CN112035980A - Construction method of isogeometric mixed Kirchhoff-Love shell unit - Google Patents

Construction method of isogeometric mixed Kirchhoff-Love shell unit Download PDF

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CN112035980A
CN112035980A CN202010932345.6A CN202010932345A CN112035980A CN 112035980 A CN112035980 A CN 112035980A CN 202010932345 A CN202010932345 A CN 202010932345A CN 112035980 A CN112035980 A CN 112035980A
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郭玉杰
童明波
曾建江
陈先民
邹志辉
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Nanjing University of Aeronautics and Astronautics
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Abstract

The invention provides a construction method of an isogeometric hybrid Kirchoff-Love shell unit, which ensures that a thin shell structure rigidity matrix still has smaller bandwidth and sparsity after being condensed by freedom degree by constructing a Bessel dual basis function and using the Bessel dual basis function for independently interpolating film strain, and overcomes the defect that the sparsity of the rigidity matrix is damaged by the conventional isogeometric hybrid Kirchoff-Love thin shell unit, namely the sparsity of the rigidity matrix is damaged by the condensation of the freedom degree. Meanwhile, the novel isogeometric mixed Kirchhoff-Love thin-shell unit can eliminate the film blocking effect and keep the advantages of the existing isogeometric mixed shell unit. The method has the characteristics of simplicity, high efficiency and high precision, and has stronger universality, so the method is easy to popularize and use in engineering structure analysis.

Description

Construction method of isogeometric mixed Kirchhoff-Love shell unit
Technical Field
The invention relates to the field of computational mechanics, in particular to a construction method of an isogeometric mixed Kirchhoff-Love shell unit.
Background
The Isogeometric Analysis (Isogeometric Analysis) is a novel finite element method, which introduces Non-Uniform Rational B Splines (NURBS) describing geometric shapes in Computer Aided Design (CAD) into isoparametric finite elements, eliminates the repeated data conversion process between Computer Aided Design (CAD) and Computer Aided Analysis (CAE) software in the product Design process, saves a large amount of preprocessing time, has the characteristics of geometric accuracy, high-order continuity and the like, and is particularly suitable for structural Analysis of plate shells with curved surface characteristics.
A large number of thin-walled structures exist in aerospace, automobile, ship and other products, which mainly benefit from the high load/weight ratio, and shell elements are often used for simulation when finite element analysis is performed on the thin-walled structures. In the finite element analysis, the commonly used shell elements are Kirchhoff-love (KL) shell element and Reissner-Mindlin (RM) shell element. Compared with the Reissner-Mindlin shell unit, the Kirchoff-Love shell unit does not need additional rotational freedom, so that for a large model, the Kirchoff-Love shell unit can save more freedom, but the basis function of the Kirchoff-Love shell unit needs to have at least C1Continuity, whereas the conventional finite element method generally has only C at the cell boundary0Continuity, it is difficult to meet the requirements. Isogeometric analysis uses non-uniform rational B-splines (NURBS) as basis functions for geometric description and physical field interpolation, which have high order continuity and are therefore well suited for building Kirchhoff-Love thin shell elements.
The problem of latch-up has been a research focus in housing units, and common latch-up phenomena include membrane latch-up, shear latch-up, volume latch-up, and the like. Kirchhoff-Love shell units are often accompanied by a film latch-up phenomenon, i.e., in a pure bending state, strain energy of the shell is mixed with film strain energy, so that the deformation of the shell is smaller, and as the slenderness ratio h/L (ratio of thickness to in-plane characteristic length) of the shell becomes smaller, the deformation of the shell becomes smaller and smaller until the deformation capability is completely lost. In isogeometric analysis, a common method for eliminating latch-up includes: (1) a mixed shell unit based on two-field variation of Hellinger-Reissner (R. Echterer, B. Oesterle, M. Bischoff, A hierarchy family of isobeometric shell definitions, Computer Methods in Applied Mechanics and Engineering,2013,254: 170-; (2) b-bar method based on local strain interpolation (L.Greco, M.Cuomo, L.Contrafatto, A transformed local B-bar formation for isobolometric Kirchoff-Love shells, Computer Methods in Applied Mechanics and Engineering,2018,332: 462. 487); (3) reduced integration based Methods (C.Adam, S.Bouabdahh, M.Zarrough, H.Maitournam, Improved numerical integration for packing and measuring in an isobolometric structural elements. part II: Plates and shells, Computer Methods in Applied Mechanics and Engineering,2015,284: 106-.
In a traditional Hellinger-Reissner two-field variation-based hybrid shell unit, independent unknown quantities of the hybrid shell unit are displacement and film strain/stress of the shell unit, and two groups of independent basis functions are selected and interpolated for the displacement and the film strain/stress respectively, so that the coupling effect between bending strain and film strain can be effectively relieved, and the film latching phenomenon is eliminated.
Disclosure of Invention
The invention provides a method for constructing an isogeometric hybrid Kirchhoff-Love shell unit, aiming at solving the problems in the prior art, wherein the constructed shell unit not only has the advantages of the traditional hybrid shell unit, but also can keep the characteristics of sparseness, banding and the like of a rigidity matrix after being subjected to freedom degree agglomeration.
A method of constructing an isogeometric hybrid Kirchhoff-Love shell cell, comprising the steps of:
1) performing surface modeling on a specific thin shell structure, establishing a surface geometric model of the thin shell structure, and extracting control point coordinates and a B spline basis function of the surface;
2) determining displacement, load boundary conditions and material properties of the thin shell structure;
3) writing a weak form of a control equation of the thin shell structure by utilizing a Hellinger-Reissner two-field variation principle and a Kirchhoff-Love hypothesis;
4) constructing a B-spline basis function of a first order lower by using the B-spline basis function of the thin-wall structure extracted in the step 1) for assuming a difference value of the film strain freedom degrees;
5) constructing a Bezier extraction operator of each unit based on the B spline basis function of the lower order generated in the step 4), and generating the Bezier basis function of each unit;
6) constructing a Gramian matrix of each unit based on the Bezier basis function generated in the step 5);
7) constructing a Bessel projection weighting matrix based on the B spline basis function of the first order generated in the step 4);
8) constructing Bezier dual basis functions based on the Bezier basis functions and Bezier extraction operators generated in the step 5), the Gramian matrix generated in the step 6) and the Bezier projection weighting matrix generated in the step 7);
9) on the basis of the weak form of the control equation of the thin shell structure obtained in the step 3), performing interpolation dispersion on the displacement of the thin shell structure by adopting the B spline function obtained in the step 1), and simultaneously performing interpolation dispersion on the assumed thin film strain and the variation thereof of the thin shell structure by adopting the low-order B spline basis function obtained in the step 4) and the Bessel dual basis function generated in the step 8) to obtain a rigidity matrix and an external load vector of the thin shell structure;
10) performing static degree of freedom condensation on the thin-shell structure rigidity matrix and the external load vector obtained in the step 9) to obtain a condensed rigidity matrix and an condensed external load vector;
11) applying a displacement boundary condition to the linear equation set established in the step 10), and solving the linear equation set to obtain the responses of the displacement, the film strain and the like of the thin shell structure under the given external load and the boundary condition;
12) interpolating the displacement response vector and the film strain response vector obtained in the step 11) by using the B-spline basis function obtained in the step 1) and the B-spline basis function of the lower order obtained in the step 4) to obtain a displacement field and film strain field description of the thin-shell structure, and obtaining a distribution field of internal force and bending moment of the thin-shell structure by using the constitutive relation of the thin-shell structure.
In a further improvement, the weak form of the control equation of the thin-shell structure in the step 3) is as follows:
Figure BDA0002670661610000031
wherein n and m represent a film force and a bending moment of the middle face of the case, and κ represents a film strain and a bending strain of the middle face, respectively,
Figure BDA0002670661610000032
representing the independent film strain variable assumed in the Hellinger-Reissner two-field variation principle,
Figure BDA0002670661610000033
is prepared by reacting with
Figure BDA0002670661610000034
Corresponding shell mid-plane film forces, n and
Figure BDA0002670661610000035
and
Figure BDA0002670661610000036
the relationship between n ═ C:, and
Figure BDA0002670661610000037
Figure BDA0002670661610000038
wherein C is an elastic matrix of a thin shell structure; denotes the variation of the variable, u denotes the displacement of the middle surface of the housing, p denotes the uniform pressure of the middle surface of the housing, t0Which represents the boundary force experienced by the boundary of the housing, omega represents the mid-plane area of the housing,tthe boundary force application region of the housing is shown, and dA and dS respectively represent the corresponding infinitesimal.
Further improving, in the process of constructing the B-spline basis function with the lower first order in the step 4), the strain tensors of the assumed thin film respectively correspond to the strain tensors of the low-order B-spline basis function
Figure BDA0002670661610000039
Component (b) of
Figure BDA00026706616100000310
And
Figure BDA00026706616100000311
three low-order B-spline basis functions are constructed.
Further improving, in the process of constructing the bezier extraction operator of each unit in step 5), the two-dimensional B-spline basis functions are firstly constructed into the bezier extraction operators of the two-dimensional B-spline functions respectively according to two parameter directions, then the bezier extraction operators of the two-dimensional units are calculated in the form of tensor products, and three types of bezier extraction operators are obtained for the three types of low-order B-spline basis functions in step 4).
The invention has the beneficial effects that:
1. by constructing Bessel dual basis functions (Bezier dual basis) and independently interpolating the film strain, the thin-shell structural rigidity matrix is ensured to have smaller bandwidth (band width) and sparsity after being subjected to degree-of-freedom condensation, and the defect that the sparsity of the rigidity matrix is damaged by degree-of-freedom condensation in the existing isogeometric mixed Kirchhoff-Love thin-shell unit is overcome.
2. The isogeometric mixing Kirchhoff-Love shell unit can eliminate the film blocking effect and maintain the advantages of the existing isogeometric mixing shell unit.
3. The method has the characteristics of simplicity, high efficiency and high precision, and has strong universality, so that the method is easy to popularize and use in engineering structure analysis.
Drawings
FIG. 1 is a schematic view of a Scordelis-Lo shell structure;
FIG. 2 is a schematic diagram of displacement and load boundary conditions of the Scordelis-Lo shell structure;
FIG. 3 is a schematic diagram of a stiffness matrix of a novel isogeometric hybrid shell unit according to the present invention;
FIG. 4 is a schematic diagram of a stiffness matrix of a conventional Kirchoff-Love shell cell based on displacement description;
FIG. 5 is a schematic diagram of a stiffness matrix of a conventional hybrid Kirchoff-Love shell cell;
FIG. 6 is a z-displacement cloud of Scordelis-Lo thin shell structure based on a novel isogeometric hybrid Kirchhoff-Love shell cell;
FIG. 7 shows the internal force n of Scordelis-Lo thin shell structure based on a novel isogeometric hybrid Kirchoff-Love shell unit11Cloud pictures;
FIG. 8 shows the internal force n of Scordelis-Lo thin shell structure of conventional Kirchoff-Love shell unit based on displacement description11Cloud pictures.
Detailed Description
The following detailed description of the invention refers to the accompanying drawings. The scope of protection of the invention is not limited to the description of the embodiments only.
Firstly, the method is based on a novel isogeometric method, finite element analysis can be directly carried out on a model in geometric modeling software, and pre-treatment operations such as grid division are not needed; secondly, the novel thin-shell unit is constructed based on a Hellinger-Reissner mixed variation principle and a Bessel dual basis function, so that the thin-film blocking effect of the Kirchoff-Love shell unit is eliminated, the sparsity of a rigidity matrix is kept, the bandwidth is small, and the calculation efficiency is improved.
The method comprises the following specific steps:
step (1), the example of the invention is a Scordelis-Lo thin-wall structure (as shown in fig. 1), and in a CAD software Rhino, a structure to be analyzed is subjected to surface modeling, and the size and material parameters of the structure are shown in table 1.
Table 1: size and Material parameters of Scordelis-Lo thin wall Structure
R(mm) L(mm) t(mm) φ(°) E(MPa) ν ρ(kg/m3) g(m/s2)
25.0 50.0 0.25 80 4.32×108 0.0 7850.0 10.0
Two parameter directions xi of the shell structure1And xi2The order of NURBS basis function of (1) is taken as p1＝p2The node vectors in two directions are respectively of order 2:
Figure BDA0002670661610000051
Figure BDA0002670661610000052
according to the order and the node vector of the basis function of the embodiment, the B-spline basis function of the Scordelis-Lo thin shell structure can be constructed by referring to a B-spline function formula
Figure BDA0002670661610000053
Step (2) determining the displacement and load boundary conditions of the Scordelis-Lo thin-wall structure according to the specific situation of the Scordelis-Lo thin-wall structure example, and determining the y-direction displacement u at the head end and the tail end of the Scordelis-Lo thin-wall structure exampleyAnd z-direction displacement uzIs fixed and the structure is subjected to its own weight g, as shown in figure 2, and its material properties are shown in table 1.
And (3) writing a weak form of a control equation of the thin shell structure by utilizing a Hellinger-Reissner two-field variation principle and a Kirchhoff-Love hypothesis.
Wint＝Wext (3)
Namely, it is
Figure BDA0002670661610000054
In the formula (4), n and m represent the film force and bending moment of the middle surface of the case, and κ represents the film strain and bending strain of the middle surface, respectively,
Figure BDA0002670661610000055
representing the independent film strain freedom assumed in Hellinger-Reissner two-field variation principle,
Figure BDA0002670661610000056
is prepared by reacting with
Figure BDA0002670661610000057
Corresponding shell mid-plane film forces, n and
Figure BDA0002670661610000058
and
Figure BDA0002670661610000059
the relationship between n ═ C:, and
Figure BDA00026706616100000510
where C is an elastic matrix of thin shell structure. In addition, in the formula (4), the variation of the variable is expressed, u represents the displacement of the surface in the housing, p represents the uniform pressure of the surface in the housing, and t0Which represents the boundary force experienced by the boundary of the housing, omega represents the mid-plane area of the housing,tthe boundary force application region of the housing is shown, and dA and dS respectively represent the corresponding infinitesimal. In the formula (4), the left side of the equal sign is the virtual work done by the internal force of the shell, and the right side of the equal sign is the virtual work done by the external force, and the two should be equal under the condition that the shell is balanced.
Step (4) utilizing the B spline basis function of the thin-wall structure obtained in the step (1)
Figure BDA0002670661610000061
The following three low-order B spline basis functions are respectively constructed:
Figure BDA0002670661610000062
and
Figure BDA0002670661610000063
respectively corresponding to the degree of freedom of film strain
Figure BDA0002670661610000064
Component (b) of
Figure BDA0002670661610000065
And
Figure BDA0002670661610000066
step (5) is based on the low-order B spline basis function generated in step (4)
Figure BDA0002670661610000067
And constructing a Bessel extraction operator of each unit. The method comprises the following basic steps: first, a two-dimensional B-spline basis function (e.g., a B-spline basis function)
Figure BDA0002670661610000068
) According to two parameter directions xi1And xi2Bessel extraction operator for respectively constructing two one-dimensional B spline functions
Figure BDA0002670661610000069
And
Figure BDA00026706616100000610
wherein ei,ejRespectively represent xi1And xi2The unit numbers of the direction B spline functions are respectively ei,ej1-48. Secondly, a two-dimensional unit e is calculated in the form of tensor productijBessel extraction operator of
Figure BDA00026706616100000611
For three low-order B-spline basis functions
Figure BDA00026706616100000612
Three Bessel extraction operators are obtained
Figure BDA00026706616100000613
On the basis, the relational expression is utilized
Figure BDA00026706616100000614
Bessel basis functions of each unit can be obtained
Figure BDA00026706616100000615
The same process can obtain the other twoLow order Bessel basis function
Figure BDA00026706616100000616
Step (6) of constructing a Gramian matrix of each unit based on the Bezier basis functions generated in the step (5)
Figure BDA00026706616100000617
The structural equation is as follows:
Figure BDA00026706616100000618
gramian matrix can be obtained by the same method
Figure BDA00026706616100000619
And
Figure BDA00026706616100000620
step (7) of constructing a Bessel projection weighting matrix based on the first-order B-spline basis function generated in step (4)
Figure BDA00026706616100000621
The equation is:
Figure BDA00026706616100000622
similarly available Bessel projection weighting matrix
Figure BDA00026706616100000623
And
Figure BDA00026706616100000624
step (8) is based on the Bessel basis function generated in step (5)
Figure BDA00026706616100000625
And Bessel extraction operator
Figure BDA00026706616100000626
Gramian matrix generated in step (6)
Figure BDA0002670661610000071
And the Bessel projection weighting matrix generated in step (7)
Figure BDA0002670661610000072
Constructing Bessel dual basis functions
Figure BDA0002670661610000073
Figure BDA0002670661610000074
The same can be obtained
Figure BDA0002670661610000075
Figure BDA0002670661610000076
Step (9) on the basis of the weak form of the control equation of the thin shell structure obtained in step (3), firstly, performing interpolation dispersion on the displacement of the thin shell structure by adopting the B spline function obtained in step (1):
Figure BDA0002670661610000077
u in equation (10)IThe degree of freedom of displacement of the control point I is indicated and the original two-dimensional index (I, j) is replaced by the index I.
Secondly, interpolating the assumed film strain by using the low-order B spline basis function obtained in the step (4)
Figure BDA0002670661610000078
Three components of
Figure BDA0002670661610000079
Figure BDA00026706616100000710
Figure BDA00026706616100000711
Figure BDA00026706616100000712
Variables in equations (11) to (13)
Figure BDA00026706616100000713
The hypothetical film strain variable representing the control point.
Finally, the presumed film strain variation is interpolated by adopting the Bessel dual basis function generated in the step (8)
Figure BDA00026706616100000714
Three components of
Figure BDA00026706616100000715
Figure BDA00026706616100000716
Figure BDA00026706616100000717
Figure BDA0002670661610000081
Variables in equations (14) to (16)
Figure BDA0002670661610000082
Representing the variation of the hypothetical film strain at the control point.
Substituting equations (10) - (16) into the weak form (4) of the control equation for the structure yields a discrete form of the control equation:
Figure BDA0002670661610000083
step (10) of performing degree of freedom condensation on the formula (17), namely assuming the degree of freedom of film strain
Figure BDA0002670661610000084
Expressed as:
Figure BDA0002670661610000085
substituting equation (18) into equation (17) yields a linear system of equations after degrees of freedom agglomeration:
Figure BDA0002670661610000086
wherein
Figure BDA0002670661610000087
Is a stiffness matrix after the degree of freedom agglomeration, and has a size of Nudof×NudofIn which N isudofThe number of degrees of freedom of displacement for the Scordelis-Lo shell structure. The stiffness matrix of the thin shell structure after the degree of freedom condensation is shown in fig. 3, and for comparison, fig. 4 is a stiffness matrix obtained by a traditional Kirchhoff-Love shell unit based on displacement degree of freedom description, and fig. 5 is a stiffness matrix obtained by a traditional hybrid Kirchhoff-Love shell unit based on Hellinger-Reissner variation principle. It can be seen that the stiffness matrix bandwidth obtained by the present invention is comparable to the traditional displacement-freedom-based shell element (fig. 4), whereas the stiffness matrix obtained by the traditional hybrid shell element (fig. 5) destroys the narrow bandwidth and sparsity of the matrix.
Step (11) applies displacement boundary conditions to the linear equation set in the formula (19), and mathematical software such as MATLAB is adopted to solve the linear equation set to obtain a displacement response vector U of the thin-shell structure under given external load and constraint conditions, and the assumed thin-film strain freedom degree can be obtained by using the relational expression (18)
Figure BDA0002670661610000088
And (12) post-processing the mechanical analysis result of the Scordelis-Lo thin shell structure, namely performing interpolation by using the B spline function obtained in the step (1) according to the displacement response vector U obtained in the step (11), and performing the hypothesis thin film strain response vector by using the low-order B spline function obtained in the step (4)
Figure BDA0002670661610000089
Interpolation is carried out to obtain the displacement field (shown in figure 6) and the thin film strain field description of the whole thin shell structure. The internal force of the thin-wall structure can be obtained by utilizing the constitutive relation of the thin-wall shell structure
Figure BDA00026706616100000810
The distributed field (as shown in fig. 7) shows that the displacement and the internal force distribution of the Scordelis-Lo thin-wall structure based on the novel isogeometric mixed Kirchoff-Love thin-shell unit have no oscillation phenomenon, and the film locking phenomenon is completely eliminated. In contrast, the oscillation phenomenon (as shown in fig. 8) occurs in the internal force of the Scordelis-Lo thin-wall structure constructed by the isogeometric Kirchoff-Love shell unit based on the displacement description, and the film locking phenomenon is obvious.
In conclusion, the invention provides a novel isogeometric hybrid Kirchhoff-Love thin-shell unit, which eliminates the phenomenon of film locking, ensures that a rigidity matrix of a thin-wall structure has smaller bandwidth (band width) and sparsity, and improves the calculation efficiency.
While the invention has been described in terms of its preferred embodiments, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention.

Claims (4)

1. A method of constructing an isogeometric hybrid Kirchhoff-Love shell cell, comprising the steps of:
1) performing surface modeling on a specific thin shell structure, establishing a surface geometric model of the thin shell structure, and extracting control point coordinates and a B spline basis function of the surface;
2) determining displacement, load boundary conditions and material properties of the thin shell structure;
3) writing a weak form of a control equation of the thin shell structure by utilizing a Hellinger-Reissner two-field variation principle and a Kirchhoff-Love hypothesis;
4) constructing a B-spline basis function of a first order lower by using the B-spline basis function of the thin-wall structure extracted in the step 1) for assuming a difference value of the film strain freedom degrees;
5) constructing a Bezier extraction operator of each unit based on the B spline basis function of the lower order generated in the step 4), and generating the Bezier basis function of each unit;
6) constructing a Gramian matrix of each unit based on the Bezier basis function generated in the step 5);
7) constructing a Bessel projection weighting matrix based on the B spline basis function of the first order generated in the step 4);
8) constructing Bezier dual basis functions based on the Bezier basis functions and Bezier extraction operators generated in the step 5), the Gramian matrix generated in the step 6) and the Bezier projection weighting matrix generated in the step 7);
9) on the basis of the weak form of the control equation of the thin shell structure obtained in the step 3), performing interpolation dispersion on the displacement of the thin shell structure by adopting the B spline function obtained in the step 1), and simultaneously performing interpolation dispersion on the assumed thin film strain and the variation thereof of the thin shell structure by adopting the low-order B spline basis function obtained in the step 4) and the Bessel dual basis function generated in the step 8) to obtain a rigidity matrix and an external load vector of the thin shell structure;
10) performing static degree of freedom condensation on the thin-shell structure rigidity matrix and the external load vector obtained in the step 9) to obtain a condensed rigidity matrix and an condensed external load vector;
11) applying a displacement boundary condition to the linear equation set established in the step 10), and solving the linear equation set to obtain the responses of the displacement, the film strain and the like of the thin shell structure under the given external load and the boundary condition;
12) interpolating the displacement response vector and the film strain response vector obtained in the step 11) by using the B-spline basis function obtained in the step 1) and the B-spline basis function of the lower order obtained in the step 4) to obtain a displacement field and film strain field description of the thin-shell structure, and obtaining a distribution field of internal force and bending moment of the thin-shell structure by using the constitutive relation of the thin-shell structure.
2. The method of constructing an isogeometric hybrid Kirchhoff-Love shell unit of claim 1, wherein: the weak form of the control equation of the thin-shell structure in the step 3) is as follows:
Figure FDA0002670661600000011
wherein n and m represent a film force and a bending moment of the middle face of the case, and κ represents a film strain and a bending strain of the middle face, respectively,
Figure FDA0002670661600000021
representing the independent film strain variable assumed in the Hellinger-Reissner two-field variation principle,
Figure FDA0002670661600000022
is prepared by reacting with
Figure FDA0002670661600000023
Corresponding shell mid-plane film forces, n and
Figure FDA0002670661600000024
and
Figure FDA0002670661600000025
the relationship between n ═ C:, and
Figure FDA0002670661600000026
Figure FDA0002670661600000027
wherein C is an elastic matrix of a thin shell structure; denotes the variation of the variable, u denotes the displacement of the middle surface of the housing, p denotes the uniform pressure of the middle surface of the housing, t0Which represents the boundary force experienced by the boundary of the housing, omega represents the mid-plane area of the housing,tthe boundary force application region of the housing is shown, and dA and dS respectively represent the corresponding infinitesimal.
3. The method of constructing an isogeometric hybrid Kirchhoff-Love shell unit of claim 1, wherein: step 4) in the process of constructing the B-spline basis function with the lower first order, respectively corresponding to the strain tensor of the hypothetical film
Figure FDA00026706616000000210
Component (b) of
Figure FDA0002670661600000028
And
Figure FDA0002670661600000029
three low-order B-spline basis functions are constructed.
4. The method of constructing an isogeometric hybrid Kirchhoff-Love shell unit of claim 3, wherein: in the process of constructing the Bezier extraction operator of each unit in the step 5), the two-dimensional B-spline basis function is firstly constructed into two Bezier extraction operators of the one-dimensional B-spline function according to two parameter directions, then the Bezier extraction operator of the two-dimensional unit is calculated in the form of tensor product, and three Bezier extraction operators are obtained aiming at the three low-order B-spline basis functions in the step 4).
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