicting the critical strains at the generation and end of the elastic circular ring water bubble-shaped buckling structure.
[0004] To achieve the above purpose, the technical solution adopted by the present invention is: a design method for an elastic circular ring water bubble-shaped buckling structure under double circular ring constraints, including an inner constraint circular ring with a radius of r, an outer constraint circular ring concentric with the inner constraint circular ring and having a radius of R, and an elastic circular ring with a perimeter of L, a thickness of h, and a width of b located in the channel between the inner constraint circular ring and the outer constraint circular ring; μ=(R - r) / R is the dimensionless constraint channel width, and λ = L / 2πR represents the perimeter ratio of the elastic circular ring to the outer constraint circular ring; when 0 < λ < λ1, the elastic circular ring adheres to the outer constraint circular ring to maintain the circular ring structure; as the perimeter of the elastic circular ring increases, when λ1 < λ < λ2, the elastic circular ring generates a water bubble-shaped buckling structure that does not contact the inner constraint circular ring; when λ2 < λ < λ3, the elastic circular ring generates a water bubble-shaped buckling structure that contacts the inner constraint circular ring; when λ3 < λ, the elastic circular ring generates an inclined water bubble-shaped buckling structure.
[0005] Further, to determine the critical perimeter ratios λ1, λ2, and λ3, the x and y coordinates of a rectangular coordinate system are introduced. With the center of the inner constraint circular ring and the outer constraint circular ring as the coordinate origin O, a differential equation system for describing the buckling structure of the elastic circular ring is established as:
[0006] Kθ″(s)-T xsinθ(s) + T y cosθ(s) = 0
[0007] x′ = (1 - ε)cosθ(s)
[0008] y′ = (1 - ε)sinθ(s)
[0009] where s represents the arc length of the elastic ring, θ(s) represents the angle between the tangent of the elastic curve at point s and the horizontal direction, K = EI represents the flexural rigidity, E represents the elastic modulus, and I represents the moment of inertia in the bending direction; θ”(s) represents the derivative of the curvature θ′(s), ε = ΔL / L represents the axial strain generated under the compressive action, ΔL is the axial deformation generated when the elastic ring is axially compressed, and the constant T x 、T y respectively represent the internal force components of the elastic ring in the x and y directions; set the vertex of the water bubble as the arc length origin s0, and the separation position of the elastic ring and the outer constraint ring is Combined with the continuity of the inclination angles and curvatures of each point on the buckling structure, and the boundary conditions satisfied by the buckling structure under the double-ring constraint, the water-bubble-shaped buckling structures under different conditions are solved; for the water-bubble-shaped buckling structure when it has not contacted the inner constraint ring, its boundary conditions are: θ(s0) = 0, x(s0) = 0, For the symmetric water-bubble-shaped buckling structure when it has contacted the inner constraint ring, the boundary adjustment of its right half adds additionally on the above basis: y(s0) = r, For the asymmetric water-bubble-shaped buckling structure when it is inclined, its boundary conditions change from to Calculate the compression energy stored when the elastic ring adheres to the outer constraint ring and the strain energy stored in the buckling structure of the elastic ring where A is the cross-sectional area of the elastic ring; the critical perimeter ratios λ1, λ2, and λ3 are respectively located at the intersection positions of the energy curves.
[0010] Furthermore, according to the differential equations and boundary conditions, the configurations of the water-bubble-shaped buckling structures under different conditions are obtained, and the deformation energy curves of different water-bubble-shaped buckling structures are further calculated. Through the intersection points of the deformation energy curves of different water-bubble-shaped buckling structures, the relationships between the critical perimeter ratios λ1, λ2, λ3 and the channel width ratio μ under different channel width ratios μ are obtained:
[0011] λ1 = 1.00232
[0012] λ2 = 0.05540μ + 0.98695
[0013] λ3 = 0.2355μ + 1.02509.
[0014] Compared with the prior art, the present invention has the following beneficial effects: It provides a design method for the water-bubble-shaped buckling structure of an elastic ring under double-ring constraints. This method can calculate the water-bubble-shaped buckling structure of an elastic ring under double-ring constraints, accurately predict the critical strains at the generation and end of the water-bubble structure, provide the conditions for the stable existence of the water-bubble structure, and provide necessary design parameters for the application of water-bubble structures under double-ring constraints of different sizes. It has a wide range of applications and is convenient to use. This method can also calculate the inclination angle, curvature, internal force, internal moment, and water-bubble arc length at any position on the water-bubble-shaped buckling structure of an elastic ring under double-ring constraints, which has important reference value for the design of related applications of the water-bubble-shaped buckling structure. BRIEF DESCRIPTION OF THE DRAWINGS
[0015] Figure 1 It is a schematic diagram of the water-bubble-shaped buckling structure of an elastic ring under double-ring constraints in an embodiment of the present invention.
[0016] Figure 2 It is a schematic diagram of the water-bubble-shaped buckling structure of an elastic ring that has not contacted the inner constraint ring in an embodiment of the present invention.
[0017] Figure 3 It is a schematic diagram of the water-bubble-shaped buckling structure of an elastic ring that has contacted the inner constraint ring in an embodiment of the present invention.
[0018] Figure 4 It is a schematic diagram of the inclined water-bubble-shaped buckling structure of an elastic ring in an embodiment of the present invention.
[0019] Figure 5 It is an evolution diagram of the buckling structure of an elastic ring under double-ring constraints in an embodiment of the present invention.
[0020] Figure 6 It is an equilibrium configuration diagram of the buckling structure of an elastic ring under double-ring constraints in an embodiment of the present invention.
[0021] Figure 7 It is a schematic diagram of the application of the water-bubble-shaped buckling structure of an elastic ring under double-ring constraints to a peristaltic pump in an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS
[0022] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.
[0023] It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the present application. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by those of ordinary skill in the technical field to which the present application belongs.
[0024] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present application. As used herein, unless the context clearly indicates otherwise, the singular forms are also intended to include the plural forms. In addition, it should also be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.
[0025] As Figure 1 shown, this embodiment provides a design method for an elastic ring buckling structure under double-ring constraints. The elastic ring buckling structure under double-ring constraints mainly includes an inner constraint ring 2 with a radius of r = 20 mm, an outer constraint ring 3 concentric with the inner constraint ring 2 and with a radius of R = 50 mm, and an elastic ring 1 with a perimeter of L, a thickness of h = 0.3 mm, and a width of b = 10 mm in the channel between the inner constraint ring 2 and the outer constraint ring 3. Let μ = (R - r) / R be the dimensionless constrained channel width, and λ = L / 2πR represent the perimeter ratio of the elastic ring 1 to the outer constraint ring 3; when 0 ≤ λ < λ1, the entire elastic ring 1 adheres to the outer constraint ring 3 to maintain the ring structure; as the perimeter of the elastic ring increases, when λ1 ≤ λ < λ2, the elastic ring 1 generates a blister-shaped buckling structure that does not contact the inner constraint ring 2; when λ2 ≤ λ < λ3, the elastic ring 1 generates a blister-shaped buckling structure that contacts the inner constraint ring 2; when λ3 ≤ λ, the elastic ring 1 generates an inclined blister-shaped buckling structure.
[0026] As Figure 5 shown, to determine the critical perimeter ratios λ1, λ2, λ3, the x and y coordinates of a rectangular coordinate system are introduced. With the center of the double-constraint ring formed by the inner constraint ring 2 and the outer constraint ring 3 as the coordinate origin O, the geometric conditions of the elastic ring are listed:
[0027] x′ = (1 - ε)cosθ(s), y′ = (1 - ε)sinθ(s) (1)
[0028] where s represents the arc length of the elastic ring, the blister vertex is set as s0 (s = 0), and the separation position of the elastic ring from the outer constraint ring is θ(s) represents the angle between the tangent of the elastic curve at point s and the horizontal direction. ε = ΔL / L represents the axial strain generated under the compression action, and ΔL is the axial deformation generated by the elastic ring 1 under the axial compression action.
[0029] Then, the energy functional equation of the elastic ring buckling structure is constructed:
[0030]
[0031] Among them, \(W\) represents the energy functional, \(K = EI\) represents the flexural rigidity, \(E\) represents the elastic modulus, \(I\) represents the moment of inertia in the bending direction, and \(A\) represents the cross-sectional area of the elastic ring. \(\theta''(s)\) represents the derivative of the curvature \(\theta'(s)\), and the constant \(T\) x 、\(T\) y respectively represent the internal force components of the elastic ring in the \(x\) and \(y\) directions. By taking the variation of the energy functional equation, the following second-order differential equations can be obtained:
[0032] \(K\theta''(s)-T\) x \(\sin\theta(s)+T\) y \(\cos\theta(s)=0\ (3)\)
[0033] Equations (1) and (3) constitute a system of differential equations describing the buckling structure of the elastic ring.
[0034] Set the vertex of the water bubble as the arc length origin \(s_0(s = 0)\), and the separation position of the elastic ring and the outer constraint ring is Combined with the continuity of the inclination angles and curvatures of each point on the buckling structure, as well as the boundary conditions satisfied by different buckling structures under the double-ring constraint, the system of differential equations composed of equations (1) and (3) can be solved, thereby obtaining the water-bubble-shaped buckling structures under different conditions. As Figure 2 shown, for the water-bubble-shaped buckling structure when it has not contacted the inner constraint ring, the boundary conditions are: \(\theta(s_0)=0\), \(x(s_0)=0\), As Figure 3 shown, for the symmetric water-bubble-shaped buckling structure when it has contacted the inner constraint ring, the boundary conditions for its right half part are additionally increased on the above basis: \(y(s_0)=r\), As Figure 4 shown, for the asymmetric water-bubble-shaped buckling structure when it is tilted, its boundary conditions change from to
[0035] Obtain the accurate configuration of the buckling structure according to the above system of differential equations and boundary conditions, and calculate the compression energy stored when the elastic ring adheres to the outer constraint ring and the strain energy stored in the buckling structure of the elastic ring The critical perimeter ratios \(\lambda_1\), \(\lambda_2\), \(\lambda_3\) are respectively located at the intersection positions of the energy curves; determine the evolution process of the buckling shape structure of the elastic ring under the double-ring constraint, with the abscissa being the perimeter ratio \(\lambda\) of the elastic ring and the outer constraint ring, and the ordinate being the dimensionless energy \(E\) bending / Eh 3 . The critical perimeter ratios \(\lambda_1\), \(\lambda_2\), \(\lambda_3\) are respectively located at the intersection positions of the energy curves.
[0036] Furthermore, calculate the critical perimeter ratios λ1, λ2, λ3 of the buckling structure at different channel width ratios μ, and perform linear fitting on the data of the three groups of critical perimeter ratios λ1, λ2, λ3 to obtain the relationship between the critical perimeter ratios λ1, λ2, λ3 and the channel width ratio μ:
[0037] λ1 = 1.00232 (4)
[0038] λ2 = 0.05540μ + 0.98695 (5)
[0039] λ3 = 0.2355μ + 1.02509 (6)
[0040] Based on equations (5) and (6), the axial strain range in which the bubble-shaped buckling structure stably exists is 0.05540μ + 0.98695 < ε < 0.2355μ + 1.02509, and draw the equilibrium configuration diagram of the elastic ring buckling structure, as Figure 6 shown.
[0041] The above energy functional model can provide necessary design parameters for the application of the bubble-shaped buckling structure. Taking the design of a peristaltic pump as an example, for the Figure 7 peristaltic pump, the rotating bubble-shaped buckling structure 4 alternately squeezes and releases the delivery hose 5 to pump the fluid. Combining the above energy functional model and the equilibrium configuration diagram of the elastic ring buckling structure, the size of the double-constrained ring and the perimeter of the elastic ring can be designed to ensure the stable existence of the bubble-shaped buckling structure. In addition, combining the above energy functional model, the pressure exerted by the bubble-shaped buckling structure 4 on the delivery hose 5 can be calculated, and then the flow rate and pressure of the liquid in the pipe can be controlled.
[0042] The above is only a preferred embodiment of the present invention, and it is not intended to limit the present invention in other forms. Any person skilled in the art may use the disclosed technical content to make changes or modifications into equivalent embodiments with equivalent changes. However, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention without departing from the technical solution content of the present invention still fall within the protection scope of the technical solution of the present invention.
Claims
1. A design method for an elastic circular ring blister buckling structure under double circular ring constraints, characterized in that It includes an inner constraint ring (2) with a radius of r, an outer constraint ring (3) concentric with the inner constraint ring (2) and having a radius of R, and an elastic ring (1) with a perimeter of L, a thickness of h, and a width of b in the channel between the inner constraint ring (2) and the outer constraint ring (3); μ = (R - r) / R is the dimensionless constraint channel width, and λ = L / 2πR represents the perimeter ratio of the elastic ring (1) to the outer constraint ring (3); when 0 ≤ λ < λ1, the elastic ring (1) adheres to the outer constraint ring (3) to maintain the ring structure; as the perimeter of the elastic ring increases, when λ1 ≤ λ < λ2, the elastic ring (1) generates a blister-shaped buckling structure that does not contact the inner constraint ring (2); when λ2 ≤ λ < λ3, the elastic ring (1) generates a blister-shaped buckling structure that contacts the inner constraint ring (2); when λ3 ≤ λ, the elastic ring (1) generates an inclined blister-shaped buckling structure.
2. The design method of an elastic ring water bubble-shaped buckling structure under the constraint of a double ring according to claim 1, characterized in that To determine the critical perimeter ratios λ1, λ2, and λ3, the x and y coordinates of a rectangular coordinate system are introduced. With the centers of the inner constraint ring (2) and the outer constraint ring (3) as the coordinate origin O, a differential equation system for describing the buckling structure of the elastic ring is established as follows: Kθ″(s) - T x sinθ(s) + T y cosθ(s) = 0 x′ = (1 - ε)cosθ(s) y′ = (1 - ε)sinθ(s) Among them, s represents the arc length of the elastic ring, θ(s) represents the angle between the tangent of the elastic curve at point s and the horizontal direction, K = EI represents the flexural rigidity, E represents the elastic modulus, and I represents the moment of inertia in the bending direction; θ”(s) represents the derivative of the curvature θ′(s), ε = ΔL / L represents the axial strain generated under the compressive action, ΔL is the axial deformation generated by the elastic ring (1) under the axial compressive action, and the constant T x and T y respectively represent the internal force components of the elastic ring in the x and y directions; set the vertex of the water bubble as the arc length origin s0, and the separation position of the elastic ring and the outer constraint ring as s. Combining the continuity of the inclination angles and curvatures of each point on the buckling structure, and the boundary conditions satisfied by the buckling structure under the double-ring constraint, the water bubble-shaped buckling structure under different conditions is solved; for the water bubble-shaped buckling structure when it has not contacted the inner constraint ring, its boundary conditions are: θ(s0) = 0, x(s0) = 0, For the symmetric water bubble-shaped buckling structure when it has contacted the inner constraint ring, an additional boundary adjustment for its right half is: y(s0) = r, For the asymmetric inclined water bubble-shaped buckling structure, its boundary conditions change from to Calculate the compression energy stored when the elastic ring adheres to the outer constraint ring and the strain energy stored in the buckling structure of the elastic ring where A is the cross-sectional area of the elastic ring; the critical perimeter ratios λ1, λ2, and λ3 are respectively located at the intersection positions of the energy curves.
3. The design method of an elastic circular ring water bubble-shaped buckling structure under the constraint of a double circular ring according to claim 2, characterized in that, According to the differential equation system and the boundary conditions, the configurations of the blister-shaped buckling structures under different conditions are obtained. Further, the deformation energy curves of different blister-shaped buckling structures are calculated. Through the intersection points of the deformation energy curves of different blister-shaped buckling structures, the relationships between the critical perimeter ratios λ1, λ2, λ3 and the channel width ratio μ under different channel width ratios μ are obtained: λ1 = 1.00232 λ2 = 0.05540μ + 0.98695 λ3 = 0.2355μ + 1.02509.