A finite element coupling simulation calculation method for interaction between steel bars and concrete

Abstract

The application relates to a finite element coupling simulation calculation method for the interaction between steel bars and concrete, which comprises the following steps: discretizing the steel bars into a whole of beam units connected by a plurality of beam units and discretizing the concrete into a whole of solid units connected by a plurality of solid units; embedding the whole of beam units into the whole of solid units; adding two coupling nodes on each beam unit; constructing a dependent beam based on the beam unit nodes on the whole of beam units and the added coupling nodes; updating the mass and momentum of any solid unit node on the first solid unit based on the mass and velocity of the first beam unit node and the two coupling nodes on the dependent beam; calculating the updated velocity of the solid unit node based on the updated mass and momentum of the solid unit node; and updating the velocity of the first beam unit node on the beam unit in the first solid unit based on the updated velocity of the solid unit node, so as to realize the coupling between the steel bars and the concrete.

Description

Technical Field

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

[0002] Existing technologies have significant drawbacks in simulating the interaction between steel and concrete, including the following:

[0003] 1. Traditional heterogeneous material models model steel bars and concrete as a whole. Although this simplifies the modeling process, the lack of explicit modeling of the steel bars prevents accurate reflection of the interfacial behavior between the steel bars and concrete (such as stress transfer and bond slip). This results in significant deviations from actual engineering conditions in simulation results when crack propagation and local stress concentration are present.

[0004] 2. The common node modeling method discretizes steel bars into beam elements and concrete into solid elements, connecting them through common nodes. The meshing process is complex and time-consuming, especially when dealing with complex geometries, requiring extensive manual adjustments to ensure node matching. Furthermore, this method is sensitive to mesh quality, and irregular meshes can lead to numerical instability or large errors.

[0005] 3. Traditional finite element methods, when coupling steel and concrete, typically require fine meshing of the entire structure, resulting in a surge in the number of degrees of freedom and high computational costs. This significantly increases computational time and resource consumption in nonlinear or dynamic response analysis, limiting their widespread application in practical engineering. Summary of the Invention

[0006] Based on this, it is necessary to provide a finite element coupling simulation calculation method for the interaction between steel bars and concrete, including:

[0007] S1: The steel bar is discretized into a beam unit connected by several beam units, and the beam unit nodes are shared at the beam unit connections; the concrete is discretized into a solid unit connected by several solid units, and the solid unit nodes are shared at the solid unit connections;

[0008] S2: The beam element is embedded in the solid element, with beam elements distributed in each solid element. Two coupling nodes are added to each beam element. A slave beam is constructed based on the beam element nodes on the entire beam element and the added coupling nodes. The first beam element node on the slave beam corresponds to the first beam element node on the first beam element.

[0009] S3: Use shape functions to obtain the velocities of the two coupled nodes on the slave beam located in the first solid element; based on the masses and velocities of the first beam element node and the two coupled nodes on the slave beam, update the mass and momentum of any solid element node on the first solid element; the first beam element node on the slave beam is located in the first solid element;

[0010] S4: Based on the updated mass and momentum of the solid unit node, the updated velocity of the solid unit node is calculated; based on the updated velocity of the solid unit node, the velocity of the first beam unit node located in the first solid unit on the beam unit is updated to achieve coupling between steel bars and concrete.

[0011] Preferably, calculating the speeds of the two coupling nodes includes:

[0012] Get the velocities of the two beam element nodes on the first beam element;

[0013] Based on the velocities of the two beam element nodes on the first beam element, the shape functions are used to obtain the velocities of the two coupled nodes on the slave beam located in the first solid element.

[0014] Preferably, the calculation formula for the speed of the two coupling nodes is:

[0015] ;

[0016] ;

[0017] ; ;

[0018] in, 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 of the first solid element; represents the velocity of the second beam element node on the beam element of the first solid element; Represents the first isoparametric coordinate of any point in the cell.

[0019] Preferably, the updating process of the mass and momentum of the entity element nodes includes:

[0020] Get the mass and momentum of any entity node in the first entity element;

[0021] Obtain the mass of the first beam element node and two coupling nodes on the slave beam;

[0022] Based on the mass of the first beam element node on the slave beam, the masses of the two coupling nodes and the shape functions at the corresponding nodes, the mass of the corresponding node assigned to the solid element node is calculated;

[0023] Add the mass of each node assigned to the solid element node to the mass of any solid element node in the first solid element, and update the mass of the corresponding solid element node;

[0024] Based on the mass of each node assigned to the solid element node and the velocity of the corresponding node, the momentum assigned to the solid element node by each node is calculated;

[0025] The momentum assigned to the solid element node of each node is added to the momentum of any solid element node in the first solid element, and the momentum of the corresponding solid element node is updated.

[0026] Preferably, the updating formula of the mass of the entity element node is:

[0027] ;

[0028] in, Indicates the updated mass of the first entity element node in the first entity element; Indicates the mass of the first entity element node in the first entity element before updating; represents the shape function at the node; represents the mass of the first beam element node on the slave beam; represents the mass of the first coupling node on the slave beam located in the first solid element; represents the mass of the second coupling node on the slave beam located in the first solid element; It represents the first isoparametric coordinate of the first beam element node on the slave beam; Represents the second isoparametric coordinate of the first beam element node on the slave beam; It represents the third isoparametric coordinate of the first beam element node on the slave 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 coupled node.

[0029] Preferably, the update formula of the momentum of the entity unit node is:

[0030] ;

[0031] in, Represents the updated momentum of the first entity element node in the first entity element; Represents the momentum of the first entity element node in the first entity element before updating; represents the velocity of the first beam element node on the slave beam, the velocity Equal to speed ; represents the velocity of the first coupling node; represents the velocity of the second coupled node.

[0032] Preferably, the process of updating the velocity of the first beam element node on the beam element includes:

[0033] Update the velocity of the first beam element node on the slave beam based on the updated velocity of the solid element node;

[0034] Assign the updated velocity of the first beam element node on the slave 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.

[0035] Preferably, the update formula for the velocity of the first beam element node on the slave beam is:

[0036] ;

[0037] in, represents the updated velocity of the first beam element node on the slave beam; represents the shape function at the node; Indicates the updated velocity of the first entity element node in the first entity element; It represents the first isoparametric coordinate of the first beam element node on the slave beam; Represents the second isoparametric coordinate of the first beam element node on the slave beam; Represents the third isoparametric coordinate of the first beam element node on the slave beam.

[0038] Beneficial effects: This method automatically establishes a connection between the steel bars and concrete by coupling the steel bars and concrete through subordinate beams, greatly reducing the dependence on meshing. Users no longer need to manually adjust the mesh matching between the steel bars and concrete, thereby significantly improving modeling efficiency. This method optimizes the construction and solution of the coupling matrix by coupling beam elements and solid elements through mass and momentum, thereby improving simulation efficiency and accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0040] Figure 1 This is a flow chart of the finite element coupling simulation calculation method for the interaction between steel bars and concrete in an embodiment of the present application.

[0041] Figure 2 Schematic diagram of the coupling between steel bars and concrete in an embodiment of the present application.

[0042] Figure 3 Schematic diagram of the coupling between concrete and subordinate beams in an embodiment of the present application.

[0043] Figure 4 Schematic diagram of the coupling between the subordinate beam and the steel bar in the embodiment of the present application. DETAILED DESCRIPTION

[0044] To make the above-mentioned objects, features, and advantages of the present application more clearly understood, the specific embodiments of the present application are described in detail below with reference to the accompanying drawings. The following description sets forth many specific details to facilitate a full understanding of the present application. However, the present application can be implemented in many other ways than those described herein, and those skilled in the art can make similar improvements without violating the scope of the present application. Therefore, the present application is not limited to the specific embodiments disclosed below.

[0045] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of the technical features being referred to. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of such features. Throughout the description of this application, "plurality" means at least two, for example, two, three, etc., unless otherwise specifically defined.

[0046] like Figure 1 As shown, this embodiment provides a finite element coupling simulation calculation method for the interaction between steel bars and concrete, including:

[0047] S1: The steel bars are discretized into a beam unit connected by four beam elements, and the beam unit nodes are shared at the beam unit connections; the concrete is discretized into a solid unit connected by four solid elements, and the solid unit nodes are shared at the solid unit connections.

[0048] In this embodiment, the steel bars are discretized using beam elements, which can accurately simulate their tensile, bending, and shear behaviors; the concrete is discretized using solid elements to capture its three-dimensional stress state and crack propagation phenomena.

[0049] S2: The beam unit is embedded in the solid unit as a whole, and beam units are distributed in each solid unit. In order to avoid the situation where there is no beam unit node in the solid unit and the coupling accuracy is reduced, two coupling nodes are added to each beam unit, such as Figure 2 As shown in the figure, a slave beam is constructed based on the beam element nodes on the entire beam element and the added coupling nodes; the first beam element node on the slave beam corresponds to the first beam element node on the first beam element, and the coupling between the slave beam and the concrete is as shown in the figure. Figure 3 As shown, the coupling between the subordinate beam and the reinforcement is as follows Figure 4 shown.

[0050] S3: Use shape functions to obtain the velocities of the two coupled nodes on the slave beam located in the first solid element; based on the mass and velocity of the first beam element node and the two coupled nodes on the slave beam, update the mass and momentum of any solid element node on the first solid element; the first beam element node on the slave beam is located in the first solid element.

[0051] Specifically, calculating the speed of two coupled nodes includes:

[0052] Get the velocities of the two beam element nodes on the first beam element;

[0053] Based on the velocities of the two beam element nodes on the first beam element, the shape functions are used to obtain the velocities of the two coupled nodes on the slave beam located in the first solid element.

[0054] Furthermore, the calculation formula for the speed of the two coupling nodes is:

[0055] ;

[0056] ;

[0057] ; ;

[0058] in, 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, 、 is the shape function acting on the one-dimensional element; 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 of the first solid element; represents the velocity of the second beam element node on the beam element of the first solid element; Represents the first isoparametric coordinate of any point in the cell.

[0059] Furthermore, the updating process of the mass and momentum of the solid element nodes includes:

[0060] Get the mass and momentum of any entity node in the first entity element;

[0061] Obtain the mass of the first beam element node and the two coupling nodes on the slave beam as follows:

[0062] by Figure 4 For example, the slave beam corresponding to the first beam element in the figure has two beam element nodes, and the masses are 、 , then the mass of the first beam element node is The mass of the nodes on the corresponding slave beams is distributed according to the mass of the slave beams ab, bc, and cd. The two added coupling nodes evenly divide the first beam element, so the masses of the slave beams ab, bc, and cd are consistent. , distribute the mass of the slave beam of each segment to the nodes on the slave beam, and obtain the mass of the first beam element node, the two coupling nodes and the mass of the second beam element node on the slave beam:

[0063] ;

[0064] ;

[0065] ;

[0066] ;

[0067] in, represents the mass of the first beam element node on the slave beam; represents the mass of the first coupling node on the slave beam located in the first solid element; represents the mass of the second coupling node on the slave beam located in the first solid element; Represents the mass of the second beam element node on the slave beam.

[0068] Based on the mass of the first beam element node on the slave beam, the masses of the two coupling nodes and the shape functions at the corresponding nodes, the mass of the corresponding node assigned to the solid element node is calculated;

[0069] Add the mass of each node assigned to the solid element node to the mass of any solid element node in the first solid element, and update the mass of the corresponding solid element node; the update formula of the mass of the solid element node is:

[0070] ;

[0071] in, Indicates the updated mass of the first entity element node in the first entity element; Indicates the mass of the first entity element node in the first entity element before updating; represents the shape function at the node; represents the mass of the first beam element node on the slave beam; represents the mass of the first coupling node on the slave beam located in the first solid element; represents the mass of the second coupling node on the slave beam located in the first solid element; represents the three-dimensional isoparametric coordinates of the first beam element node on the slave beam; represents the three-dimensional isoparametric coordinates of the first coupling node; represents the three-dimensional isoparametric coordinates of the second coupling node; It represents the first isoparametric coordinate of the first beam element node on the slave beam; Represents the second isoparametric coordinate of the first beam element node on the slave beam; It represents the third isoparametric coordinate of the first beam element node on the slave 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 coupled node.

[0072] In this embodiment, the shape function at the node It is the shape function acting on the three-dimensional element. Taking the hexahedron element as an example, the shape function of each point on the hexahedron element is:

[0073] ;

[0074] ;

[0075] ;

[0076] ;

[0077] ;

[0078] ;

[0079] ;

[0080] ;

[0081] in, Represents the first isoparametric coordinates of any point in the cell; Represents the second isoparametric coordinate of any point in the cell; Represents the third isoparametric coordinate of any point in the cell.

[0082] Based on the mass of each node assigned to the solid element node and the velocity of the corresponding node, the momentum assigned to the solid element node by each node is calculated;

[0083] Add the momentum of each node assigned to the entity unit node to the momentum of any entity unit node in the first entity unit, and update the momentum of the corresponding entity unit node; the update formula of the momentum of the entity unit node is:

[0084] ;

[0085] in, Represents the updated momentum of the first entity element node in the first entity element; Represents the momentum of the first entity element node in the first entity element before updating; represents the velocity of the first beam element node on the slave beam, the velocity Equal to speed ; represents the velocity of the first coupling node; represents the velocity of the second coupled node.

[0086] S4: Based on the updated mass and momentum of the solid unit node, the updated velocity of the solid unit node is calculated; based on the updated velocity of the solid unit node, the velocity of the first beam unit node located in the first solid unit on the beam unit is updated to achieve coupling between steel bars and concrete.

[0087] Specifically, the calculation formula for the updated velocity of the entity element node is:

[0088] ;

[0089] in, Indicates the updated velocity of the first entity element node in the first entity element; Represents the updated momentum of the first entity element node in the first entity element; Represents the updated mass of the first entity element node in the first entity element.

[0090] The process of updating the velocity of the first beam element node on a beam element includes:

[0091] Update the velocity of the first beam element node on the slave beam based on the updated velocity of the solid element node;

[0092] Assign the updated velocity of the first beam element node on the slave 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.

[0093] Furthermore, the update formula for the velocity of the first beam element node on the slave beam is:

[0094] ;

[0095] in, represents the updated velocity of the first beam element node on the slave beam; represents the shape function at the node; Indicates the updated velocity of the first entity element node in the first entity element; It represents the first isoparametric coordinate of the first beam element node on the slave beam; Represents the second isoparametric coordinate of the first beam element node on the slave beam; Represents the third isoparametric coordinate of the first beam element node on the slave beam.

[0096] Furthermore, the updated velocity of the first beam element node on the slave beam , assigned to the velocity of the first beam element node on the beam element located at the first solid element , get the updated velocity of the first beam element node on the beam element .

[0097] The finite element coupling simulation calculation method for the interaction between steel bars and concrete provided in this embodiment has the following beneficial effects:

[0098] 1. This method proposes an adaptive finite element coupling algorithm, which constructs a subordinate beam according to the relative position and geometric characteristics of the steel bar and concrete, automatically adjusts the coupling parameters to ensure the accuracy and stability of the calculation, and achieves mesh arbitrariness without the need for shared nodes, simplifying the modeling process and avoiding the mesh dependency problem of traditional methods.

[0099] 2. This method optimizes the construction and solution of the coupling matrix by coupling beam elements and solid elements through mass and momentum, thereby improving simulation efficiency and accuracy.

[0100] 3. Combining advanced nonlinear material models with adaptive finite element methods significantly enhances the ability to simulate complex material behaviors.

[0101] The technical features of the above-mentioned embodiments can be combined arbitrarily. In order to make the description concise, not all possible combinations of the technical features in the above-mentioned embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0102] The above-described embodiments merely represent several implementation methods of the present application. While the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the patent application. It should be noted that a person of ordinary skill in the art may make various modifications and improvements without departing from the spirit of the present application, and these modifications and improvements fall within the scope of protection of the present application. Therefore, the scope of protection of the present patent application shall be determined by the appended claims.

Claims

1. A finite element coupling simulation calculation method for the interaction between steel bars and concrete, characterized in that: include: S1: The steel bar is discretized into a beam unit connected by several beam units, and the beam unit nodes are shared at the beam unit connections; the concrete is discretized into a solid unit connected by several solid units, and the solid unit nodes are shared at the solid unit connections; S2: The beam element is embedded in the solid element as a whole, with beam elements distributed in each solid element. Two coupling nodes are added to each beam element, with the two coupling nodes added to the first beam element equally dividing the first beam element. A slave beam is constructed based on the beam element nodes on the entire beam element and the added coupling nodes. The first beam element node on the slave beam corresponds to the first beam element node on the first beam element. S3: Use shape functions to obtain the velocities of the two coupled nodes on the slave beam located in the first solid element; Update the mass and momentum of any solid element node on the first solid element based on the mass and velocity of the first beam element node and the two coupled nodes on the slave beam; The first beam element node on the slave beam is located in the first solid element; The updating process of the mass and momentum of the solid element nodes includes: Get the mass and momentum of any entity node in the first entity element; Obtain the mass of the first beam element node and two coupling nodes on the slave beam; Based on the mass of the first beam element node on the slave beam, the masses of the two coupling nodes and the shape functions at the corresponding nodes, the mass of the corresponding node assigned to the solid element node is calculated; Add the mass of each node assigned to the solid element node to the mass of any solid element node in the first solid element, and update the mass of the corresponding solid element node; Based on the mass of each node assigned to the solid element node and the velocity of the corresponding node, the momentum assigned to the solid element node by each node is calculated; Add the momentum of each node assigned to the entity element node to the momentum of any entity element node in the first entity element, and update the momentum of the corresponding entity element node; S4: Based on the updated mass and momentum of the solid unit node, the updated velocity of the solid unit node is calculated; based on the updated velocity of the solid unit node, the velocity of the first beam unit node located in the first solid unit on the beam unit is updated to achieve coupling between steel bars and concrete.

2. The finite element coupling simulation calculation method for the interaction between steel bars and concrete according to claim 1 is characterized in that: Calculating the speed of two coupled nodes involves: Get the velocities of the two beam element nodes on the first beam element; Based on the velocities of the two beam element nodes on the first beam element, the shape functions are used to obtain the velocities of the two coupled nodes on the slave beam located in the first solid element.

3. The finite element coupling simulation calculation method for the interaction between steel bars and concrete according to claim 2 is characterized in that: The speed of the two coupled nodes is calculated as: ； ； ； ； in, 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 of the first solid element; represents the velocity of the second beam element node on the beam element of the first solid element; Represents the first isoparametric coordinate of any point in the cell.

4. The finite element coupling simulation calculation method for the interaction between steel bars and concrete according to claim 1 is characterized in that: The update formula of the mass of the solid element node is: ； in, Indicates the updated mass of the first entity element node in the first entity element; Indicates the mass of the first entity element node in the first entity element before updating; represents the shape function at the node; represents the mass of the first beam element node on the slave beam; represents the mass of the first coupling node on the slave beam located in the first solid element; represents the mass of the second coupling node on the slave beam located in the first solid element; It represents the first isoparametric coordinate of the first beam element node on the slave beam; Represents the second isoparametric coordinate of the first beam element node on the slave beam; It represents the third isoparametric coordinate of the first beam element node on the slave 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 coupled node.

5. The finite element coupling simulation calculation method for the interaction between steel bars and concrete according to claim 4 is characterized in that: The update formula of the momentum of the solid element node is: ； in, Represents the updated momentum of the first entity element node in the first entity element; Represents the momentum of the first entity element node in the first entity element before updating; represents the velocity of the first beam element node on the slave beam, the velocity Equal to speed ; represents the velocity of the first coupling node; represents the velocity of the second coupled node.

6. The finite element coupling simulation calculation method for the interaction between steel bars and concrete according to claim 1 is characterized in that: The process of updating the velocity of the first beam element node on a beam element includes: Update the velocity of the first beam element node on the slave beam based on the updated velocity of the solid element node; Assign the updated velocity of the first beam element node on the slave 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.

7. The finite element coupling simulation calculation method for the interaction between steel bars and concrete according to claim 6, characterized in that: The update formula for the velocity of the first beam element node on the slave beam is: ； in, represents the updated velocity of the first beam element node on the slave beam; represents the shape function at the node; Indicates the updated velocity of the first entity element node in the first entity element; It represents the first isoparametric coordinate of the first beam element node on the slave beam; Represents the second isoparametric coordinate of the first beam element node on the slave beam; Represents the third isoparametric coordinate of the first beam element node on the slave beam.

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