Finite element coupling simulation calculation method for interaction of reinforcing steel bars and concrete

Abstract

The invention relates to a finite element coupling simulation calculation method for interaction of reinforcing steel bars and concrete, which comprises the following steps: dispersing the reinforcing steel bars into a beam unit whole formed by connecting a plurality of beam units, and dispersing the concrete into an entity unit whole formed by connecting a plurality of entity units; embedding the whole beam unit into the whole entity unit; two coupling nodes are added on each beam unit; constructing a subordinate beam based on the beam unit nodes on the whole beam unit and the added coupling nodes; updating the mass and momentum of any entity unit node on the first entity unit based on the mass and speed of the first beam unit node and the two coupling nodes on the slave beam; calculating the updated speed of the entity unit node based on the updated quality and momentum of the entity unit node; and on the basis of the updated speed of the entity unit nodes, the speed of the first beam unit node located in the first entity unit on the beam unit is updated, and coupling of the reinforcing steel bars and the concrete is achieved.

Description

Technical Field

[0001] This application relates to the technical field of numerical simulation analysis, and particularly to a finite element coupling simulation calculation method for the interaction between steel bars and concrete. Background Art

[0002] There are significant defects in the prior art when simulating the interaction between steel bars and concrete, mainly including the following points: 1. Traditional non - homogeneous material models model steel bars and concrete as a whole. Although the modeling process is simplified, since steel bars are not explicitly modeled, the interface behavior between steel bars and concrete (such as stress transfer and bond - slip) cannot be accurately reflected, resulting in a large deviation between the simulation results and the actual engineering situation in cases such as crack propagation and local stress concentration.

[0003] 2. The co - node modeling method discretizes steel bars into beam elements, discretizes concrete into solid elements, and connects the two through shared nodes. The mesh generation process is complex and time - consuming. Especially when dealing with complex geometric structures, a large amount of manual adjustment is required to ensure node matching. In addition, this method is sensitive to mesh quality, and irregular meshes are likely to lead to numerical instability or large errors.

[0004] 3. When the traditional finite element method couples steel bars and concrete, it usually requires fine mesh generation for the entire structure, resulting in a sharp increase in the number of degrees of freedom and high computational costs. Especially in nonlinear analysis or dynamic response analysis, the calculation time and resource consumption increase significantly, restricting its wide application in actual engineering. Summary of the Invention

[0005] Based on this, it is necessary to provide a finite element coupling simulation calculation method for the interaction between steel bars and concrete, including: S1: Discretize the steel bars into an overall beam element connected by several beam elements, and share beam element nodes at the connections of the beam elements; discretize the concrete into an overall solid element connected by several solid elements, and share solid element nodes at the connections of the solid elements; S2: Embed the overall beam element into the overall solid element, and distribute beam elements in each solid element; add two coupling nodes to each beam element; construct a subordinate beam based on the beam element nodes on the overall beam element and the added coupling nodes; the first beam element node on the subordinate beam corresponds to the first beam element node on the first beam element; S3: Use the shape function to obtain the velocities of the two coupling nodes located in the first solid element on the subordinate beam; update the mass and momentum of any solid element node on the first solid element based on the mass and velocities of the first beam element node and the two coupling nodes on the subordinate beam; the first beam element node on the subordinate beam is located in the first solid element; S4: Calculate the updated velocity of the entity element nodes based on the updated mass and momentum of the entity element nodes; update the velocity of the first beam element node on the beam element located in the first entity element based on the updated velocity of the entity element nodes, so as to realize the coupling of the steel bar and the concrete.

[0006] Preferably, calculating the velocities of two coupled nodes includes: Obtain the velocities of two beam element nodes on the first beam element; According to the velocities of two beam element nodes on the first beam element, and using the shape function, obtain the velocities of two coupled nodes on the subordinate beam located in the first entity element.

[0007] Preferably, the calculation formula for the velocities of two coupled nodes is: ; ; ; ; Wherein, represents the velocity of the first coupled node; represents the velocity of the second coupled node; represents the first shape function; represents the second shape function; represents the first isoparametric coordinate of the first coupled node; represents the first isoparametric coordinate of the second coupled node; represents the velocity of the first beam element node on the beam element located in the first entity element; represents the velocity of the second beam element node on the beam element located in the first entity element; represents the first isoparametric coordinate of any point within the element.

[0008] Preferably, the update process of the mass and momentum of the entity element nodes includes: Obtain the mass and momentum of any entity element node in the first entity element; Obtain the masses of the first beam element node and two coupled nodes on the subordinate beam; Based on the mass of the first beam element node on the subordinate beam, the masses of two coupled nodes, and the shape functions at the corresponding nodes, calculate the mass assigned to the entity element node by the corresponding node; Add the mass assigned to the entity element node by each node to the mass of any entity element node in the first entity element to update the mass of the corresponding entity element node; Based on the mass assigned to the entity element node by each node and the velocity of the corresponding node, calculate the momentum assigned to the entity element node by each node; The momentum of each node assigned to the entity unit node is added to the momentum of any one entity unit node in the first entity unit, and the momentum of the corresponding entity unit node is updated.

[0009] Preferably, the update formula for the mass of the entity unit node is: ; Wherein, represents the updated mass of the first entity unit node in the first entity unit; represents the mass of the first entity unit node in the first entity unit before update; represents the shape function at the node; represents the mass of the first beam element node on the subordinate beam; represents the mass of the first coupling node located in the first entity unit on the subordinate beam; represents the mass of the second coupling node located in the first entity unit on the subordinate beam; represents the first isoparametric coordinate of the first beam element node on the subordinate beam; represents the second isoparametric coordinate of the first beam element node on the subordinate beam; represents the third isoparametric coordinate of the first beam element node on the subordinate beam; represents the first isoparametric coordinate of the first coupling node; represents the second isoparametric coordinate of the first coupling node; represents the third isoparametric coordinate of the first coupling node; represents the first isoparametric coordinate of the second coupling node; represents the second isoparametric coordinate of the second coupling node; represents the third isoparametric coordinate of the second coupling node.

[0010] Preferably, the update formula for the momentum of the entity unit node is: ; Wherein, represents the updated momentum of the first entity unit node in the first entity unit; represents the momentum of the first entity unit node in the first entity unit before update; represents the velocity of the first beam element node on the subordinate beam, and the velocity is equal to the velocity ; represents the velocity of the first coupling node; represents the velocity of the second coupling node.

[0011] Preferably, the update process of the velocity of the first beam element node on the beam element includes: Update the velocity of the first beam element node on the subordinate beam based on the updated velocity of the entity unit node; Assign the updated velocity of the first beam element node on the subordinate beam to the velocity of the first beam element node on the beam element to obtain the updated velocity of the first beam element node on the beam element.

[0012] Preferably, the update formula for the velocity of the first beam element node on the subordinate beam is: ; Where represents the updated velocity of the first beam element node on the subordinate beam; represents the shape function at the node; represents the updated velocity of the first entity unit node in the first solid unit; represents the first isoparametric coordinate of the first beam element node on the subordinate beam; represents the second isoparametric coordinate of the first beam element node on the subordinate beam; represents the third isoparametric coordinate of the first beam element node on the subordinate beam.

[0013] Beneficial effects: This method couples steel bars and concrete through the subordinate beam, automatically establishing the connection relationship between steel bars and concrete, greatly reducing the dependence on mesh division. Users do not need to manually adjust the mesh matching between steel bars and concrete, thus significantly improving the modeling efficiency; this method couples beam elements and solid elements through mass and momentum, optimizing the construction and solution of the coupling matrix, and improving the simulation efficiency and accuracy. Description of the Drawings

[0014] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings required for use in the description of the embodiments or the prior art. Obviously, the drawings in the following description are only some embodiments of the present application. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0015] Figure 1 is the flowchart of the finite element coupling simulation calculation method for the interaction between steel bars and concrete in the embodiments of the present application.

[0016] Figure 2 is the coupling schematic diagram of steel bars and concrete in the embodiments of the present application.

[0017] Figure 3 is the coupling schematic diagram of concrete and the subordinate beam in the embodiments of the present application.

[0018] Figure 4 is the coupling schematic diagram of the subordinate beam and steel bars in the embodiments of the present application. Detailed Implementation Manner

[0019] To make the above objects, features, and advantages of the present application more obvious and understandable, the following will provide a detailed description of the specific implementation manner of the present application in conjunction with the accompanying drawings. Many specific details are set forth in the following description in order to fully understand the present application. However, the present application can be implemented in many other ways different from those described herein, and those skilled in the art can make similar improvements without departing from the connotation of the present application. Therefore, the present application is not limited by the specific embodiments disclosed below.

[0020] In addition, the terms "first" and "second" are only used for descriptive purposes and cannot be construed as indicating or implying relative importance or implicitly specifying the quantity of the indicated technical features. Thus, the features defined with "first" and "second" may explicitly or implicitly include at least one of such features. In the description of the present application, "a plurality of" means at least two, such as two, three, etc., unless otherwise specifically defined.

[0021] As Figure 1 shown, this embodiment provides a finite element coupling simulation calculation method for the interaction between steel bars and concrete, including: S1: Discretize the steel bars into a beam element assembly connected by 4 beam elements, and share beam element nodes at the connections of the beam elements; discretize the concrete into a solid element assembly connected by 4 solid elements, and share solid element nodes at the connections of the solid elements.

[0022] In this embodiment, the steel bars are discretized using beam elements to accurately simulate their tensile, bending, and shear behaviors; the concrete is discretized using solid elements to capture its three-dimensional stress state and phenomena such as crack propagation.

[0023] S2: Embed the beam element assembly into the solid element assembly, and beam elements are distributed in each solid element; to avoid the situation of reduced coupling accuracy caused by the absence of beam element nodes in the solid element, add two coupling nodes to each beam element, as Figure 2 shown; construct a subordinate beam based on the beam element nodes on the beam element assembly and the added coupling nodes; the first beam element node on the subordinate beam corresponds to the first beam element node on the first beam element, and the coupling of the subordinate beam with the concrete is as Figure 3 shown, and the coupling of the subordinate beam with the steel bars is as Figure 4 shown.

[0024] S3: Obtain the velocities of the two coupling nodes located in the first solid element on the subordinate beam using the shape function; update the mass and momentum of any solid element node on the first solid element based on the mass and velocities of the first beam element node and the two coupling nodes on the subordinate beam; the first beam element node on the subordinate beam is located in the first solid element.

[0025] Specifically, calculating the velocities of two coupled nodes includes: Obtaining the velocities of two beam element nodes on the first beam element; Based on the velocities of the two beam element nodes on the first beam element, and using the shape function to obtain the velocities of the two coupled nodes located in the first solid element on the subordinate beam.

[0026] Furthermore, the calculation formula for the velocities of the two coupled nodes is: ; ; ; ; where represents the velocity of the first coupled node; represents the velocity of the second coupled node; represents the first shape function; represents the second shape function, and are shape functions acting on a one-dimensional element; represents the first isoparametric coordinate of the first coupled node; represents the first isoparametric coordinate of the second coupled node; represents the velocity of the first beam element node on the beam element located in the first solid element; represents the velocity of the second beam element node on the beam element located in the first solid element; represents the first isoparametric coordinate of any point within the element.

[0027] Even further, the update process of the mass and momentum of the solid element nodes includes: Obtaining the mass and momentum of any solid element node in the first solid element; Obtaining the masses of the first beam element node and the two coupled nodes on the subordinate beam, and the specific method is as follows: Taking the subordinate beam corresponding to the first beam element in Figure 4 as an example, there are two beam element nodes on the first beam element, with masses and respectively, then the mass of the first beam element node is ; and the mass of the corresponding node on the subordinate beam is distributed according to the masses of the subordinate beams ab, bc, and cd. The added two coupled nodes evenly divide the first beam element, so the masses of the subordinate beams ab, bc, and cd are the same, all being , by distributing the mass of the subordinate beams in each segment to the nodes on the subordinate beams, the mass of the first beam element node, the masses of the two coupling nodes, and the mass of the second beam element node on the subordinate beam can be obtained: ; ; ; ; Among them, represents the mass of the first beam element node on the subordinate beam; represents the mass of the first coupling node in the first solid element on the subordinate beam; represents the mass of the second coupling node in the first solid element on the subordinate beam; represents the mass of the second beam element node on the subordinate beam.

[0028] Based on the mass of the first beam element node on the subordinate beam, the masses of the two coupling nodes, and the shape functions at the corresponding nodes, calculate the mass assigned by the corresponding nodes to the solid element nodes; Add the mass assigned by each node to the solid element nodes to the mass of any one solid element node in the first solid element to update the mass of the corresponding solid element node; the update formula for the mass of the solid element node is: ; Among them, represents the updated mass of the first solid element node in the first solid element; represents the mass of the first solid element node in the first solid element before update; represents the shape function at the node; represents the mass of the first beam element node on the subordinate beam; represents the mass of the first coupling node in the first solid element on the subordinate beam; represents the mass of the second coupling node in the first solid element on the subordinate beam; represents the three-dimensional isoparametric coordinates of the first beam element node on the subordinate beam; represents the three-dimensional isoparametric coordinates of the first coupling node; represents the three-dimensional isoparametric coordinates of the second coupling node; represents the first isoparametric coordinate of the first beam element node on the subordinate beam; represents the second isoparametric coordinate of the first beam element node on the subordinate beam; represents the third isoparametric coordinate of the first beam element node on the subordinate beam; represents the first isoparametric coordinate of the first coupling node; Represents the second isoparametric coordinate of the first coupling node; Represents the third isoparametric coordinate of the first coupling node; Represents the first isoparametric coordinate of the second coupling node; Represents the second isoparametric coordinate of the second coupling node; Represents the third isoparametric coordinate of the second coupling node.

[0029] In this embodiment, the shape function at the node Is the shape function acting on the three-dimensional element. Taking the hexahedron element as an example, the shape functions of each point on the hexahedron element are: ; ; ; ; ; ; ; ; Among them, Represents the first isoparametric coordinate of any point within the element; Represents the second isoparametric coordinate of any point within the element; Represents the third isoparametric coordinate of any point within the element.

[0030] Based on the mass assigned to the solid element node by each node and the velocity of the corresponding node, calculate the momentum assigned to the solid element node by each node; Add the momentum assigned to the solid element node by each node to the momentum of any one solid element node in the first solid element to update the momentum of the corresponding solid element node; The update formula for the momentum of the solid element node is: ; Among them, Represents the updated momentum of the first solid element node in the first solid element; Represents the momentum of the first solid element node in the first solid element before update; Represents the velocity of the first beam element node on the subordinate beam, and the velocity Is equal to the velocity ; Represents the velocity of the first coupling node; Represents the velocity of the second coupling node.

[0031] S4: Calculate the updated velocity of the solid element nodes based on the updated mass and momentum of the solid element nodes; update the velocity of the first beam element node on the beam element located in the first solid element based on the updated velocity of the solid element nodes, thereby realizing the coupling between the steel bars and the concrete.

[0032] Specifically, the calculation formula for the updated velocity of the solid element nodes is: ; where represents the updated velocity of the first solid element node in the first solid element; represents the updated momentum of the first solid element node in the first solid element; represents the updated mass of the first solid element node in the first solid element.

[0033] The process of updating the velocity of the first beam element node on the beam element includes: Update the velocity of the first beam element node on the subordinate beam based on the updated velocity of the solid element nodes; Assign the updated velocity of the first beam element node on the subordinate beam to the velocity of the first beam element node on the beam element to obtain the updated velocity of the first beam element node on the beam element.

[0034] Furthermore, the update formula for the velocity of the first beam element node on the subordinate beam is: ; where represents the updated velocity of the first beam element node on the subordinate beam; represents the shape function at the node; represents the updated velocity of the first solid element node in the first solid element; represents the first isoparametric coordinate of the first beam element node on the subordinate beam; represents the second isoparametric coordinate of the first beam element node on the subordinate beam; represents the third isoparametric coordinate of the first beam element node on the subordinate beam.

[0035] Even further, assign the updated velocity of the first beam element node on the subordinate beam to the velocity of the first beam element node on the beam element located in the first solid element to obtain the updated velocity of the first beam element node on the beam element.

[0036] The finite element coupling simulation calculation method for the interaction between steel bars and concrete provided in this embodiment has the following beneficial effects: 1. This method proposes an adaptive finite element coupling algorithm. It constructs subordinate beams according to the relative positions and geometric features of steel bars and concrete, automatically adjusts the coupling parameters, ensures the accuracy and stability of calculations, and realizes mesh arbitrariness without sharing nodes, simplifies the modeling process, and avoids the mesh dependence problem of traditional methods.

[0037] 2. This method optimizes the construction and solution of the coupling matrix by coupling beam elements and solid elements through mass and momentum, improving the simulation efficiency and accuracy. 3. Combining an advanced nonlinear material model with the adaptive finite element method significantly enhances the ability to simulate complex material behaviors.

[0038] The technical features of the above-described embodiments can be combined arbitrarily. For the sake of brevity of description, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, it should be considered to be within the scope described in this specification.

[0039] The above-described embodiments merely represent several implementation manners of the present application. Their descriptions are relatively specific and detailed, but should not be construed as limiting the scope of the patent application. It should be noted that for those of ordinary skill in the art, without departing from the concept of the present application, several modifications and improvements can be made, and these all belong to the protection scope of the present application. Therefore, the protection scope of the patent of the present application shall be subject to the appended claims.

Claims

1. A finite element coupling simulation calculation method for the interaction between steel bars and concrete, characterized in that Including: S1: Discretize the steel bars into an overall beam element connected by several beam elements, and the beam element joints share beam element nodes; discretize the concrete into an overall solid element connected by several solid elements, and the solid element joints share solid element nodes; S2: Embed the overall beam element into the overall solid element, and beam elements are distributed in each solid element; add two coupling nodes to each beam element; construct a subordinate beam based on the beam element nodes on the overall beam element and the added coupling nodes; the first beam element node on the subordinate beam corresponds to the first beam element node on the first beam element; S3: Use the shape function to obtain the velocities of the two coupling nodes located in the first solid element on the subordinate beam; Based on the masses and velocities of the first beam element node and the two coupling nodes on the subordinate beam, update the mass and momentum of any solid element node on the first solid element; The first beam element node on the subordinate beam is located in the first solid element; S4: Calculate the updated velocity of the solid element node based on the updated mass and momentum of the solid element node; update the velocity of the first beam element node located in the first solid element on the beam element based on the updated velocity of the solid element node, realizing the coupling of the steel bars and the concrete.

2. The finite element coupling simulation calculation method for the interaction between steel bars and concrete according to claim 1, characterized in that Calculating the velocities of the two coupling nodes includes: Obtain the velocities of the two beam element nodes on the first beam element; According to the velocities of the two beam element nodes on the first beam element, and use the shape function to obtain the velocities of the two coupling nodes located in the first solid element on the subordinate beam.

3. The finite element coupling simulation calculation method for the interaction between steel bars and concrete according to claim 2, characterized in that, The calculation formula for the velocities of the two coupling nodes is: ； ； ； ； Among them, represents the velocity of the first coupling node; represents the velocity of the second coupling node; represents the first shape function; represents the second shape function; represents the first isoparametric coordinate of the first coupling node; represents the first isoparametric coordinate of the second coupling node; represents the velocity of the first beam element node on the beam element located in the first solid element; represents the velocity of the second beam element node on the beam element located in the first solid element; represents the first isoparametric coordinate of any point within the element.

4. The finite element coupling simulation calculation method for the interaction between steel bars and concrete according to claim 3, characterized in that The update process of the mass and momentum of the solid element node includes: Obtain the mass and momentum of any solid element node in the first solid element; Obtain the masses of the first beam element node and the two coupling nodes on the subordinate beam; Based on the mass of the first beam element node on the subordinate beam, the masses of the two coupling nodes, and the shape function at the corresponding nodes, calculate the mass assigned by the corresponding nodes to the solid element node; Add the masses assigned by each node to the solid element node to the mass of any solid element node in the first solid element to update the mass of the corresponding solid element node; Based on the masses assigned by each node to the solid element node and the velocities of the corresponding nodes, calculate the momentum assigned by each node to the solid element node; Add the momenta assigned by each node to the solid element node to the momentum of any solid element node in the first solid element to update the momentum of the corresponding solid element node.

5. The finite element coupling simulation calculation method for the interaction between steel bars and concrete according to claim 4, characterized in that, The update formula for the mass of the solid element node is: ； Among them, represents the updated mass of the first entity unit node in the first entity unit; represents the mass of the first entity unit node in the first entity unit before update; represents the shape function at the node; represents the mass of the first beam element node on the subordinate beam; represents the mass of the first coupling node located in the first entity unit on the subordinate beam; represents the mass of the second coupling node located in the first entity unit on the subordinate beam; represents the first isoparametric coordinate of the first beam element node on the subordinate beam; represents the second isoparametric coordinate of the first beam element node on the subordinate beam; represents the third isoparametric coordinate of the first beam element node on the subordinate beam; represents the first isoparametric coordinate of the first coupling node; represents the second isoparametric coordinate of the first coupling node; represents the third isoparametric coordinate of the first coupling node; represents the first isoparametric coordinate of the second coupling node; represents the second isoparametric coordinate of the second coupling node; represents the third isoparametric coordinate of the second coupling node.

6. The finite element coupling simulation calculation method for the interaction between steel bars and concrete according to claim 5, wherein The update formula for the momentum of the solid element node is: ； Among them, represents the updated momentum of the first entity unit node in the first entity unit; represents the momentum of the first entity unit node in the first entity unit before update; represents the velocity of the first beam element node on the subordinate beam, and the velocity is equal to the velocity ; represents the velocity of the first coupling node; represents the velocity of the second coupling node.

7. The finite element coupling simulation calculation method for the interaction between steel bars and concrete according to claim 1, characterized in that The update process of the velocity of the first beam element node on the beam element includes: Based on the updated velocity of the solid element node, update the velocity of the first beam element node on the subordinate beam; Assign the updated velocity of the first beam element node on the subordinate beam to the velocity of the first beam element node on the beam element to obtain the updated velocity of the first beam element node on the beam element.

8. The finite element coupling simulation calculation method for the interaction between steel bars and concrete according to claim 7, characterized in that The update formula for the velocity of the first beam element node on the subordinate beam is: ； Among them, represents the updated velocity of the first beam element node on the subordinate beam; represents the shape function at the node; represents the updated velocity of the first solid element node in the first solid element; represents the first isoparametric coordinate of the first beam element node on the subordinate beam; represents the second isoparametric coordinate of the first beam element node on the subordinate beam; represents the third isoparametric coordinate of the first beam element node on the subordinate beam.

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