Deformation decomposition method of components with irregular boundaries based on regular tetrahedron elements

Abstract

The present invention belongs to the field of mechanical analysis technology and discloses a deformation decomposition method for irregular-boundary components based on regular tetrahedron units, comprising the following steps: constructing the spatial deformation of regular tetrahedron units in a spatial rectangular coordinate system based on mathematical orthogonality and mechanical equilibrium to obtain a deformation decomposition basis matrix; establishing a spatial irregular-boundary component model, using regular tetrahedron units to divide any part of the component, obtaining the basic deformation and basic displacement projection coefficient vector of the regular tetrahedron units after any displacement and deformation under any load condition; obtaining the basic deformation information of the regular tetrahedron units under any load condition, distinguishing the main deformation and secondary deformation of the regular tetrahedron units under any load condition, and then realizing the deformation decomposition and deformation performance quantitative analysis of any part of the spatial component. The deformation decomposition method based on regular tetrahedron units of the present invention can be better used for performance quantitative analysis of irregular-boundary components in space.

Description

Technical Field

[0001] The invention belongs to the field of mechanical analysis and relates to a deformation decomposition method of a component with irregular boundaries based on regular tetrahedron units. Background Art

[0002] Deformation information is a crucial basis for component analysis and design. Current component design methods focus on macroscopic deformations, such as bending and shear resistance, while common component analysis methods often focus on comprehensive responses, such as maximum sideways drift and interstory drift angle. Single basic deformation information is included in the comprehensive deformation, making it difficult to separate the basic deformation from the comprehensive deformation. Therefore, decomposing the total deformation of a unit and quantifying the basic deformations is crucial for component performance analysis and optimal design.

[0003] Current deformation decomposition methods for spatial components have several shortcomings. Deformation decomposition methods based on cuboid elements are only applicable to the performance analysis of regular components; and those based on triangular prism elements are only applicable to the performance analysis of components with irregular boundaries within a plane within space. Therefore, there is still a lack of a deformation decomposition method that can be applied to the performance analysis of components with arbitrary irregular boundaries within space. From the perspective of discrete element decomposition, regular tetrahedron elements can meet the requirements of irregular spatial boundaries. Therefore, it is necessary to propose a corresponding deformation decomposition method for components with irregular boundaries based on the geometric characteristics of regular tetrahedron elements and in combination with orthogonality theory, thereby identifying quantitative information about the macroscopic deformation of spatial components. Summary of the Invention

[0004] The purpose of the present invention is to provide a deformation decomposition method for irregular boundary components based on regular tetrahedron units, which can identify the main basic deformation and secondary basic deformation of regular tetrahedron units, thereby realizing quantitative analysis of the deformation of any part of the irregular boundary component in space.

[0005] To achieve the above object, the present invention adopts the following technical solutions:

[0006] A deformation decomposition method for a component with irregular boundaries based on regular tetrahedron elements comprises the following steps:

[0007] Step 1: Based on mathematical orthogonality and mechanical equilibrium, construct the spatial deformation of the regular tetrahedron unit in the spatial rectangular coordinate system and obtain the deformation decomposition basis matrix of the regular tetrahedron unit;

[0008] Step 2: Establish a model of an irregular component with a spatial boundary, use regular tetrahedron elements to divide any part of the irregular component and perform finite element solution to obtain the node coordinate values ​​of the regular tetrahedron elements in the spatial rectangular coordinate system and the node coordinate values ​​of the regular tetrahedron elements after arbitrary displacement and deformation under arbitrary load conditions, and then obtain the node displacement vectors of the regular tetrahedron elements after arbitrary displacement and deformation under arbitrary load conditions;

[0009] Step 3: Project the node displacement vectors of the regular tetrahedron element after generating arbitrary displacement and deformation under any load condition onto the deformation decomposition basis matrix to obtain the basic deformation and basic displacement projection coefficient vector of the regular tetrahedron element after generating arbitrary displacement and deformation under any load condition;

[0010] Step 4: Based on the basic deformation projection coefficient of the regular tetrahedron unit after any displacement or deformation under any load condition, the basic deformation information of the regular tetrahedron unit under any load condition is obtained, and the main deformation and secondary deformation of the regular tetrahedron unit under any load condition are identified, thereby realizing the deformation decomposition and deformation quantification analysis of any part of the spatial component.

[0011] Furthermore, the deformation decomposition method of the regular tetrahedron unit based on the orthogonal theory is characterized in that the regular tetrahedron unit has four nodes, and the coordinates of the four nodes in the X, Y and Z directions are x1, y1, z1, x2, y2, z2, x3, y3, z3, x4, y4, z4; the spatial deformation of the regular tetrahedron unit is composed of 12 basic deformations and basic displacements: X-axial tensile and compressive deformation, Y-axial tensile and compressive deformation, Z-axial tensile and compressive deformation, shear deformation in the XOY plane, shear deformation in the XOZ plane, shear deformation in the YOZ plane, X-axial rigid body translation, Y-axial rigid body translation, Z-axial rigid body translation, XOY plane rigid body rotation, XOZ plane rigid body rotation and YOZ plane rigid body rotation;

[0012] The basic vectors of the basic deformation and basic displacement of the regular tetrahedron unit are d1~d 12 , as follows:

[0013] d1 is the x-axis tensile and compressive deformation basis vector of the regular tetrahedron element:

[0014]

[0015] d2 is the Y-axis tensile and compressive deformation basis vector of the regular tetrahedron element:

[0016]

[0017] d3 is the Z-axis tensile and compressive deformation basis vector of the regular tetrahedron element:

[0018]

[0019] d4 is the shear deformation basis vector in the XOY plane of the regular tetrahedron element:

[0020]

[0021] d5 is the shear deformation basis vector in the XOZ plane of the regular tetrahedron element:

[0022]

[0023] d6 is the shear deformation basis vector in the YOZ plane of the regular tetrahedron element:

[0024]

[0025] d7 is the x-axis rigid body translation basis vector of the regular tetrahedron element:

[0026]

[0027] d8 is the Y-axis rigid body translation basis vector of the regular tetrahedron unit:

[0028]

[0029] d9 is the rigid body translation basis vector of the regular tetrahedron unit along the Z axis:

[0030]

[0031] d 10 is the rigid body rotation basis vector in the XOY plane of the regular tetrahedron unit:

[0032]

[0033] d 11 is the rigid body rotation basis vector in the XOZ plane of the regular tetrahedron unit:

[0034]

[0035] d 12 is the rigid body rotation basis vector in the YOZ plane of the regular tetrahedron unit:

[0036]

[0037] The above basic deformation and basic displacement basis vectors satisfy mathematical orthogonality, that is:

[0038]

[0039] The basic vectors of the basic deformation and basic displacement of the above-mentioned regular tetrahedron unit are d1~d 12 Construct the deformation decomposition basis matrix D of the regular tetrahedron unit,

[0040] D=(d1 d2…d 11 d 12 ) T .

[0041] Furthermore, the node coordinate vector of the regular tetrahedron unit in the space rectangular coordinate system is d p ,

[0042] d p =(x1 y1 z1 x2 y2 z2 x3 y3 z3 x4 y4 z4),

[0043] The node coordinate vector of the tetrahedron element after any displacement and deformation under any load condition is d q ,

[0044] d q =(x1'y1'z1'x'2y'2z'2x'3y'3z'3x'4y'4z'4),

[0045] By d q -d p The node displacement vector d after the regular tetrahedron element produces arbitrary displacement and deformation under any load condition can be obtained r ,

[0046]

[0047] Furthermore, step 3 is specifically as follows:

[0048] The node displacement vector d after the regular tetrahedron element produces arbitrary displacement and deformation under any load condition r Projected onto the deformation decomposition basis matrix D, that is

[0049] w=d r ·D -1 ,

[0050] w is the basic deformation and basic displacement projection coefficient vector of the regular tetrahedron element:

[0051] w=(w1 w2…w 11 w 12 ),

[0052] Among them: w1 is the projection coefficient of the tensile and compressive deformation of the unit in the X axis, w2 is the projection coefficient of the tensile and compressive deformation in the Y axis, w3 is the projection coefficient of the tensile and compressive deformation in the Z axis, w4 is the projection coefficient of the shear deformation in the XOY plane, w5 is the projection coefficient of the shear deformation in the XOZ plane, w6 is the projection coefficient of the shear deformation in the YOZ plane, w7 is the projection coefficient of the rigid body translation in the X axis, w8 is the projection coefficient of the rigid body translation in the Y axis, w9 is the projection coefficient of the rigid body translation in the Z axis, w10 is the XOY plane rigid body rotation projection coefficient, w 11 is the XOZ plane rigid body rotation projection coefficient, w 12 YOZ plane rigid body rotation projection coefficient.

[0053] Furthermore, the step 4 specifically includes:

[0054] The decomposition results are subjected to rigid-flexible separation, i.e. the basic displacement projection coefficient w7-w is ignored. 12 In order to eliminate the influence of the deformation, only the absolute values ​​of the basic deformation projection coefficients w1-w6 in the component information are compared. The deformation corresponding to the maximum absolute value of the projection coefficient is determined as the main deformation of the regular tetrahedron unit. Similarly, the second largest one is determined as the secondary deformation of the regular tetrahedron unit, thereby realizing the quantitative analysis of the deformation of any part of the spatial component.

[0055] Furthermore, the positive and negative properties of the tensile and compressive deformation projection coefficients w1-w3 of the regular tetrahedron unit are used to further judge the tensile and compressive state of the unit. If w1 is positive, it means that the regular tetrahedron unit is in an X-axis tensile deformation state; if w1 is negative, it means that the regular tetrahedron unit is in an X-axis compressive deformation state, and the same applies to w2 and w3.

[0056] Compared with the prior art, the present invention has the following beneficial effects:

[0057] Based on mathematical complete orthogonality and mechanical force equilibrium conditions, this paper proposes a deformation decomposition method for irregular boundary components based on regular tetrahedron units. By decomposing the comprehensive deformation of regular tetrahedron units into basic deformations, quantitative deformation information of regular tetrahedron units is obtained. By identifying the major and minor deformations of regular tetrahedron units, this paper achieves a detailed analysis of the deformation performance of any part of irregular boundary components in space, thereby guiding the targeted reinforcement and optimization design of the components. More importantly, compared with regular units such as square units and rectangular units, the deformation decomposition method based on regular tetrahedron units can be better used for quantitative performance analysis of irregular boundary components in space. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 The figure is a flow chart of the deformation decomposition method of a component with irregular boundaries based on regular tetrahedron units according to the present invention.

[0059] Figure 2 Schematic diagram of a four-node regular tetrahedron unit in a spatial rectangular coordinate system in the present invention.

[0060] Figure 3 It is a schematic diagram of the X-axial tensile and compressive deformation and stress conditions of a four-node regular tetrahedron unit in a spatial rectangular coordinate system in the present invention.

[0061] Figure 4It is a schematic diagram of the Y-axial tensile and compressive deformation and stress conditions of the four-node regular tetrahedron unit in the spatial rectangular coordinate system in the present invention.

[0062] Figure 5 It is a schematic diagram of the Z-axial tensile and compressive deformation and stress conditions of a four-node regular tetrahedron unit in a spatial rectangular coordinate system in the present invention.

[0063] Figure 6 It is a schematic diagram of shear deformation and force conditions in the XOY plane of a four-node regular tetrahedron unit in a spatial rectangular coordinate system in the present invention.

[0064] Figure 7 Schematic diagram of shear deformation and stress conditions in the XOZ plane of a four-node regular tetrahedron unit in a spatial rectangular coordinate system in the present invention.

[0065] Figure 8 It is a schematic diagram of shear deformation and stress conditions in the YOZ plane of a four-node regular tetrahedron unit in a spatial rectangular coordinate system in the present invention.

[0066] Figure 9 Schematic diagram of the X-axis rigid body translation and force conditions of the four-node regular tetrahedron unit in the spatial rectangular coordinate system in the present invention.

[0067] Figure 10 It is a schematic diagram of the Y-axis rigid body translation and force working conditions of the four-node regular tetrahedron unit in the spatial rectangular coordinate system in the present invention.

[0068] Figure 11 It is a schematic diagram of the Z-axis rigid body translation and force working conditions of the four-node regular tetrahedron unit in the spatial rectangular coordinate system in the present invention.

[0069] Figure 12 It is a schematic diagram of the rotation and force working conditions of the XOY plane rigid body of the four-node regular tetrahedron unit in the spatial rectangular coordinate system in the present invention.

[0070] Figure 13 Schematic diagram of the rigid body rotation and force conditions of the four-node regular tetrahedron unit XOZ plane in the spatial rectangular coordinate system in the present invention.

[0071] Figure 14 It is a schematic diagram of the YOZ plane rigid body rotation and force working conditions of the four-node regular tetrahedron unit in the spatial rectangular coordinate system in the present invention.

[0072] Figure 15 Schematic diagram of the counterclockwise rotation of the XOY plane of the four-node regular tetrahedron unit in the spatial rectangular coordinate system in the present invention.

[0073] Figure 16 Schematic diagram of the counterclockwise rotation of the XOZ plane of the four-node regular tetrahedron unit in the spatial rectangular coordinate system in the present invention.

[0074] Figure 17 Schematic diagram of the counterclockwise rotation of the YOZ plane of the four-node regular tetrahedron unit in the spatial rectangular coordinate system in the present invention.

[0075] Figure 18 It is a schematic diagram of a self-weight plate with irregular quadrilateral consolidation at the boundary in a rectangular coordinate system in space in the present invention. DETAILED DESCRIPTION

[0076] The following examples are used to illustrate the present invention, but are not intended to limit the scope of protection of the present invention. Unless otherwise specified, the technical means used in the examples are conventional means well known to those skilled in the art.

[0077] Figure 1 The flow chart of the method for decomposing irregular boundary components based on regular tetrahedron elements is shown in the figure. Figure 2 As shown in the figure, the 12 basic deformations and basic displacements in the rectangular coordinate system are as follows: Figures 3 to 14 As shown in the figure, the coordinates of the four nodes of the regular tetrahedron element in the X, Y, and Z directions are x1, y1, z1, x2, y2, z2, x3, y3, z3, x4, y4, z4; the spatial deformation of the regular tetrahedron element is composed of 12 basic deformations and basic displacements: X-axis tension and compression deformation, Y-axis tension and compression deformation, Z-axis tension and compression deformation, shear deformation in the XOY plane, shear deformation in the XOZ plane, shear deformation in the YOZ plane, X-axis rigid body translation, Y-axis rigid body translation, Z-axis rigid body translation, XOY plane rigid body rotation, XOZ plane rigid body rotation, and YOZ plane rigid body rotation, a total of 12 basic deformations and basic displacements.

[0078] The basic vectors of the basic deformation and basic displacement of the regular tetrahedron unit are d1~d 12 , as follows:

[0079] d1 is the x-axis tensile and compressive deformation basis vector of the regular tetrahedron element:

[0080]

[0081] d2 is the Y-axis tensile and compressive deformation basis vector of the regular tetrahedron element:

[0082]

[0083] d3 is the Z-axis tensile and compressive deformation basis vector of the regular tetrahedron element:

[0084]

[0085] d4 is the shear deformation basis vector in the XOY plane of the regular tetrahedron element:

[0086]

[0087] d5 is the shear deformation basis vector in the XOZ plane of the regular tetrahedron element:

[0088]

[0089] d6 is the shear deformation basis vector in the YOZ plane of the regular tetrahedron element:

[0090]

[0091] d7 is the x-axis rigid body translation basis vector of the regular tetrahedron element:

[0092]

[0093] d8 is the Y-axis rigid body translation basis vector of the regular tetrahedron unit:

[0094]

[0095] d9 is the rigid body translation basis vector of the regular tetrahedron unit along the Z axis:

[0096]

[0097] d 10 is the rigid body rotation basis vector in the XOY plane of the regular tetrahedron unit:

[0098]

[0099] d 11 is the rigid body rotation basis vector in the XOZ plane of the regular tetrahedron unit:

[0100]

[0101] d 12 is the rigid body rotation basis vector in the YOZ plane of the regular tetrahedron unit:

[0102]

[0103] The above basic deformation and basic displacement basis vectors satisfy mathematical orthogonality, that is:

[0104]

[0105] The basic vectors of the basic deformation and basic displacement of the above-mentioned regular tetrahedron unit are d1~d 12 Construct the deformation decomposition basis matrix D of the regular tetrahedron unit,

[0106] D=(d1 d2…d 11 d 12 ) T .

[0107] The node coordinate vector of the regular tetrahedron element in the space rectangular coordinate system is d p ,

[0108] d p =(x1 y1 z1 x2 y2 z2 x3 y3 z3 x4 y4 z4),

[0109] Then the node coordinate vector of the regular tetrahedron element after any displacement and deformation under any load condition is d q ,

[0110] d q =(x'1 y'1 z'1 x'2 y'2 z'2 x'3 y'3 z'3 x'4 y'4 z'4),

[0111] by u q -u p The node displacement vector d after the regular tetrahedron element produces arbitrary displacement and deformation under any load condition can be obtained r ,

[0112]

[0113] The node displacement vector d after the regular tetrahedron element produces arbitrary displacement and deformation under any load condition r Projected onto the deformation decomposition basis matrix D, that is

[0114] w=d r ·D -1 ,

[0115] w is the basic deformation and basic displacement projection coefficient vector of the regular tetrahedron element:

[0116] w=(w1 w2…w 11 w 12 ),

[0117] Among them: w1 is the projection coefficient of the tensile and compressive deformation of the unit in the X axis, w2 is the projection coefficient of the tensile and compressive deformation in the Y axis, w3 is the projection coefficient of the tensile and compressive deformation in the Z axis, w4 is the projection coefficient of the shear deformation in the XOY plane, w5 is the projection coefficient of the shear deformation in the XOZ plane, w6 is the projection coefficient of the shear deformation in the YOZ plane, w7 is the projection coefficient of the rigid body translation in the X axis, w8 is the projection coefficient of the rigid body translation in the Y axis, w9 is the projection coefficient of the rigid body translation in the Z axis, w 10 is the XOY plane rigid body rotation projection coefficient, w 11 is the XOZ plane rigid body rotation projection coefficient, w 12 YOZ plane rigid body rotation projection coefficient.

[0118] The decomposition results are subjected to rigid-flexible separation, i.e. the basic displacement projection coefficient w7-w is ignored. 12 In order to eliminate the influence of the deformation, only the absolute values ​​of the basic deformation projection coefficients w1-w6 in the component information are compared. The deformation corresponding to the maximum absolute value of the projection coefficient is determined as the main deformation of the regular tetrahedron unit. Similarly, the second largest one is determined as the secondary deformation of the regular tetrahedron unit, thereby realizing the quantitative analysis of the deformation of any part of the spatial component.

[0119] Furthermore, the positive and negative properties of the tensile and compressive deformation projection coefficients w1-w3 of the regular tetrahedron unit are used to further judge the tensile and compressive state of the unit. If w1 is positive, it means that the regular tetrahedron unit is in an X-axis tensile deformation state; if w1 is negative, it means that the regular tetrahedron unit is in an X-axis compressive deformation state, and the same applies to w2 and w3.

[0120] Analysis of rigid body rotation displacement error

[0121] Since rotational displacement is a nonlinear displacement, errors will occur during linear decomposition. That is, the unit rotational displacement vector not only has projection coefficients on the rigid body rotation basis vectors, but may also have projection coefficients on other basic deformations and rigid body displacement basis vectors. Therefore, it is necessary to analyze and calculate the errors caused by the rigid body rotational displacement to determine whether they affect the calculation accuracy.

[0122] like Figure 15 As shown, let the side length of the four-node regular tetrahedron element r be 2l, and rotate the element r counterclockwise around the centroid by an angle θ1 in the XOY plane. The coordinate displacement vectors of the four nodes of the element are:

[0123]

[0124] The node displacement vector of element r when it undergoes counterclockwise rotation displacement in the XOY plane is projected onto the deformation decomposition basis matrix. The element's rotation displacement vector is only projected on the XOY plane rigid body rotation, X-axis tensile and compressive deformation, and Y-axis tensile and compressive deformation. The projection coefficient on other basic deformations and basic displacements is 0. Therefore, the solution results of the 12 constraint equations obtained by projecting the coordinate displacement vector of the element's counterclockwise rotation in the XOY plane are as follows:

[0125]

[0126] For w1, w2, w 10 Perform Taylor expansion at θ1 = 0:

[0127]

[0128] It can be seen that when the unit undergoes rigid body rotation, there is still a projection coefficient on the rigid body rotation displacement in the X-axis and Y-axis tensile and compressive deformation, resulting in a certain error. However, when θ1 approaches 0, w1 and w2 are w10 Therefore, when small deformation occurs, the error caused by the rotation displacement of the XOY plane rigid body can be ignored.

[0129] like Figure 16 As shown in the figure, after the four-node regular tetrahedron element r is rotated counterclockwise around the centroid in the XOZ plane by an angle θ2, the coordinate displacement vectors of the four nodes of the element are:

[0130]

[0131] The node displacement vector of element r when it undergoes counterclockwise rotational displacement in the XOZ plane is projected onto the deformation decomposition basis matrix. The element's rotational displacement vector is only projected on the XOZ plane rigid body rotation, X-axis tensile and compressive deformation, and Z-axis tensile and compressive deformation. The projection coefficient on other basic deformations and basic displacements is 0. Therefore, the solution results of the 12 constraint equations obtained by projecting the coordinate displacement vector of the element's counterclockwise rotation in the XOZ plane are as follows:

[0132]

[0133] For w1, w3, w 11 Perform Taylor expansion at θ2 = 0:

[0134]

[0135] It can be seen that when the unit undergoes rigid body rotation, there is still a projection coefficient on the tensile and compressive deformation of the rigid body rotation displacement in the X-axis and Z-axis, resulting in a certain error. However, when θ2 approaches 0, w1 and w3 are w 11 Therefore, when small deformation occurs, the error caused by the rotation displacement of the XOZ plane rigid body can be ignored.

[0136] like Figure 17 As shown in the figure, after the four-node regular tetrahedron element r rotates counterclockwise around the centroid in the YOZ plane by an angle θ3, the coordinate displacement vectors of the four nodes of the element are:

[0137]

[0138] The node displacement vector of element r when it undergoes counterclockwise rotation displacement in the YOZ plane is projected onto the deformation decomposition basis matrix. The element's rotation displacement vector is only projected on the YOZ plane rigid body rotation, Y-axis tension and compression deformation, and Z-axis tension and compression deformation. The projection coefficient on other basic deformations and basic displacements is 0. Therefore, the solution results of the 12 constraint equations obtained by projecting the coordinate displacement vector of the element's counterclockwise rotation in the YOZ plane are as follows:

[0139]

[0140] For w2, w3, w 12 Perform Taylor expansion at θ3 = 0:

[0141]

[0142] It can be seen that when the unit undergoes rigid body rotation, there is still a projection coefficient on the Y-axis and Z-axis tensile and compressive deformation of the rigid body rotation displacement, which produces a certain error. However, when θ3 approaches 0, w2 and w3 are w 12 Therefore, when a small deformation occurs, the error caused by the rotation displacement of the YOZ plane rigid body can be ignored.

[0143] In summary, the constructed deformation decomposition basis matrix has sufficient accuracy.

[0144] Implementation Cases

[0145] like Figure 18 As shown, taking the irregular quadrilateral consolidation plate as an example, the bottom and top surfaces of the plate are parallelograms, the vertical sides are inclined, the plate thickness is 0.163m, the elastic modulus E = 30GPa, the Poisson's ratio μ = 0.2, and the density is 2500kg / m 3 .

[0146] Apply deadweight load to the plate. Figure 18 The node displacement vectors of the tetrahedral elements No. 1 and No. 2 are:

[0147] u r1 =(-8.20E-06,-8.55E-06,-8.14E-05,-8.28E-06,-6.34E-06,-5.94E-05 ,-6.58E-06,-7.65E-06,-5.38E-05,7.55E-06,7.13E-06,-6.51E-05)mm;

[0148] u r2 =(-4.14E-06,-3.24E-06,-2.25E-04,-1.58E-06,-3.58E-06,-2.33E-04 ,-3.09E-06,2.13E-07,-2.34E-04,3.15E-06,2.32E-06,-2.32E-04)mm.

[0149] The deformation decomposition results of the regular tetrahedron unit No. 1-2 are shown in Table 1.

[0150] Table 1 Deformation decomposition results of regular tetrahedron elements 1-2

[0151]

[0152] It can be seen from Table 1 that the XOY plane shear deformation projection coefficient of unit 1 is 2.07E-06, that is, the XOY plane shear is the main deformation in the area where unit 1 is located; the XOZ plane shear deformation projection coefficient is the second largest, that is, the XOZ plane shear is the secondary deformation in the area where unit 1 is located.

[0153] Similarly, the Y-axial tensile and compressive deformation projection coefficient of unit 2 is 2.96E-06, which means that the area where unit 2 is located is mainly deformed by Y-axial tension; the X-axial tensile and compressive deformation projection coefficient is the second largest and positive, which means that the area where unit 2 is located is mainly deformed by X-axial tension.

[0154] The embodiments described above are only preferred embodiments of the present invention and are only used to explain the present invention, not to limit the scope of implementation of the present invention. For those skilled in the art, it is of course possible to easily make other implementation methods by replacing or changing the technical content disclosed in this specification. Therefore, all changes and improvements made on the principles of the present invention should be included in the scope of the patent application of the present invention.

Claims

1. A deformation decomposition method for components with irregular boundaries based on regular tetrahedron elements, characterized in that: The following steps are involved: Step 1: Based on mathematical orthogonality and mechanical equilibrium, construct the spatial deformation of the regular tetrahedron unit in the spatial rectangular coordinate system and obtain the deformation decomposition basis matrix of the regular tetrahedron unit; The regular tetrahedron unit has four nodes, and the coordinates of the four nodes in the X, Y and Z directions are x1, y1, z1, x2, y2, z2, x3, y3, z3, x4, y4, z4; the spatial deformation of the regular tetrahedron unit is composed of 12 basic deformations and basic displacements: X-axial tension and compression deformation, Y-axial tension and compression deformation, Z-axial tension and compression deformation, shear deformation in the XOY plane, shear deformation in the XOZ plane, shear deformation in the YOZ plane, X-axial rigid body translation, Y-axial rigid body translation, Z-axial rigid body translation, XOY plane rigid body rotation, XOZ plane rigid body rotation and YOZ plane rigid body rotation; The basic vectors of the basic deformation and basic displacement of the regular tetrahedron unit are d1~d 12 , as follows: d1 is the x-axis tensile and compressive deformation basis vector of the regular tetrahedron element: d2 is the Y-axis tensile and compressive deformation basis vector of the regular tetrahedron element: d3 is the Z-axis tensile and compressive deformation basis vector of the regular tetrahedron element: d4 is the shear deformation basis vector in the XOY plane of the regular tetrahedron element: d5 is the shear deformation basis vector in the XOZ plane of the regular tetrahedron element: d6 is the shear deformation basis vector in the YOZ plane of the regular tetrahedron element: d7 is the x-axis rigid body translation basis vector of the regular tetrahedron element: d8 is the Y-axis rigid body translation basis vector of the regular tetrahedron unit: d9 is the rigid body translation basis vector of the regular tetrahedron unit along the Z axis: d 10 is the rigid body rotation basis vector in the XOY plane of the regular tetrahedron unit: d 11 is the rigid body rotation basis vector in the XOZ plane of the regular tetrahedron unit: d 12 is the rigid body rotation basis vector in the YOZ plane of the regular tetrahedron unit: The above basic deformation and basic displacement basis vectors satisfy mathematical orthogonality, that is: The basic vectors of the basic deformation and basic displacement of the above-mentioned regular tetrahedron unit are d1~d 12 Construct the deformation decomposition basis matrix D of the regular tetrahedron unit, D=(d1 d2…d 11 d 12 ) T ; Step 2: Establish a spatial irregular boundary component model, use regular tetrahedron elements to divide any part of the irregular boundary component and perform finite element solution to obtain the node coordinate values ​​of the regular tetrahedron elements in the spatial rectangular coordinate system and the node coordinate values ​​of the regular tetrahedron elements after arbitrary displacement and deformation under arbitrary load conditions, and then obtain the node displacement vectors of the regular tetrahedron elements after arbitrary displacement and deformation under arbitrary load conditions; Step 3: Project the node displacement vectors of the regular tetrahedron element after generating arbitrary displacement and deformation under any load condition onto the deformation decomposition basis matrix to obtain the basic deformation and basic displacement projection coefficient vector of the regular tetrahedron element after generating arbitrary displacement and deformation under any load condition; Step 4: Based on the basic deformation projection coefficient of the regular tetrahedron element after any displacement or deformation under any load condition, the basic deformation information of the regular tetrahedron element under any load condition is obtained, and the main deformation and secondary deformation of the regular tetrahedron element under any load condition are identified, thereby realizing the deformation decomposition and deformation quantification analysis of any part of the component with irregular boundaries.

2. The method for decomposing irregular boundary components based on regular tetrahedron elements according to claim 1, characterized in that: The node coordinate vector of the regular tetrahedron unit in the space rectangular coordinate system is d p , <h2 style=";text-align:left;direction:ltr">d<h2 style=";text-align:left;direction:ltr"> p <h2 style=";text-align:left;direction:ltr"> (x1 y1 z1 x2 y2 z2 x3 y3 z3 x4 y4 z4) The node coordinate vector of the tetrahedron element after any displacement and deformation under any load condition is d q , <h2 style=";text-align:left;direction:ltr">d<h2 style=";text-align:left;direction:ltr"> q <h2 style=";text-align:left;direction:ltr"> (x1'y1'z1'x'2y'2z'2x'3y'3z'3x'4y'4z'4) By d q -d p The node displacement vector d after the regular tetrahedron element produces arbitrary displacement and deformation under any load condition can be obtained r , 3. The method for decomposing irregular boundary components based on regular tetrahedron elements according to claim 2, characterized in that: Step 3 is as follows: The node displacement vector d after the regular tetrahedron element produces arbitrary displacement and deformation under any load condition r Projected onto the deformation decomposition basis matrix D, that is w=d r ·D -1 , w is the basic deformation and basic displacement projection coefficient vector of the regular tetrahedron element: in=(in1 in2…in 11 In 12 ), Among them: w1 is the projection coefficient of the tensile and compressive deformation of the unit in the X axis, w2 is the projection coefficient of the tensile and compressive deformation in the Y axis, w3 is the projection coefficient of the tensile and compressive deformation in the Z axis, w4 is the projection coefficient of the shear deformation in the XOY plane, w5 is the projection coefficient of the shear deformation in the XOZ plane, w6 is the projection coefficient of the shear deformation in the YOZ plane, w7 is the projection coefficient of the rigid body translation in the X axis, w8 is the projection coefficient of the rigid body translation in the Y axis, w9 is the projection coefficient of the rigid body translation in the Z axis, w 10 is the XOY plane rigid body rotation projection coefficient, w 11 is the XOZ plane rigid body rotation projection coefficient, w 12 YOZ plane rigid body rotation projection coefficient.

4. The method for decomposing a component with irregular boundary based on regular tetrahedron elements according to claim 1 or 3, characterized in that: The step 4 specifically includes: The decomposition results are subjected to rigid-flexible separation, i.e. the basic displacement projection coefficient w7-w is ignored. 12 In order to eliminate the influence of the deformation, only the absolute values ​​of the basic deformation projection coefficients w1-w6 in the component information are compared. The deformation corresponding to the maximum absolute value of the projection coefficient is determined as the main deformation of the regular tetrahedron unit. Similarly, the second largest one is determined as the secondary deformation of the regular tetrahedron unit, thereby realizing the quantitative analysis of the deformation of any part of the spatial component.

5. The method for decomposing deformation of components with irregular boundaries based on regular tetrahedron elements according to claim 3, characterized in that: The positive and negative properties of the projection coefficients w1-w3 of the regular tetrahedron element's tensile and compressive deformation are used to further judge the tensile and compressive state of the element. If w1 is positive, it means that the regular tetrahedron element is in an X-axis tensile deformation state; if w1 is negative, it means that the regular tetrahedron element is in an X-axis compressive deformation state, and the same applies to w2 and w3.

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