CN114186310A - Structural deformation decomposition method based on space 8-node wall unit - Google Patents

Abstract

The invention belongs to the technical field of mechanical analysis and the field of structural design, and discloses a structural deformation decomposition method based on a space 8-node wall unit, which comprises the following steps: constructing basic displacement and basic deformation basis vectors of the 8-node wall units to obtain orthogonal mechanical basis matrices of the 8-node space wall unitsP(ii) a Selecting 4 angular points of the quadrilateral shell unit and the middle point on each edge to form an 8-node wall unit, and obtaining the displacement vector of each node of the 8-node wall units(ii) a Obtaining the projection coefficient vector of the basic deformation and the basic displacement of each wall unitr(ii) a According to projection coefficient vectorrThe magnitude of the middle projection coefficient is used to obtain the primary basic deformation and the secondary basic deformation of each wall unit, namelyAnd realizing the deformation decomposition and the deformation identification of the space structure model. The method can identify the deformation conditions of the shear walls, the coupling beams and other members in different directions in the space structure in detail, and particularly can accurately identify the out-of-plane deformation of the wall unit.

Description

Structural deformation decomposition method based on space 8-node wall unit

Technical Field

The invention belongs to the technical field of mechanical analysis and the field of structural design, and relates to a structural deformation decomposition method based on a space 8-node wall unit.

Technical Field

In recent years, shear wall structures have been widely used at home and abroad, and in actual structures, not only can the shear wall generate deformation such as in-plane tension and compression, shearing, bending and the like, but also out-of-plane deformation after being stressed. However, in the structural design, only the stress performance in the plane of the shear wall is usually considered, and the deformation outside the plane of the shear wall is neglected, so that the structural design scheme is incomplete. The shear wall is weak outside the plane, and out-of-plane deformation and damage can be generated under the action of earthquake load. Therefore, the method has important significance in accurately identifying the deformation conditions in and out of the shear wall surface in the structure, analyzing the weak part of the structure and providing corresponding reinforcing measures.

Disclosure of Invention

The invention aims to provide a structural deformation decomposition method based on a space 8-node wall unit, which finds out a weak part of a shear wall structure through finite element analysis of a space structure model and deformation decomposition of the wall unit and can assist in designing the structure model in the shear wall structure design stage.

In order to achieve the purpose, the invention adopts the following technical scheme:

the invention provides a structural deformation decomposition method based on a space 8-node wall unit, which comprises the following steps of:

step 1: in a three-dimensional space, constructing basic displacement and basic deformation basis vectors of 8-node wall units according to a stress balance condition and an orthogonal decomposition theory, thereby obtaining an orthogonal mechanical basis matrix P of the 8-node space wall units;

step 2: establishing a space structure model under a space rectangular coordinate system, dividing the space structure model by adopting a quadrilateral shell unit, selecting 4 angular points of the quadrilateral shell unit and a middle point on each edge to form an 8-node wall unit, and obtaining a displacement vector s of each node of the 8-node wall unit;

and step 3: projecting the displacement vector s of each node of the 8-node wall unit onto an orthogonal mechanical basis matrix P of the 8-node wall unit to obtain a projection coefficient vector r of the basic deformation and the basic displacement of each wall unit;

and 4, step 4: and obtaining the primary basic deformation and the secondary basic deformation of each wall unit according to the size of the projection coefficient in the projection coefficient vector r, so that the deformation decomposition and the deformation identification of the space structure model can be realized.

Preferably, the basic displacement and basic deformation of the 8-node wall unit comprises: the method comprises the following steps of X axial rigid body translation displacement, Y axial rigid body translation displacement, Z axial rigid body translation displacement, rotation displacement around an X axial rigid body, rotation displacement around a Y axial rigid body, rotation displacement around a Z axial rigid body, XOY plane X axial tension-compression deformation, XOY plane Y axial tension-compression deformation, XOY plane X axial in-plane bending deformation, XOY plane Y axial in-plane bending deformation, XOY plane shearing deformation, XOY plane angular buckling deformation, XOY plane X axial expansion-contraction deformation, XOY plane Y axial buckling deformation, XOY plane X axial buckling deformation, XOY plane Y axial punching deformation, XOY plane outside bending deformation, XOY plane side buckling deformation, X axial reverse buckling deformation around an X axis, reverse deformation around a Y axis, XOY plane X axial reverse symmetry bending deformation, and XOY axial reverse symmetry bending deformation.

Preferably, the step 1 specifically comprises the following steps:

step 1.1: under a space rectangular coordinate system, 24 basic displacement and basic deformation bases p are constructed aiming at 8 node wall units according to the adoption of a stress balance condition, a moment balance condition and an orthogonal theory₁～p₂₄The method comprises the following steps:

p₁representing the rigid body translation displacement in the X axial direction:

p₂expressing the rigid body translation displacement in the Y axial direction:

p₃representing the rigid body translation displacement in the Z axial direction:

p₄representing rigid body rotational displacement around the X axis:

p₅representing rigid body rotational displacement around the Y axis:

p₆representing rigid body rotational displacement around the Z axis:

p₇represents the XOY plane X axial tension-compression deformation:

p₈represents the XOY plane Y axial tension-compression deformation:

p₉represents the XOY plane X-axis in-plane bending deformation:

p₉＝(-0.5,0,0,0.5,0,0,-0.5,0,0,0.5,0,0,0,0,0,0,0,0,0,0,0,0,0,0)^T

p₁₀represents the XOY plane Y axial in-plane bending deformation:

p₁₀＝(0，0.5，0，0，-0.5，0，0，0.5，0，0，-0.5，0，0，0，0，0，0，0，0，0，0，0，0，0)^T，

p₁₁represents XOY plane shear deformation:

p₁₂represents XOY face angle warp:

p₁₂＝(0，0，-0.5，0，0，0.5，0，0，-0.5，0，0，0.5，0，0，0，0，0，0，0，0，0，0，0，0)^T，

p₁₃represents the XOY plane X axial expansion and contraction deformation:

p₁₄represents the XOY plane Y axial expansion and contraction deformation:

p₁₅represents XOY plane Y axial deflection:

p₁₅＝(0,0,0,0,0,0,0,0,0,0,0,0,0,0.5,0,0,-0.5,0,0,0.5,0,0,-0.5,0)^T，

p₁₆represents the XOY plane X axial deflection:

p₁₆＝(0，0，0，0，0，0，0，0，0，0，0，0，0.5，0，0，-0.5，0，0，0.5，0，0，-0.5，0，0)^T，

p₁₇represents the XOY plane Y axial die-cut deformation:

p₁₈represents the XOY plane X axial die-cut deformation:

p₁₉represents the XOY out-of-plane bending deformation:

p₂₀represents XOY face edge warp deformation:

p₂₀＝(0，0，0，0，0，0，0，0，0，0，0，0，0，0，0.5，0，0，-0.5，0，0，0.5，0，0，-0.5)^T，

p₂₁represents reverse buckling deformation around the X axis:

p₂₂represents reverse buckling deformation around the Y axis:

p₂₃represents the XOY plane X axial antisymmetric bending deformation:

p₂₄represents the XOY plane Y axial antisymmetric bending deformation:

wherein m is the axial length of the unit Y, and n is the axial length of the unit X;

step 1.2: combining the 6 basic displacement vectors and 18 basic deformation vectors shown in the step 1.1 to construct a complete orthonormal mechanical basis matrix P of the space wall unit:

P＝[p₁ p₂ p₃ p₄ p₅ p₆ p₇ p₈ p₉ p₁₀ p₁₁ p₁₂ p₁₃ p₁₄ p₁₅ p₁₆ p₁₇ p₁₈ p₁₉ p₂₀ p₂₁p₂₂ p₂₃ p₂₄]。

preferably, step 2 specifically comprises the following steps:

step 2.1: establishing a space structure model under a three-dimensional rectangular coordinate system by using finite element software, dividing the space structure model by adopting the quadrilateral shell units, selecting 4 angular points of the quadrilateral shell units and the middle point on each edge to form 8-node wall units, and then selecting the node coordinate d of the ith 8-node wall unit_i：

d_i＝(x_i1，y_i1，z_i1，x_i2，y_i2，z_i2，x_i3，y_i3，z_i3，x_i4，y_i4，z_i4，x_i5，y_i5，z_i5，x_i6，y_i6，z_i6，x_i7，y_i7，z_i7，x_i8，y_i8，z_i8)，

Wherein:

d_irepresenting the node coordinates of the ith wall element in the space model, i ═ 1,2, 3.., k, where k is the number of wall elements;

x_ijcoordinate values on an X axis representing a jth node of an ith wall element;

y_ija coordinate value on the Y axis representing the jth node of the ith wall element;

z_ija coordinate value on the Z axis representing the jth node of the ith wall element; j is 1,2,3,4,5,6,7, 8;

step 2.2: the space model is displaced and deformed under any load action, and the deformed ith wall unit node coordinate d 'is generated'_i：

d'_i＝(x'_i1,y'_i1,z'_i1,x'_i2,y'_i2,z'_i2,x'_i3,y'_i3,z'_i3,x'_i4,y'_i4,z'_i4,x'_i5,y'_i5,z'_i5,x'_i6,y'_i6,z'_i6,x'_i7,y'_i7,z'_i7,x'_i8,y'_i8,z'_i8)，

Wherein:

d'_irepresenting the node coordinates of the ith wall unit after the spatial structure model is deformed, wherein i is 1,2,3, and k is the number of the wall units;

x'_ija coordinate value on the X axis of the j node after the deformation of the ith wall unit is represented;

y'_ija coordinate value on the Y axis of the j node after the deformation of the ith wall unit is represented;

z'_ija coordinate value on the Z axis of the j node after the deformation of the ith wall unit is represented; j is 1,2,3,4,5,6,7, 8;

step 2.3: the deformed wall unit node coordinates d'_iSubtracting the coordinates d of the node of the wall unit before deformation_iObtaining a node displacement vector s of the ith wall unit_i：

S_i＝(x'_i1-x_i1,y'_i1-y_i1,z'_i1-z_i1,x'_i2-x_i2,y'_i2-y_i2,z'_i2-z_i2,x'_i3-x_i3,y'_i3-y_i3,z'_i3-z_i3,x'_i4-x_i4,y'_i4-y_i4,z'_i5-z_i5,x'_i5-x_i5,y'_i5-y_i5,z'_i5-z_i5,x'_i6-x_i6,y'_i6-y_i6,z'_i6-z_i6,x'_i7-x_i7,y'_i7-y_i7,z'_i7-z_i7,x'_i8-x_i8,y'_i8-y_i8,z'_i8-z_i8)，

Preferably, the step 3 specifically comprises:

step 3.1: the node coordinate displacement vector s of the ith 8-node wall unit_iProjected to a corresponding complete orthonormal mechanical basis matrix P_iTo obtain:

s_i＝r_i·p_i；

step 3.2: the above formula is converted to obtain the projection coefficient vector r of the basic displacement and the basic deformation of the ith 8-node wall unit in the space structure model_i：

Wherein:

s_ithe node displacement vector of the ith 8-node wall unit; p_iIs a complete orthonormal mechanical basis matrix, P, of the ith 8-node wall unit_i ^TIs P_iThe transposed matrix of (p)_i)^-1Is p_iThe inverse matrix of (d); r is_iProjection coefficient vectors of basic deformation and basic displacement of the ith 8-node wall unit;

p_i＝[p_i1,p_i2,p_i3,p_i4,p_i5,p_i6,p_i7,p_i8,p_i9,p_i10,p_i11,p_i12,p_i13,p_i14,p_i15,p_i16,p_i17,p_i18,p_i19,p_i20,p_i21,p_i22,p_i23,p_i24]，

r_i＝(r_i1,r_i2,r_i3,r_i4,r_i5,r_i6,r_i7,r_i8,r_i9,r_i10,r_i11,r_i12,r_i13,r_i14,r_i15,r_i16,r_i17,r_i18,r_i19,r_i20,r_i21,r_i22,r_i23,r_i24)，

wherein p is_ilThe ith basic displacement and basic deformation basic vector of the ith rectangular unit;

r_ijthe projection coefficients corresponding to the ith elementary displacement and distortion elementary vector in the ith rectangular unit are 1, 2.

Preferably, the step 4 specifically includes:

eliminating projection coefficient vector r of each wall unit_iThe projection coefficients r corresponding to the 6 basic displacements in (1)_i1～r_i6And comparing the projection coefficients r corresponding to the remaining 18 basic deformations of each unit in the structure one by one_i7～r_i24The absolute value of the deformation analysis model is the maximum absolute value of the main deformation of the wall unit, the absolute value of the deformation analysis model is the minimum absolute value of the deformation analysis model, the maximum absolute value of the deformation analysis model is the main deformation of the wall unit, the minimum absolute value of the deformation analysis model is the minor deformation of the rectangular unit, and the main basic deformation and various minor basic deformations of each wall unit are obtained, so that the deformation decomposition and the deformation identification of the structure model are realized.

Compared with the prior art, the invention has the beneficial effects that:

the method is different from the prior method that other units can only analyze the in-plane deformation of the shear wall and cannot analyze the whole structure model in the space, and the wall unit can accurately identify the in-plane and out-of-plane basic deformation conditions of the shear wall and the cross-height smaller coupling beam. Compared with an entity unit, the shear wall model built by adopting the spatial quadrilateral shell units is more convenient, the calculation efficiency is higher, and the deformation decomposition speed of the 8-node wall unit is higher than that of the 8-node entity unit. The shear wall structure is analyzed by the space wall units, and the deformation condition of the shear wall at each part can be identified, so that the weak parts of the structure and the component are obtained, different designs are made for the shear walls at different parts, and the defects of structural design are overcome.

Drawings

Fig. 1 is a schematic flow chart illustrating a method for decomposing a space wall unit according to the present invention.

Fig. 2 is a schematic diagram of a space wall unit in a rectangular space coordinate system.

Fig. 3 is a schematic diagram of any deformation of a space wall unit in a rectangular space coordinate system.

Fig. 4 is a schematic diagram of X-axis rigid body translational displacement of a space wall unit in a space rectangular coordinate system.

Fig. 5 is a schematic diagram of the Y-axis rigid body translational displacement of the space wall unit in the space rectangular coordinate system.

Fig. 6 is a schematic diagram of the Z-axis rigid body translational displacement of the space wall unit in the rectangular space coordinate system.

Fig. 7 is a schematic diagram of the rotational displacement of the rigid body in the X axis direction of the space wall unit in the rectangular spatial coordinate system.

Fig. 8 is a schematic diagram of the Y-axis rigid body rotational displacement of the space wall unit in the rectangular spatial coordinate system.

Fig. 9 is a schematic view of Z-axis rigid body rotational displacement of a space wall unit in a rectangular spatial coordinate system.

Fig. 10 is a schematic diagram of the XOY plane X axial tension-compression deformation of the space wall unit in the rectangular space coordinate system.

Fig. 11 is a schematic diagram of XOY plane Y axial tension-compression deformation of a space wall unit in a rectangular space coordinate system.

Fig. 12 is a schematic diagram of the XOY plane X-axis in-plane bending deformation of the space wall unit in the rectangular spatial coordinate system.

Fig. 13 is a schematic diagram of XOY plane Y axis in-plane bending deformation of a space wall unit in a rectangular spatial coordinate system.

Fig. 14 is a schematic diagram of XOY plane shear deformation of a space wall unit in a rectangular space coordinate system.

Fig. 15 is a schematic view of XOY face angle warp deformation of a space wall unit in a rectangular spatial coordinate system.

Fig. 16 is a schematic diagram of the XOY plane X axial expansion and contraction deformation of the space wall unit in the rectangular space coordinate system.

Fig. 17 is a schematic diagram of XOY plane Y axial expansion and contraction deformation of a space wall unit in a rectangular spatial coordinate system.

Fig. 18 is a schematic diagram of XOY plane Y axial deflection deformation of a space wall unit in a rectangular spatial coordinate system.

Fig. 19 is a schematic diagram of the XOY plane X-direction deflection deformation of the space wall unit in the rectangular space coordinate system.

Fig. 20 is a schematic diagram of XOY plane Y axial punching deformation of a space wall unit in a rectangular space coordinate system.

Fig. 21 is a schematic diagram of XOY plane X-axis punching deformation of a space wall unit in a rectangular space coordinate system.

Fig. 22 is a schematic view of XOY out-of-plane bending deformation of a space wall element in a rectangular spatial coordinate system.

Fig. 23 is a schematic diagram of XOY plane edge warp deformation of a space wall unit in a rectangular spatial coordinate system.

Fig. 24 is a schematic diagram of the reverse buckling deformation of the space wall unit around the X-axis in the rectangular space coordinate system.

Fig. 25 is a schematic diagram of reverse buckling deformation of a space wall unit around the Y-axis in a rectangular spatial coordinate system.

Fig. 26 is a schematic diagram of XOY plane X-axis anti-symmetric bending deformation of a space wall unit in a rectangular space coordinate system.

Fig. 27 is a schematic diagram of XOY plane Y axial antisymmetric bending deformation of a space wall unit in a rectangular space coordinate system.

FIG. 28 is a schematic diagram of a finite element model of a space shear wall structure.

Fig. 29 is a building plan view of a shear wall structure.

Fig. 30 is a schematic view of two shear walls at the rightmost side of the shear wall structure and the selection of units.

Detailed Description

The following examples are intended to illustrate the invention, but are not intended to limit the scope of the invention. Unless otherwise specified, the technical means used in the examples are conventional means well known to those skilled in the art. The test methods in the following examples are conventional methods unless otherwise specified.

Fig. 1 is a flowchart of a structural deformation decomposition method based on a space 8-node wall unit.

Fig. 2 is a schematic diagram of an 8-node wall unit in a space, where 8 nodes of the 8-node wall unit are respectively located at 4 vertexes and midpoints on 4 opposite sides of a rectangular wall, the 4 vertexes are respectively marked as node 1, node 2, node 3, and node 4 from the lower left corner counterclockwise, and points on the 4 sides are respectively marked as node 5, node 6, node 7, and node 8 from the lower midpoint counterclockwise.

Fig. 3 shows any deformation of the space 8 node wall unit after being stressed. Fig. 4 to 27 are schematic diagrams of 6 basic displacements and 18 basic deformations of a space 8-node wall unit, which are respectively: the method comprises the following steps of X axial rigid body translation displacement, Y axial rigid body translation displacement, Z axial rigid body translation displacement, rotation displacement around an X axial rigid body, rotation displacement around a Y axial rigid body, rotation displacement around a Z axial rigid body, XOY plane X axial tension-compression deformation, XOY plane Y axial tension-compression deformation, XOY plane X axial in-plane bending deformation, XOY plane Y axial in-plane bending deformation, XOY plane shearing deformation, XOY plane angular buckling deformation, XOY plane X axial expansion-contraction deformation, XOY plane Y axial buckling deformation, XOY plane X axial buckling deformation, XOY plane Y axial punching deformation, XOY plane outside bending deformation, XOY plane side buckling deformation, X axial reverse buckling deformation around an X axis, reverse deformation around a Y axis, XOY plane X axial reverse symmetry bending deformation, and XOY axial reverse symmetry bending deformation.

The base vectors of the above basic displacement and basic deformation are respectively p₁～p₂₄：

p₁Representing the rigid body translation displacement in the X axial direction:

p₂expressing the rigid body translation displacement in the Y axial direction:

p₃representing the rigid body translation displacement in the Z axial direction:

p₄representing rigid body rotational displacement around the X axis:

p₅representing rigid body rotational displacement around the Y axis:

p₆representing rigid body rotational displacement around the Z axis:

p₇represents the XOY plane X axial tension-compression deformation:

p₈represents the XOY plane Y axial tension-compression deformation:

p₉represents the XOY plane X-axis in-plane bending deformation:

p₉＝(-0.5,0,0,0.5,0,0,-0.5,0,0,0.5,0,0,0,0,0,0,0,0,0,0,0,0,0,0)^T

p₁₀represents the XOY plane Y axial in-plane bending deformation:

p₁₀＝(0，0.5，0，0，-0.5，0，0，0.5，0，0，-0.5，0，0，0，0，0，0，0，0，0，0，0，0，0)^T，

p₁₁represents XOY plane shear deformation:

p₁₂represents XOY face angle warp:

p₁₂＝(0，0，-0.5，0，0，0.5，0，0，-0.5，0，0，0.5，0，0，0，0，0，0，0，0，0，0，0，0)^T，

p₁₃represents the XOY plane X axial expansion and contraction deformation:

p₁₄represents the XOY plane Y axial expansion and contraction deformation:

p₁₅represents XOY plane Y axial deflection:

p₁₅＝(0,0,0,0,0,0,0,0,0,0,0,0,0,0.5,0,0,-0.5,0,0,0.5,0,0,-0.5,0)^T，

p₁₆represents the XOY plane X axial deflection:

p₁₆＝(0，0，0，0，0，0，0，0，0，0，0，0，0.5，0，0，-0.5，0，0，0.5，0，0，-0.5，0，0)^T，

p₁₇represents the XOY plane Y axial die-cut deformation:

p₁₈represents the XOY plane X axial die-cut deformation:

p₁₉represents the XOY out-of-plane bending deformation:

p₂₀represents XOY face edge warp deformation:

p₂₀＝(0，0，0，0，0，0，0，0，0，0，0，0，0，0，0.5，0，0，-0.5，0，0，0.5，0，0，-0.5)^T，

p₂₁represents reverse buckling deformation around the X axis:

p₂₂represents reverse buckling deformation around the Y axis:

p₂₃represents the XOY plane X axial antisymmetric bending deformation:

p₂₄represents the XOY plane Y axial antisymmetric bending deformation:

wherein m is the length of the unit in the y direction, and n is the length of the unit in the x direction;

combined base vectorp₁～p₂₄Forming a complete orthogonal mechanical basis matrix P:

P＝[p₁ p₂ p₃ p₄ p₅ p₆ p₇ p₈ p₉ p₁₀ p₁₁ p₁₂ p₁₃ p₁₄ p₁₅ p₁₆ p₁₇ p₁₈ p₁₉ p₂₀ p₂₁p₂₂ p₂₃ p₂₄]。

establishing a structural model under a space rectangular coordinate system by using finite element software, selecting 4 corner points of the quadrilateral shell unit and the middle point on each edge to form an 8-node wall unit, and then selecting the node coordinate d of the ith 8-node wall unit_i：

d_i＝(x_i1，y_i1，z_i1，x_i2，y_i2，z_i2，x_i3，y_i3，z_i3，x_i4，y_i4，z_i4，x_i5，y_i5，z_i5，x_i6，y_i6，z_i6，x_i7，y_i7，z_i7，x_i8，y_i8，z_i8)，

Wherein:

d_irepresenting the node coordinates of the ith wall unit in the space model, wherein i is 1,2, 3.

x_ijCoordinate values on an x-axis representing a jth node of an ith wall element;

y_ija coordinate value on the y-axis representing the jth node of the ith wall element;

z_ija coordinate value on a z-axis representing a jth node of an ith wall element; j is 1,2,3,4,5,6,7, 8.

The spatial model is displaced and deformed under the action of any load, discrete units in the spatial model are also displaced and deformed, and the deformed ith wall unit node coordinate d is generated_i'：

d'_i＝(x'_i1,y'_i1,z'_i1,x'_i2,y'_i2,z'_i2,x'_i3,y'_i3,z'_i3,x'_i4,y'_i4,z'_i4,x'_i5,y'_i5,z'_i5,x'_i6,y'_i6,z'_i6,x'_i7,y'_i7,z'_i7,x'_i8,y'_i8,z'_i8)，

Wherein:

d'_irepresenting the node coordinates of the ith wall unit after the spatial structure model is deformed, wherein i is 1,2,3, and k is the number of the wall units;

x'_ija coordinate value on an x axis of a j node after the i wall unit is deformed;

y'_ija coordinate value on the y axis of the j node after the deformation of the ith wall unit is represented;

z'_ija coordinate value on the z axis of the j node after the deformation of the ith wall unit is represented; j is 1,2,3,4,5,6,7, 8.

The deformed wall unit node coordinate d_i' subtract the wall element node coordinate d before deformation_iObtaining a node displacement vector s of the ith wall unit_i：

The node coordinate displacement vector s of the ith 8-node wall unit_iProjected to a corresponding complete orthonormal mechanical basis matrix P_iTo obtain:

s_i＝r_i·p_i；

and then the above formula is converted to obtain the basic displacement and deformation projection coefficient vector r of the ith wall unit in the space structure model_i：

Wherein:

s_inode position of ith 8-node wall unitA shift quantity; p_iIs a complete orthonormal mechanical basis matrix, P, of the ith 8-node wall unit_i ^TIs P_iThe transposed matrix of (p)_i)^-1Is p_iThe inverse matrix of (d); r is_iProjection coefficient vectors of basic deformation and basic displacement of the ith 8-node wall unit;

p_i＝[p_i1,p_i2,p_i3,p_i4,p_i5,p_i6,p_i7,p_i8,p_i9,p_i10,p_i11,p_i12,p_i13,p_i14,p_i15,p_i16,p_i17,p_i18,p_i19,p_i20,p_i21,p_i22,p_i23,p_i24]，

r_i＝(r_i1,r_i2,r_i3,r_i4,r_i5,r_i6,r_i7,r_i8,r_i9,r_i10,r_i11,r_i12,r_i13,r_i14,r_i15,r_i16,r_i17,r_i18,r_i19,r_i20,r_i21,r_i22,r_i23,r_i24)，

wherein p is_ilThe ith basic displacement and basic deformation basic vector of the ith rectangular unit;

r_ijthe projection coefficients corresponding to the ith elementary displacement and distortion elementary vector in the ith rectangular unit are 1, 2.

Because the rigid body displacement can not cause the structure and the component to generate stress and strain, the projection coefficient vector r of each unit is rejected_iThe projection coefficients r corresponding to the 6 basic displacements in (1)_i1～r_i6And comparing the projection coefficients r corresponding to the remaining 18 basic displacements of each unit in the structure one by one_i7～r_i24Wherein the absolute value is the main deformation of the wall unit with the largest absolute value, and the absolute value is the secondary deformation of the rectangular unit with the smaller absolute value, so as to obtain the main basic deformation and various secondary basic deformations of each wall unit, thereby realizing the deformation classification of the structure modelSolution and deformation identification.

It should be noted that the projection coefficient may have a negative value, and the positive and negative values indicate the deformation direction, such as the X-direction tension-compression deformation base p₇Corresponding projection coefficient r₇Is positive, expressed as tensile deformation, r₇Negative, indicating compressive deformation; also as X-direction bending deformation group p₉Corresponding projection coefficient r₉Positive indicates that the bend is a bend in which the upper side of the cell is compressed and the lower side is pulled, and vice versa if negative. In addition, the wall elements on the XOZ surface and the YOZ surface under the rectangular space coordinate system have the same deformation decomposition method as the wall elements on the XOY surface.

Rigid body rotational displacement error analysis

The rigid body rotation displacement is nonlinear displacement, and an error is generated during linear decomposition, namely, the wall unit rigid body rotation displacement not only has a projection coefficient on a rigid body rotation displacement base vector, but also has a projection coefficient on other displacement and deformation base vectors, and an error exists with a theoretical condition, so that error analysis needs to be performed on the magnitude of the projection coefficient of the wall unit rigid body rotation displacement on other deformation and displacement base vectors, and whether the rigid body rotation displacement affects the calculation precision is judged.

Setting the side length of the wall unit as l, when the unit rotates anticlockwise around a central point by theta, the displacement vectors of 8 nodes of the unit are as follows:

projecting the rotation displacement vector of the wall unit to a constructed complete orthogonal mechanical base to obtain that the projection coefficients of the rotation displacement vector of the wall unit are not 0 only on a rigid body rotation displacement base vector around a Z axis, an X axial tension-compression deformation base vector and a Y axial tension-compression deformation base vector, and the projection coefficients on other basic displacement and basic deformation base vectors are both 0; therefore, the 24 constraint equations obtained by the projection of the coordinate displacement vector of the rigid body rotation of the wall unit are simplified into 3 independent constraint equations as follows:

wherein: r is₆Is a projection coefficient of the rigid body rotational displacement around the Z-axis direction on the rigid body rotational displacement base, r₇、r₈The projection coefficients of the rigid body rotation displacement around the Z axis on the X tension and compression deformation base and the Y tension and compression deformation base are respectively.

Solving the above equation yields:

taylor expansion is carried out on sin theta and cos theta in the formula and high-order infinitesimal is ignored, so that:

then there are:

the rotational displacement in the Z-axis direction is known as p₇And p₈The projection coefficient of (A) is its in p₆The projection coefficients of the X-axis displacement and the Y-axis displacement are negligible and the error is within the allowable range of the method.

Application examples

A shear wall structure as shown in FIG. 28, a plan view of the structure as shown in FIG. 29, and a concrete elastic modulus of 3X 10¹¹pa, poisson's ratio 0.2. The deformation of cells No. 1-7 in fig. 30 under top load (the direction and location of force loading is shown in fig. 28).

Modeling by means of finite element software, dividing the model by adopting quadrilateral shell units, then carrying out stress analysis to obtain the deformation condition of the structure, and extracting the coordinates and relative displacement information of each node and unit in the structure; importing the file into mathematical analysis software for further analysis, and analyzing each fileAnd reassembling the unit information and the node information to enter a deformation decomposition calculation process. Because of the large number of structural units, only the calculation process of the wall unit (the wall unit No. 1 in fig. 30) of the first layer of the shear wall closest to the shaft No. 1 on the shaft a is listed here. Analyzing by finite element software to obtain a node coordinate vector d of the No. 1 unit₁And a displacement vector s₁：

d₁＝(0,0,0,1.5,0,0,1.5,0,1.2,0,0,1.2,0.75,0,0,1.5,0,0.6,0.75,0,1.2,0,0,0.6)，

s₁＝(0,0,0,0,0,0,4.969×10^-5,4.45×10^-6,-2×10^-5,5.614×10^-5,9.23×10^-6,6.814×10^-5,0,0,0,1.433×10^-5,2.8×10^-7,-1.239×10^-5,5.079×10^-5,7.9×10^-6,2.614×10^-5,2.005×10^-5,6.15×10^-6,3.517×10^-5)。

Since the plane of the unit No. 1 is the XOZ plane, the coordinates are first converted to convert the deformation decomposition base of the XOY plane into the deformation decomposition base of the XOZ plane, and the node coordinate vector d is used₁The length and width of the wall unit can be known, the length and width of the No. 1 unit are input into the orthogonal mechanical basis of the wall unit, and a complete orthogonal mechanical basis matrix P corresponding to the No. 1 unit is obtained₁。

P₁＝[p₁ p₂ p₃ p₄ p₅ p₆ p₇ p₈ p₉ p₁₀ p₁₁ p₁₂ p₁₃ p₁₄ p₁₅ p₁₆ p₁₇ p₁₈ p₁₉ p₂₀ p₂₁p₂₂ p₂₃ p₂₄]，

Wherein:

p₁＝(0.3536，0，0，0.3536，0，0，0.3536，0，0，0.3536，0，0，0.3536，0，0，0.3536，0，0，0.3536，0，0，0.3536，0，0)^T，

p₂＝(0，0，0.3536，0，0，0.3536，0，0，0.3536，0，0，0.3536，0，0，0.3536，0，0，0.3536，0，0，0.3536，0，0，0.3536)^T，

p₃＝(0，0.3536，0，0，0.3536，0，0，0.3536，0，0，0.3536，0，0，0.3536，0，0，0.3536，0，0，0.3536，0，0，0.3536，0)^T，

p₄＝(0，0.4082，0，0，0.4082，0，0，-0.4082，0，0，-0.4082，0，0，0.4082，0，0，0，0，0，-0.4082，0，0，0，0)^T，

p₅＝(0，-0.4082，0，0，0.4082，0，0，0.4082，0，0，-0.4082，0，0，0，0，0，0.4082，0，0，0，0，0，-0.4082，0)^T，

p₆＝(-0.2550，0，0.3188，-0.2550，0，-0.3188，0.2550，0，-0.3188，0.2550，0，0.3188，-0.2550，0，0，0，0，-0.3188，0.2550，0，0，0，0，0.3188)^T，

p₇＝(-0.4082，0，0，0.4082，0，0，0.4082，0，0，-0.4082，0，0，0，0，0，0.4082，0，0，0，0，0，-0.4082，0，0)^T，

p₈＝(0，0，-0.4082，0，0，-0.4082，0，0，0.4082，0，0，0.4082，0，0，-0.4082，0，0，0，0，0，0.4082，0，0，0)^T，

p₉＝(-0.5，0，0，0.5，0，0，-0.5，0，0，0.5，0，0，0，0，0，0，0，0，0，0，0，0，0，0)^T，

p₁₀＝(0，0，0.5，0，0，-0.5，0，0，0.5，0，0，-0.5，0，0，0，0，0，0，0，0，0，0，0，0)^T，

p₁₁＝(-0.3188，0，-0.2550，-0.3188，0，0.2550，0.3188，0，0.2550，0.3188，0，-0.2550，-0.3188，0，0，0，0，0.2550，0.3188，0，0，0，0，-0.2550)^T，

p₁₂＝(0，0.5，0，0，-0.5，0，0，0.5，0，0，-0.5，0，0，0，0，0，0，0，0，0，0，0，0，0)^T，

p₁₃＝(0.2887，0，0，-0.2887，0，0，-0.2887，0，0，0.2887，0，0，0，0，0，0.5774，0，0，0，0，0，-0.5774，0，0)^T，

p₁₄＝(0，0，0.2887，0，0，0.2887，0，0，-0.2887，0，0，-0.2887，0，0，-0.5774，0，0，0，0，0，0.5774，0，0，0)^T，

p₁₅＝(0，0，0，0，0，0，0，0，0，0，0，0，0，0，0.5，0，0，-0.5，0，0，0.5，0，0，-0.5)^T，

p₁₆＝(0，0，0，0，0，0，0，0，0，0，0，0，0.5，0，0，-0.5，0，0，0.5，0，0，-0.5，0，0)^T，

p₁₇＝(0，0，0.3536，0，0，0.3536，0，0，0.3536，0，0，0.3536，0，0，-0.3536，0，0，-0.3536，0，0，-0.3536，0，0，-0.3536)^T，

p₁₈＝(0.3536，0，0，0.3536，0，0，0.3536，0，0，0.3536，0，0，-0.3536，0，0，-0.3536，0，0，-0.3536，0，0，-0.3536，0，0)^T，

p₁₉＝(0，0.3536，0，0，0.3536，0，0，0.3536，0，0，0.3536，0，0，-0.3536，0，0，-0.3536，0，0，-0.3536，0，0，-0.3536，0)^T，

p₂₀＝(0，0，0，0，0，0，0，0，0，0，0，0，0，0.5，0，0，-0.5，0，0，0.5，0，0，-0.5，0)^T，

p₂₁＝(0，0.2887，0，0，0.2887，0，0，-0.2887，0，0，-0.2887，0，0，-0.5774，0，0，0，0，0，0.5774，0，0，0，0)^T，

p₂₂＝(0，0.2887，0，0，-0.2887，0，0，-0.2887，0，0，0.2887，0，0，0，0，0，0.5774，0，0，0，0，0，-0.5774，0)^T，

p₂₃＝(-0.2887，0，0，-0.2887，0，0，0.2887，0，0，0.2887，0，0，0.5774，0，0，0，0，0，-0.5774，0，0，0，0，0)^T，

p₂₄＝(0，0，0.2887，0，0，-0.2887，0，0，-0.2887，0，0，0.2887，0，0，0，0，0，0.5774，0，0，0，0，0，-0.5774)^T，

displacing the node by a vector s₁Projection onto an orthogonal mechanical basis matrix P₁The projection coefficient vector r of the unit can be obtained by calculation₁Comprises the following steps:

r₁＝(6.75×10^-5，3.43×10^-5，9.90×10^-6，-8.81×10^-6，-4.35×10^-6，8.32×10^-5，-4.97×10^-6，3.03×10^-5，3.23×10^-6，-4.41×10^-5，1.53×10^-5，-2.39×10^-6，-1.44×10^-6，1.20×10^-6，1.68×10^-6，8.21×10^-6，-2.76×10^-7，7.31×10^-6，-2.30×10^-7，7.35×10^-7，6.12×10^-7，-2.01×10^-6，1.23×10^-6，-2.02×10^-6)。

the basic deformation and displacement projection coefficients of the No. 2 unit to the No. 8 unit can be obtained, because the basic rigid body displacement does not cause the structure to generate stress, strain and damage, the projection coefficients corresponding to the 6 basic rigid body displacements in each unit are removed, and the proportion of the absolute values of the projection coefficients of the basic deformations of the No. 1 unit to the No. 7 unit to the total deformation is shown in the table 1.

TABLE 1 absolute ratio of each basic deformation and displacement projection coefficient of wall unit

From table 1, the proportion of various basic deformations in each unit can be known, and the shear wall at the position of each unit can be designed in a targeted manner according to the deformation characteristics of each unit. For example, the proportion of bending deformation in the XOZ plane Z direction in the unit No. 1 is the largest, then the tensile deformation in the XOZ plane Z direction and the shear deformation in the XOZ plane are the next, and the three basic deformations are the main deformations in the unit No. 2, so when designing the shear wall of the corresponding region of the unit No. 1 and the unit No. 2, special attention needs to be paid to the arrangement of the vertical steel bars and the resistance to shear deformation.

The above-mentioned embodiments are only for explaining the present invention, and not for limiting the implementation scope of the present invention, and it is obvious to those skilled in the art that other embodiments can be easily made by replacing or changing the technical contents disclosed in the present specification, so that the changes and modifications made on the principle of the present invention should be included in the claims of the present invention.

Claims (6)

1. A structural deformation decomposition method based on a space 8-node wall unit is characterized by comprising the following steps:

step 1: in a three-dimensional space, constructing basic displacement and basic deformation basis vectors of 8-node wall units according to a stress balance condition and an orthogonal decomposition theory, thereby obtaining an orthogonal mechanical basis matrix P of the 8-node space wall units;

step 2: establishing a space structure model under a space rectangular coordinate system, dividing the space structure model by adopting a quadrilateral shell unit, selecting 4 angular points of the quadrilateral shell unit and a middle point on each edge to form an 8-node wall unit, and obtaining a displacement vector s of each node of the 8-node wall unit;

and step 3: projecting the displacement vector s of each node of the 8-node wall unit onto an orthogonal mechanical basis matrix P of the 8-node wall unit to obtain a projection coefficient vector r of the basic deformation and the basic displacement of each wall unit;

and 4, step 4: and obtaining the primary basic deformation and the secondary basic deformation of each wall unit according to the size of the projection coefficient in the projection coefficient vector r, so that the deformation decomposition and the deformation identification of the space structure model can be realized.

2. The structural deformation decomposition method based on the space 8-node wall unit according to claim 1, wherein the basic displacement and the basic deformation of the 8-node wall unit comprise: the method comprises the following steps of X axial rigid body translation displacement, Y axial rigid body translation displacement, Z axial rigid body translation displacement, rotation displacement around an X axial rigid body, rotation displacement around a Y axial rigid body, rotation displacement around a Z axial rigid body, XOY plane X axial tension-compression deformation, XOY plane Y axial tension-compression deformation, XOY plane X axial in-plane bending deformation, XOY plane Y axial in-plane bending deformation, XOY plane shearing deformation, XOY plane angular buckling deformation, XOY plane X axial expansion-contraction deformation, XOY plane Y axial buckling deformation, XOY plane X axial buckling deformation, XOY plane Y axial punching deformation, XOY plane outside bending deformation, XOY plane side buckling deformation, X axial reverse buckling deformation around an X axis, reverse deformation around a Y axis, XOY plane X axial reverse symmetry bending deformation, and XOY axial reverse symmetry bending deformation.

3. The structural deformation decomposition method based on the space 8-node wall unit according to claim 2, wherein the step 1 specifically comprises the following steps:

step 1.1: under a space rectangular coordinate system, 24 basic displacement and basic deformation bases p are constructed aiming at 8 node wall units according to the adoption of a stress balance condition, a moment balance condition and an orthogonal theory₁～p₂₄The method comprises the following steps:

p₁representing the rigid body translation displacement in the X axial direction:

p₂expressing the rigid body translation displacement in the Y axial direction:

p₃indicating the translational position of rigid body in Z-axisMoving:

p₄representing rigid body rotational displacement around the X axis:

p₅representing rigid body rotational displacement around the Y axis:

p₆representing rigid body rotational displacement around the Z axis:

p₇represents the XOY plane X axial tension-compression deformation:

p₈represents the XOY plane Y axial tension-compression deformation:

p₉represents the XOY plane X-axis in-plane bending deformation:

p₉＝(-0.5,0,0,0.5,0,0,-0.5,0,0,0.5,0,0,0,0,0,0,0,0,0,0,0,0,0,0)^T

p₁₀represents the XOY plane Y axial in-plane bending deformation:

p₁₀＝(0，0.5，0，0，-0.5，0，0，0.5，0，0，-0.5，0，0，0，0，0，0，0，0，0，0，0，0，0)^T，

p₁₁represents XOY plane shear deformation:

p₁₂represents XOY face angle warp:

p₁₂＝(0，0，-0.5，0，0，0.5，0，0，-0.5，0，0，0.5，0，0，0，0，0，0，0，0，0，0，0，0)^T，

p₁₃represents the XOY plane X axial expansion and contraction deformation:

p₁₄represents the XOY plane Y axial expansion and contraction deformation:

p₁₅represents XOY plane Y axial deflection:

p₁₅＝(0,0,0,0,0,0,0,0,0,0,0,0,0,0.5,0,0,-0.5,0,0,0.5,0,0,-0.5,0)^T，

p₁₆represents the XOY plane X axial deflection:

p₁₆＝(0，0，0，0，0，0，0，0，0，0，0，0，0.5，0，0，-0.5，0，0，0.5，0，0，-0.5，0，0)^T，

p₁₇represents the XOY plane Y axial die-cut deformation:

p₁₈represents the XOY plane X axial die-cut deformation:

p₁₉represents the XOY out-of-plane bending deformation:

p₂₀represents XOY face edge warp deformation:

p₂₀＝(0，0，0，0，0，0，0，0，0，0，0，0，0，0，0.5，0，0，-0.5，0，0，0.5，0，0，-0.5)^T，

p₂₁represents reverse buckling deformation around the X axis:

p₂₂represents reverse buckling deformation around the Y axis:

p₂₃represents the XOY plane X axial antisymmetric bending deformation:

p₂₄represents the XOY plane Y axial antisymmetric bending deformation:

wherein m is the axial length of the unit Y, and n is the axial length of the unit X;

step 1.2: combining the 6 basic displacement vectors and 18 basic deformation vectors shown in the step 1.1 to construct a complete orthonormal mechanical basis matrix P of the space wall unit:

P＝[p₁ p₂ p₃ p₄ p₅ p₆ p₇ p₈ p₉ p₁₀ p₁₁ p₁₂ p₁₃ p₁₄ p₁₅ p₁₆ p₁₇ p₁₈ p₁₉ p₂₀ p₂₁ p₂₂ p₂₃p₂₄]。

4. the structural deformation decomposition method based on the space 8-node wall unit according to claim 1, wherein the step 2 specifically comprises the following steps:

step 2.1: establishing a space structure model under a three-dimensional rectangular coordinate system by using finite element software, dividing the space structure model by adopting the quadrilateral shell units, selecting 4 angular points of the quadrilateral shell units and the middle point on each edge to form 8-node wall units, and then selecting the node coordinate d of the ith 8-node wall unit_i：

d_i＝(x_i1，y_i1，z_i1，x_i2，y_i2，z_i2，x_i3，y_i3，z_i3，x_i4，y_i4，z_i4，x_i5，y_i5，z_i5，x_i6，y_i6，z_i6，x_i7，y_i7，z_i7，x_i8，y_i8，z_i8)，

Wherein:

d_irepresenting the node coordinates of the ith wall element in the space model, i ═ 1,2, 3.., k, where k is the number of wall elements;

x_ijcoordinate values on an X axis representing a jth node of an ith wall element;

y_ija coordinate value on the Y axis representing the jth node of the ith wall element;

z_ija coordinate value on the Z axis representing the jth node of the ith wall element; j is 1,2,3,4,5,6,7, 8;

step 2.2: the space model is displaced and deformed under any load action, and the deformed ith wall unit node coordinate d 'is generated'_i：

d'_i＝(x'_i1,y'_i1,z'_i1,x'_i2,y'_i2,z'_i2,x'_i3,y'_i3,z'_i3,x'_i4,y'_i4,z'_i4,x'_i5,y'_i5,z'_i5,x'_i6,y'_i6,z'_i6,x'_i7,y'_i7,z'_i7,x'_i8,y'_i8,z'_i8)，

Wherein:

d'_irepresenting the node coordinates of the ith wall unit after the spatial structure model is deformed, wherein i is 1,2,3, and k is the number of the wall units;

x'_ija coordinate value on an x axis of a j node after the i wall unit is deformed;

y'_ija coordinate value on the y axis of the j node after the deformation of the ith wall unit is represented;

z'_ija coordinate value on the z axis of the j node after the deformation of the ith wall unit is represented; j is 1,2,3,4,5,6,7, 8;

step 2.3: the deformed wall unit node coordinates d'_iSubtracting the coordinates d of the node of the wall unit before deformation_iObtaining a node displacement vector s of the ith wall unit_i：

5. The structural deformation decomposition method based on the space 8-node wall unit according to claim 4, wherein the step 3 is specifically:

step 3.1: the node coordinate displacement vector s of the ith 8-node wall unit_iProjected to a corresponding complete orthonormal mechanical basis matrix P_iTo obtain:

s_i＝r_i·p_i；

step 3.2: the above formula is converted to obtain the projection coefficient vector r of the basic displacement and the basic deformation of the ith 8-node wall unit in the space structure model_i：

Wherein:

s_ithe node displacement vector of the ith 8-node wall unit; p_iIs a complete orthonormal mechanical basis matrix, P, of the ith 8-node wall unit_i ^TIs P_iThe transposed matrix of (p)_i)^-1Is p_iThe inverse matrix of (d); r is_iProjection coefficient vectors of basic deformation and basic displacement of the ith 8-node wall unit;

p_i＝[p_i1,p_i2,p_i3,p_i4,p_i5,p_i6,p_i7,p_i8,p_i9,p_i10,p_i11,p_i12,p_i13,p_i14,p_i15,p_i16,p_i17,p_i18,p_i19,p_i20,p_i21,p_i22,p_i23,p_i24]，

r_i＝(r_i1,r_i2,r_i3,r_i4,r_i5,r_i6,r_i7,r_i8,r_i9,r_i10,r_i11,r_i12,r_i13,r_i14,r_i15,r_i16,r_i17,r_i18,r_i19,r_i20,r_i21,r_i22,r_i23,r_i24)，

wherein p is_ilIs the ith base of the ith rectangular unitThe present displacement and the basic deformation basis vector;

r_ijthe projection coefficients corresponding to the ith elementary displacement and distortion elementary vector in the ith rectangular unit are 1, 2.

6. The structural deformation decomposition method based on the space 8-node wall unit according to claim 5, wherein the step 4 specifically comprises:

eliminating projection coefficient vector r of each wall unit_iThe projection coefficients r corresponding to the 6 basic displacements in (1)_i1～r_i6And comparing the projection coefficients r corresponding to the remaining 18 basic deformations of each unit in the structure one by one_i7～r_i24The absolute value of the deformation analysis model is the maximum absolute value of the main deformation of the wall unit, the absolute value of the deformation analysis model is the minimum absolute value of the deformation analysis model, the maximum absolute value of the deformation analysis model is the main deformation of the wall unit, the minimum absolute value of the deformation analysis model is the minor deformation of the rectangular unit, and the main basic deformation and various minor basic deformations of each wall unit are obtained, so that the deformation decomposition and the deformation identification of the structure model are realized.

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