A simulation method of extrusion deformation of mortise and tenon joints based on finite element analysis

Abstract

The present invention provides a method for simulating the extrusion deformation of mortise and tenon joints based on finite element analysis, comprising the following steps: first, simplifying the three-dimensional force model of the mortise and tenon joint into a two-dimensional plane stress model; dividing the structure into beam-column extrusion deformation influence areas, through-beam extrusion deformation boundaries and other areas according to the extrusion influence range of through-beams and wooden columns; respectively cutting out the above areas in the finite element model, and dividing them using different grid densities or sizes; and setting the two-dimensional model boundary conditions and contacts according to the force mechanism of the original structure and theoretical analysis. The precise extrusion deformation curve of the contact area of ​​the mortise and tenon joint can be extracted through finite element calculation. The present invention effectively simplifies the method for simulating the extrusion deformation of the mortise and tenon joint, and reduces the number of grids in the finite element analysis by performing grid encryption at key force-bearing positions. The length of the grid unit at the contact boundary position can reach 0.1 mm, thereby improving the accuracy of the simulation of the extrusion deformation of the mortise and tenon joint.

Description

Technical Field

[0001] The invention relates to the field of civil engineering, and in particular to a finite element analysis-based method for simulating extrusion deformation of mortise and tenon joints. Background Art

[0002] The mortise and tenon joint is a common connection method in ancient Chinese wooden structures. In traditional through-beam wooden structures, a large number of "throughs" are used, that is, a beam is used to pass through the columns to connect the columns together. Under the action of external forces, the extrusion areas on both sides of the node will produce symmetrical deformation, and at the same time, forces of equal magnitude and opposite directions will be generated, providing a restoring torque to the node.

[0003] At present, the deformation of mortise and tenon joints is often studied and verified by three-dimensional finite element solid simulation. When the mesh size of the three-dimensional solid model is large, the finite element simulation calculation speed is fast, but the accuracy cannot be guaranteed, and the deformation is often distorted; however, when the mesh size of the three-dimensional solid model is small, the finite element simulation accuracy is guaranteed, but the excessive number of meshes seriously affects its calculation rate. Summary of the invention

[0004] Purpose of the invention: To solve the above technical problems, the present invention provides a method for simulating the extrusion deformation of mortise and tenon joints based on finite element analysis.

[0005] Technical solution: A method for simulating the extrusion deformation of mortise and tenon joints based on finite element analysis of the present invention comprises the following steps:

[0006] S1: According to the analysis of stress characteristics, the continuous three-dimensional mortise and tenon joint model is simplified into a discrete two-dimensional plane stress model;

[0007] S2: Input the dimensions of the crossbeam and wooden column of the mortise and tenon joint;

[0008] S3: Based on the component sizes in S2, calculate the influence range of the through beam and wooden column extrusion deformation;

[0009] S4: intercept the area calculated in S3 on the crossbeam and wooden column, and set the mesh size inside the extrusion influence area, the boundary of the extrusion area and outside the extrusion area;

[0010] S5: Set the node domain of the boundary of the through-beam extrusion influence area to Nodeset-1;

[0011] S6: According to the loading conditions of the mortise and tenon joint test, the boundary conditions at both ends of the through beam and column and the contact relationship between the two are set;

[0012] S7: According to the finite element calculation results, the deformation of all nodes of Nodeset-1 is derived to obtain the deformation diagram of the extrusion area.

[0013] As a further preferred solution, in step 1, since the stresses of the through beams and wooden columns of the mortise and tenon joints are the same and evenly distributed along the thickness direction, the three-dimensional mortise and tenon joint model can be cut along the central axis in the thickness direction of the beam and simplified into a two-dimensional plane strain problem.

[0014] As a further preferred solution, in step S3, according to the input width b, height h and length l of the mortise and tenon joint, the diameter d and length L of the wood column and the empirical calculation formula obtained by finite element simulation, the radius R of the extrusion deformation area of ​​the wood column and the through-beam is determined. 1 and R 2 Quarter circles and semicircles of:

[0015] R 1 =d / 2 Formula (1)

[0016] R 2 =R 1 / 6 Formula (2)

[0017] As a further preferred solution, in step S4, a circle with a radius of R is cut in the crossbeam and the wooden column with the initial contact point as the center. 1 and R 2 The grid size in this area is set to 1mm, the boundary grid size is set to 0.1mm, and the grid size outside the extrusion area is set to 10mm.

[0018] As a further preferred solution, in step S5, all nodes at the edge of the through-beam and wooden column extrusion deformation area are selected and set as Nodeset-1.

[0019] As a further preferred solution, in step S6, according to the loading conditions of the mortise and tenon joint test, the boundary conditions of the column and beam are simplified in the finite element calculation software, and the simplification principle is as follows:

[0020]

[0021] The normal direction of the contact part between the through-beam and the wooden column is set to "hard contact", the tangential direction is set to "penalty friction", and the friction coefficient is 0.5.

[0022] As a further preferred solution, the precise value of the extrusion deformation displacement of the mortise and tenon joint is calculated based on the node domain coordinate values ​​of Nodeset-1 before and after the finite element analysis in S7.

[0023] Beneficial effects: The present invention has the following beneficial effects:

[0024] The present invention effectively simplifies the method for simulating the extrusion deformation of mortise and tenon joints. By encrypting the grid at key stress-bearing positions, the number of grids in the finite element analysis is reduced. The length of the grid unit at the contact boundary position can reach 0.1 mm, thereby improving the accuracy of the simulation of the extrusion deformation of the mortise and tenon joints. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 It is a flow chart of the method for simulating the extrusion deformation of the mortise and tenon joints by finite element analysis in the present invention;

[0026] Figure 2 Simplify the 2D model diagram for the mortise and tenon joint;

[0027] Figure 3 This is a schematic diagram of the deformation-affected area of ​​the through beams and wooden columns;

[0028] Figure 4 Schematic diagram of mesh division in deformation-affected area;

[0029] Figure 5 Schematic diagram of mesh division of deformation-affected area boundary;

[0030] Figure 6 This is a schematic diagram of Nodeset-1;

[0031] Figure 7 This is the displacement diagram of the extrusion deformation of the mortise and tenon joint;

[0032] Among them, 1. wooden pillars, 2. through beams. DETAILED DESCRIPTION

[0033] The technical solution of the present invention is further introduced below in conjunction with specific implementation modes and drawings.

[0034] like Figure 1 As shown, a method for simulating the extrusion deformation of mortise and tenon joints based on finite element analysis of the present invention comprises the following steps: (A1) simplifying the three-dimensional mortise and tenon joint model into a two-dimensional plane stress model according to the force characteristic analysis; (A2) calculating the influence range of the extrusion deformation of the through beams and wooden columns according to the sizes of the through beams and wooden columns of the mortise and tenon joints, and intercepting the area on the finite element models of the through beams and wooden columns; (A3) setting the grid size within the extrusion influence zone, the boundary of the extrusion zone and outside the extrusion zone; (A4) setting the node domain of the boundary of the through beam extrusion zone to Nodeset-1; (A5) setting the boundary conditions at both ends of the through beam and the column and the contact relationship between the two according to the test loading conditions of the mortise and tenon joint; (A6) deriving the deformation of all nodes of Nodeset-1 according to the finite element calculation results to obtain the deformation diagram of the extrusion zone.

[0035] Preferably, in the finite element analysis-based simulating method for extrusion deformation of mortise and tenon joints disclosed in the present invention, the step (A1) further comprises: in order to reduce the large load caused by the excessive number of meshes in the three-dimensional model, combined with the theoretical analysis results: the stresses of the through-beam and the wooden column of the mortise and tenon joint are the same and evenly distributed along the thickness direction, so the three-dimensional mortise and tenon joint model can be cut along the central axis of the thickness direction of the beam and simplified to a two-dimensional plane strain problem, such as Figure 2 As shown in Figure 3, this method reduces the number of computing units while ensuring accuracy.

[0036] Preferably, in the finite element analysis-based finite element analysis method for simulating the extrusion deformation of the mortise and tenon joint disclosed in the present invention, the step (A2) further comprises: determining, according to the empirical calculation formula obtained by the finite element simulation, that the extrusion deformation areas of the wooden column and the through-beam are respectively R 1 and R 2 Quarter circle and semicircle: R 1 =d / 2, R 2 =R 1 / 6, where d is the diameter of the wood column, Figure 3 The figure below shows the schematic diagram of the extrusion deformation area at four contact points.

[0037] Preferably, in the finite element analysis-based finite element analysis method for simulating the extrusion deformation of mortise and tenon joints disclosed in the present invention, the step (A3) further comprises: according to the divided areas in A2, in the finite element models of the crossbeam and the wooden column, respectively, a circle with a radius of R is intercepted with the initial contact point as the center. 1 and R 2 The calculation efficiency and accuracy are further balanced by encrypting the grid in key parts. The recommended grid density or size is as follows: Figure 4 , Figure 5 As shown in the figure: the grid size in the extrusion deformation area is set to 1mm, the boundary grid size is 0.1mm, and the grid size outside the extrusion area is 10mm.

[0038] Preferably, in the finite element analysis-based mortise and tenon joint extrusion deformation simulation method disclosed in the present invention, the step (A4) further comprises: selecting all nodes of the extrusion deformation area diameter (extrusion deformation area boundary) of the through beam and the wooden column, and setting them as Nodeset-1, such as Figure 6 shown.

[0039] Preferably, in the finite element analysis-based mortise and tenon joint extrusion deformation simulation method disclosed in the present invention, the step (A5) further includes: according to the loading conditions of the mortise and tenon joint test, the boundary conditions of the beam and the crossbeam are simplified in the finite element calculation software, and the simplification principle is as follows: if the two ends of the crossbeam or column are hinged, only the degrees of freedom in the horizontal and vertical directions are constrained, and the torsion degree of freedom is not constrained; if the two ends of the crossbeam or column are fixed, the degrees of freedom in the horizontal, vertical and torsion directions are constrained. At the same time, in the finite element calculation software, the force between the crossbeam and the wooden column is simulated by setting the normal and tangential force transmission mode (i.e. "contact") of the crossbeam and the wooden column: the normal direction of the contact part between the crossbeam and the wooden column is set to "hard contact", and the tangential direction is set to "penalty friction", and the friction coefficient is 0.5.

[0040] Preferably, in the method for simulating the extrusion deformation of the mortise and tenon joint based on finite element analysis disclosed in the present invention, the step (A6) further comprises: calculating the precise displacement value of the extrusion deformation of the mortise and tenon joint according to the node domain coordinate values ​​of Nodeset-1 before and after the finite element analysis, such as Figure 7 shown.

Claims

1. A method for simulating the extrusion deformation of mortise and tenon joints based on finite element analysis, characterized in that: The following steps are involved: S1: According to the analysis of stress characteristics, the continuous three-dimensional mortise and tenon joint model is simplified into a discrete two-dimensional plane stress model; In step S1, since the stresses of the through beam and the wooden column of the mortise and tenon joint are the same and evenly distributed along the thickness direction, the three-dimensional mortise and tenon joint model is cut along the central axis of the beam thickness direction to simplify it into a two-dimensional plane strain problem; S2: Input the dimensions of the crossbeam and wooden column of the mortise and tenon joint; S3: Based on the component sizes in S2, calculate the influence range of the through beam and wooden column extrusion deformation; In step S3, according to the input width b, height h and length l of the mortise and tenon joint, the diameter d and length L of the wood column and the empirical calculation formula obtained by finite element simulation, it is determined that the extrusion deformation areas of the wood column and the through-beam are a quarter circle and a semicircle with radii R1 and R2 respectively: R1=d / 2 Formula (1) R2= R1 / 6 Formula (2); S4: intercept the area calculated in S3 on the crossbeam and wooden column, and set the mesh size inside the extrusion influence area, the boundary of the extrusion area and outside the extrusion area; In step S4, a quarter circle and a semicircle with radii R1 and R2 are respectively intercepted in the crossbeam and the wooden column with the initial contact point as the center, and the grid size is set to 1 mm in the area, the boundary grid size is set to 0.1 mm, and the grid size outside the extrusion area is set to 10 mm; S5: Set the node domain of the boundary of the through-beam extrusion influence area to Nodeset-1; S6: According to the loading conditions of the mortise and tenon joint test, the boundary conditions at both ends of the through beam and column and the contact relationship between the two are set; S7: According to the finite element calculation results, the deformation of all nodes of Nodeset-1 is derived to obtain the deformation diagram of the extrusion area.

2. The method for simulating extrusion deformation of mortise and tenon joints based on finite element analysis according to claim 1, characterized in that: In step S5, all nodes at the edge of the extrusion deformation area of ​​the through beam and the wooden column are selected and set as Nodeset-1.

3. The method for simulating extrusion deformation of mortise and tenon joints based on finite element analysis according to claim 2, characterized in that: In step S6, according to the loading conditions of the mortise and tenon joint test, the boundary conditions of the column and beam are simplified in the finite element calculation software. The simplification principle is as follows: The normal direction of the contact part between the through-beam and the wooden column is set to "hard contact", the tangential direction is set to "penalty friction", and the friction coefficient is 0.

5.

4. The method for simulating extrusion deformation of mortise and tenon joints based on finite element analysis according to claim 3 is characterized in that: According to the node domain coordinate values ​​of Nodeset-1 before and after the finite element analysis in S7, the precise value of the extrusion deformation displacement of the mortise and tenon joint is calculated.

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