KR101604319B1 - Geometrically exact isogeometric shape sensitivity analysis method in curvilinear coordinate system of shell structure - Google Patents

Geometrically exact isogeometric shape sensitivity analysis method in curvilinear coordinate system of shell structure Download PDF

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KR101604319B1
KR101604319B1 KR1020150060355A KR20150060355A KR101604319B1 KR 101604319 B1 KR101604319 B1 KR 101604319B1 KR 1020150060355 A KR1020150060355 A KR 1020150060355A KR 20150060355 A KR20150060355 A KR 20150060355A KR 101604319 B1 KR101604319 B1 KR 101604319B1
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curved surface
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하윤도
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군산대학교산학협력단
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Abstract

The present invention relates to a design sensitivity analysis method of a geometrically exact isogeometric curved shape for obtaining an exact shape design sensitivity analysis result by providing boundary integral which represents a boundary condition of a curved structure with a normal and spatial differential (curvature, etc.) of the normal of the exact and continuous curved surface in a procedure of analyzing design sensitivity of the curved surface. The method includes: a step of inputting NURBS data via a NURBS data input unit; a step in which a curvilinear coordinate generating unit generates a generalized curvilinear coordinate system by using the input NURBS data; a step in which an isogeometric analysis model normalizing unit normalizes an isogeometric analysis model by using the generalized curvilinear coordinate system which is generated; a step in which a curved surface analyzing unit analyzes the geometrically exact curved surface by using the normalized isogeometric analysis model; and a step in which a design sensitivity analyzing unit analyzes the design sensitivity of the curved surface by using information on the analyzed curved surface.

Description

[0001] GEOMETRICALLY EXACT ISOGEOMETRIC SHAPE SENSITIVITY ANALYSIS METHOD IN CURVILINEAR COORDINATE SYSTEM SHELL STRUCTURE [0002]

The present invention relates to geometrically rigid isogeometric curvature shape design sensitivity analysis methods, and more particularly, to an accurate and continuous curved surface normal, To a geometrically rigorous isometric geometry design sensitivity sensitivity analysis method that can provide a precise shape design sensitivity analysis result by providing spatial derivatives (curvature, etc.) of the normal.

In general, to model and interpret a curved surface structure such as a shell structure in a Cartesian coordinate system in which a CAD model is implemented, a solid element widely used in finite element technology should be used. This solid element is relatively simple to form because it interpolates the nodal values through an isoparametric transformation to construct the shell surface from the solid element. However, since the analytical model consisting of only the nodal information expressed in the orthogonal coordinate system can not take into account the geometric information of the higher order such as the spatial differential (curvature, etc.) of the normal, a geometrically rigorous interpretation including the bending- it's difficult. In addition, since the solid element needs to be integrated in spite of the surface model, additional integration points in the thickness direction are required, and the integration points used in the actual calculation are ineffective because they are required for the analysis of the two-dimensional surface model. In addition, the influence of missing or inaccurate higher order geometric information becomes more important in the shape design sensitivity analysis of curved surfaces such as the shell structure.

SUMMARY OF THE INVENTION It is an object of the present invention to provide a method and apparatus for correcting curved surface design sensitivity in a curved surface design sensitivity analysis, Dimensional curvature shape design sensitivity sensitivity analysis method capable of obtaining a rigid shape design sensitivity analysis result by providing a spatial differential (curvature, etc.) of a normal line.

According to an aspect of the present invention, there is provided a geometrically rigid isothiometry curve design sensitivity analysis method comprising: inputting NURBS data by a NURBS data input unit; Generating a generalized curved surface coordinate system using the input NURBS data in a curved surface coordinate system generating unit; Normalizing the isothiometry analysis model by the iso geometry analysis model normalization unit using the generated generalized curved surface coordinate system; Analyzing the geometrically rigid curved surface by the curved surface analyzing unit using the normalized iso-geometric analytical model; And analyzing the design sensitivity of the curved surface shape by the design sensitivity analysis unit using the analyzed information of the curved surface.

In the geometrically rigid isometric geometric design sensitivity sensitivity analysis method of the present invention, the generalized curved surface coordinate system generation step may include a step of, by the curved surface coordinate system generation unit, Transforming the position vector in the orthogonal coordinate system into the position vector of the curved surface coordinate system, and obtaining the covariance basis vector of the curvature coordinate system.

In the geometrically rigorous isometric geometric design sensitivity analysis method according to the present invention, the step of normalizing the isometrics model is performed by the isomorphic model normalization section, Lt; RTI ID = 0.0 >

Figure 112015041752201-pat00001

[here,

Figure 112015041752201-pat00002
Represents a covariance basis vector of a curved surface coordinate system, x represents a position vector of a curved surface coordinate system,
Figure 112015041752201-pat00003
Represents a basal basis function,
Figure 112015041752201-pat00004
Represents a control point. CP = the total number of control points]

Acquiring a Nurib basis function using the NURBS basis function; And using the obtained NLBF and the control point,

Figure 112015041752201-pat00005

[S represents the specified NURBS surface,

Figure 112015041752201-pat00006
And
Figure 112015041752201-pat00007
Represents surface coordinates]

To define the NURBS surface.

In the geometrically rigid isometric geometric design sensitivity sensitivity analysis method according to the present invention, the step of analyzing the curved surface may include the step of: ≪ / RTI >

Figure 112015041752201-pat00008

[

Figure 112015041752201-pat00009
Represents the response coefficient of the control point, and d represents the displacement]

To obtain the displacement.

In the geometrically rigorous isometric geometric design sensitivity analysis method according to the present invention, the step of analyzing the design sensitivity of the curved surface shape may be performed by the design sensitivity analysis unit using the position vector of the curved surface coordinate system and / Using the position vector of the neutral plane of the shell,

Figure 112015041752201-pat00010

[x represents the position vector of the curved coordinate system,

Figure 112015041752201-pat00011
Represents the position vector of the neutral plane of the shell,
Figure 112015041752201-pat00012
Represents the unit normal vector for a given plane,
Figure 112015041752201-pat00013
Represents the thickness coordinate of the shell]

Obtaining a unit normal vector for a given plane; Using the NURBS basis function, the design change amount of the control point, and the unit normal vector, the following equations

Figure 112015041752201-pat00014

Figure 112015041752201-pat00015

[V represents the design speed field,

Figure 112015041752201-pat00016
Represents the design variation of the control point]

Acquiring a design speed field by means of a control unit; And using the velocity fields and displacements,

Figure 112015041752201-pat00017

[z represents displacement,

Figure 112015041752201-pat00018
Represents the amount of change in the shape of the design variable direction,
Figure 112015041752201-pat00019
Represents the design sensitivity of the displacement field]

To obtain the design sensitivity of the displacement field.

According to the geometrically rigorous geometric isometric geometric design sensitivity analysis method of the present invention, a generalized surface coordinate system is generated by using input NURBS data, and an iso geometric analysis is performed using the generated generalized surface coordinate system In the sensitivity analysis of a curved surface design of a curved surface structure, it is possible to obtain accurate and continuous curved surface normals and normals in boundary integrations expressing the boundary conditions of a curved surface structure, (Curvature or the like) of the shape-design sensitivity can be obtained.

1 is a control block diagram of an apparatus for performing a geometrically rigorous isothiometric curved surface design sensitivity analysis method according to an embodiment of the present invention.
FIG. 2 is a flowchart for explaining a geometrically rigorous isothiometric curved shape design sensitivity analysis method according to an embodiment of the present invention.
3 is a diagram showing a change in the domain of a shell.

Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings.

1 is a control block diagram of an apparatus for performing a geometrically rigorous isothiometric curved surface design sensitivity analysis method according to an embodiment of the present invention.

As shown in FIG. 1, an apparatus for performing a geometrically rigorous geometric shape design sensitivity analysis method according to an embodiment of the present invention includes a NURBS data input unit 100, a curved surface coordinate system generation unit 200, A geometric analysis model normalization unit 300, a curved surface analysis unit 400, and a design sensitivity analysis unit 500.

The NURBS data input unit 100 inputs NURBS data, which is CAD data, to the surface coordinate system generation unit 200. The NURBS data is based on the NURBS basis function

Figure 112015041752201-pat00020
) And a control point (
Figure 112015041752201-pat00021
).

The curved surface coordinate system generation unit 200 generates a generalized curved surface coordinate system using the NURBS data input from the NURBS data input unit 100.

The iso-geometric analysis model normalization unit 300 serves to normalize the iso-geometric analysis model using the curved surface coordinate system generated by the curved surface coordinate system generation unit 200.

The curved surface analysis unit 400 serves to analyze the geometrically rigid curved surface using the normalized iso-geometric analysis model input from the iso-geometric analysis model normalization unit 300. [

The design sensitivity analyzing unit 500 analyzes the design sensitivity of the curved surface shape using the information of the curved surface analyzed by the curved surface analyzing unit 400.

The NURBS data input unit 100, the curved surface coordinate system generating unit 200, the iso-geometric analysis model normalizing unit 300, the curved surface analyzing unit 400 and the design sensitivity analyzing unit 500 are connected to one terminal device (e.g., A personal computer, a PDA, a PMP, a smart phone, or the like).

A geometrically rigid isothiometric curved surface design sensitivity sensitivity analysis method using the apparatus according to an embodiment of the present invention will be described.

FIG. 2 is a flow chart for explaining a geometrically rigorous isothiometrical curved surface design sensitivity sensitivity analysis method according to an embodiment of the present invention, where S denotes a step.

First, the NURBS data is input from the NURBS data input unit 100 to the curved surface coordinate system generating unit 200 (S10). The NURBS data is based on the NURBS basis function

Figure 112015041752201-pat00022
) And control point (
Figure 112015041752201-pat00023
=
Figure 112015041752201-pat00024
).

In step S20, the curved surface coordinate system generation unit 200 generates a generalized curved surface coordinate system using the input Nurbs data. More specifically, in step S20, the curved surface coordinate system generation unit 200 generates a control point of the NURBS data

Figure 112015041752201-pat00025
=
Figure 112015041752201-pat00026
) And the fixed base vector (
Figure 112015041752201-pat00027
) ≪ / RTI > in the Cartesian coordinate system
Figure 112015041752201-pat00028
) To the position vector of the surface coordinate system (
Figure 112015041752201-pat00029
), Then transforms the covariance basis vector of the surface coordinate system (
Figure 112015041752201-pat00030
).

The covariance base vector (

Figure 112015041752201-pat00031
)
Figure 112015041752201-pat00032
(≪ RTI ID = 0.0 >
Figure 112015041752201-pat00033
). Covalent base vectors are not necessarily orthogonal to each other, and covalent base vectors (
Figure 112015041752201-pat00034
) Is the relationship between common base vector pairs
Figure 112015041752201-pat00035
). Then, the inner product of the other basis vectors and the covariance / semi-basis vectors defines a useful metric coefficient as shown in the following equation (1).

Figure 112015041752201-pat00036

The determinant of the inner product is expressed as a Jacobian matrix < RTI ID = 0.0 >

Figure 112015041752201-pat00037
≪ / RTI >

Figure 112015041752201-pat00038

Since the basis vectors are no longer constant and their derivatives need not be considered, the derivatives in the surface coordinate system are more complex than the Cartesian coordinate system. To represent the partial derivative of the basis vectors, a second cristopel symbol is introduced as: < EMI ID = 3.0 >

Figure 112015041752201-pat00039

Has a covariance of the basis vector as shown in the following Equation (4).

Figure 112015041752201-pat00040

Figure 112015041752201-pat00041
The surface area of this constant differential parallelepiped surface
Figure 112015041752201-pat00042
).
Figure 112015041752201-pat00043
The tangent curves are plotted on a coordinate curve (
Figure 112015041752201-pat00044
) (
Figure 112015041752201-pat00045
≪ / RTI >
Figure 112015041752201-pat00046
Is constant. therefore
Figure 112015041752201-pat00047
Silver surface (
Figure 112015041752201-pat00048
). Similarly on other surfaces,
Figure 112015041752201-pat00049
And
Figure 112015041752201-pat00050
Respectively. Surface area (
Figure 112015041752201-pat00051
) Is calculated in accordance with the following equation (5), and the same is true in the other aspects.

Figure 112015041752201-pat00052

The volume of the differential parallelepiped body (

Figure 112015041752201-pat00053
) ≪ / RTI >

Figure 112015041752201-pat00054

Note that the regular orthogonal coordinate system can be obtained by the following equation (7).

Figure 112015041752201-pat00055

Thereafter, in step S30, the ice geometric analysis model normalization unit 300 normalizes the iso-geometric analysis model using the generalized surface coordinate system generated in step S20. In more detail, in step S30, the iso-geometric analysis model normalization unit 300 obtains the Nyburs basis function from the covariance base vector using the following equation (8)

Figure 112015041752201-pat00056

[here,

Figure 112015041752201-pat00057
Represents a covariance basis vector of a curved surface coordinate system, x represents a position vector of a curved surface coordinate system,
Figure 112015041752201-pat00058
Represents a basal basis function,
Figure 112015041752201-pat00059
Represents a control point. CP = the total number of control points]

The iso-geometric analytical model normalization unit 300 obtains the obtained norbus basis function (

Figure 112015041752201-pat00060
) And control point (
Figure 112015041752201-pat00061
), The surface of the NURBS is defined by the following equation (9).

Figure 112015041752201-pat00062

[S represents the specified NURBS surface,

Figure 112015041752201-pat00063
And
Figure 112015041752201-pat00064
Represents surface coordinates]

The process of obtaining Equation (9) will be described in detail as follows.

First, the coordinates in the parametric space (

Figure 112015041752201-pat00065
) Is a set of knot vectors in a one-dimensional space as follows.

Figure 112015041752201-pat00066

[Where p and m represent the order and number of basis functions, respectively]

If the knots are equally spaced in the parametric space, they are called uniform knot vectors, otherwise they are uneven knot backers. The knots are repeated when the knots are repeated at the same coordinates, and the knots are opened when the end knots are repeated ( p +1) times. The B-spline basis functions are recursively defined as: < EMI ID = 11.0 >

Figure 112015041752201-pat00067

Figure 112015041752201-pat00068

Note that denominators with knot differences can be zero (in the case of repeated knots). In this case, the quotient is assumed to be zero. The B-spline has the desired characteristics as a basis function as shown in the following Equation (13).

Figure 112015041752201-pat00069

The NURBS curves are based on the glass basis functions (

Figure 112015041752201-pat00070
) And corresponding control points (
Figure 112015041752201-pat00071
). ≪ / RTI > The p -order B-spline basis function (
Figure 112015041752201-pat00072
) And the corresponding m pairs of corresponding (projecting) control points, the Nurbsc curve is represented by a single parametric coordinate (
Figure 112015041752201-pat00073
).

Figure 112015041752201-pat00074

In Equation (14), the following equations (15), (16) and (17) are derived.

Figure 112015041752201-pat00075

Figure 112015041752201-pat00076

Figure 112015041752201-pat00077

Points in the three-dimensional Euclidean space (d = 3)

Figure 112015041752201-pat00078
), For example, the homogeneous coordinates in the four-dimensional space
Figure 112015041752201-pat00079
, ≪ / RTI >
Figure 112015041752201-pat00080
). The same weight (
Figure 112015041752201-pat00081
) Is used, the NURBS curve becomes a B-spline curve. Using the tensor product of the coordinates, the NURBS planes are defined by the following equation (18).

Figure 112015041752201-pat00082

Expression (18) is concisely expressed to derive Equation (9).

In step S40, the curved surface analyzing unit 400 analyzes the geometrically rigid curved surface using the iso-geometric analytical model normalized in step S30. More specifically, in step S40, the curved surface analyzing unit 400 calculates the NURBS basis function obtained in step S30

Figure 112015041752201-pat00083
) And the response coefficient of the control point (
Figure 112015041752201-pat00084
) Using the following equation (19)

Figure 112015041752201-pat00085

Obtain displacement (d). The displacement d may be expressed by Equation (20).

Figure 112015041752201-pat00086

Subsequently, in step S50, the design sensitivity analysis unit 500 analyzes the design sensitivity of the curved surface shape using the information of the curved surface analyzed in step S40. More specifically, in step S50, the design sensitivity analysis unit 500 calculates the position vector x of the curved surface coordinate system and the position vector of the neutral plane of the shell

Figure 112015041752201-pat00087
), The following equation 21

Figure 112015041752201-pat00088

[x represents the position vector of the curved coordinate system,

Figure 112015041752201-pat00089
Represents the position vector of the neutral plane of the shell,
Figure 112015041752201-pat00090
Represents the unit normal vector for a given plane,
Figure 112015041752201-pat00091
Represents the thickness coordinate of the shell]

The unit normal vector (< RTI ID = 0.0 >

Figure 112015041752201-pat00092
),

The design sensitivity analysis unit 500 calculates the Nybond basis function

Figure 112015041752201-pat00093
), Design change amount of control point (
Figure 112015041752201-pat00094
) And the unit normal vector (
Figure 112015041752201-pat00095
) And the following equations (22) and

Figure 112015041752201-pat00096

Figure 112015041752201-pat00097

[V represents the design speed field,

Figure 112015041752201-pat00098
Represents the design variation of the control point]

To obtain a design speed field (V)

The design sensitivity analysis unit 500 calculates the following equation (24) using the velocity field V and the displacement z,

Figure 112015041752201-pat00099

[z represents displacement,

Figure 112015041752201-pat00100
Represents the amount of change in the shape of the design variable direction,
Figure 112015041752201-pat00101
Represents the design sensitivity of the displacement field]

Design sensitivity of the displacement field by

Figure 112015041752201-pat00102
).

In Equation 24,

Figure 112015041752201-pat00103
Represents the partial differentiation of the displacement z, and is expressed by the following equation 25

Figure 112015041752201-pat00104

.

In Equation 25,

Figure 112015041752201-pat00105
,
Figure 112015041752201-pat00106
,
Figure 112015041752201-pat00107
) ≪ RTI ID = 0.0 >

Figure 112015041752201-pat00108

[d 'represents the partial differential of the displacement (d =)

Figure 112015041752201-pat00109
Lt; / RTI >
Figure 112015041752201-pat00110
And
Figure 112015041752201-pat00111
Indicates that the explicit change condition with the dependence of the argument on the shape design parameter is suppressed)

And the remaining components in Equation 25 are calculated from NURBS data and the drawing information in FIG.

In Equation 24, the convection term (

Figure 112015041752201-pat00112
) ≪ RTI ID = 0.0 >

Figure 112015041752201-pat00113

Lt; / RTI >

On the other hand, the performance measurements of the shell structure are generally defined in the neutral plane,

Figure 112015041752201-pat00114

As shown in Fig.

The first-order change with respect to the shape design parameter is derived as the following equation (29)

Figure 112015041752201-pat00115

Here, the following Equation 30

Figure 112015041752201-pat00116

, The material differential of the determinant of the Jacobian matrix is given by the following equation 31

Figure 112015041752201-pat00117

.

The acquisition process of Equation (26) will be described in detail as follows.

First, considering the first-order change of the biaxial strain energy form and the linear load form with respect to the shape design parameter, the following equations (32) and

Figure 112015041752201-pat00118

Figure 112015041752201-pat00119

.

Here, the following facts (

Figure 112015041752201-pat00120
) Is used to obtain the shape sensitivity equation (Equation 26).

Here, Equation 34

Figure 112015041752201-pat00121

And Equation 35

Figure 112015041752201-pat00122

.

Referring to Equation (35), the following boundary integral equation expressing the boundary condition of the curved surface structure

Figure 112015041752201-pat00123
And
Figure 112015041752201-pat00124
The normal of the continuous surface (
Figure 112015041752201-pat00125
), The spatial differential of the normal (curvature, etc.) (
Figure 112015041752201-pat00126
), It can be seen that a precise shape design sensitivity analysis result can be obtained.

According to the geometrically rigorous geometric shape design sensitivity analysis method according to the embodiment of the present invention, a generalized surface coordinate system is generated using input Nurbst data, and an iso geometric analysis is performed using the generated generalized surface coordinate system In the sensitivity analysis of a curved surface design of a curved surface structure, it is possible to obtain accurate and continuous curved surface normals and normals in boundary integrations expressing the boundary conditions of a curved surface structure, (Curvature, etc.) of the geometric design can be obtained.

Although the best mode has been shown and described in the drawings and specification, certain terminology has been used for the purpose of describing the embodiments of the invention and is not intended to be limiting or to limit the scope of the invention described in the claims. It is not. Therefore, it will be understood by those skilled in the art that various changes and modifications may be made without departing from the scope of the present invention. Accordingly, the true scope of the present invention should be determined by the technical idea of the appended claims.

100: NURBS data input unit 200: Curved surface coordinate system generating unit
300: Isothermometric analysis model normalization section
400: Surface analysis unit 500: Design sensitivity analysis unit

Claims (5)

delete delete In a generalized isogeometric curved shape design sensitivity analysis method,
Inputting NURBS data by a NURBS data input unit;
Generating a generalized curved surface coordinate system using the input NURBS data in a curved surface coordinate system generating unit;
Normalizing the isothiometry analysis model by the iso geometry analysis model normalization unit using the generated generalized curved surface coordinate system;
Analyzing the geometrically rigid curved surface by the curved surface analyzing unit using the normalized iso-geometric analytical model; And
And analyzing the design sensitivity of the curved surface shape by the design sensitivity analysis unit using the analyzed information of the curved surface,
The generalized curved surface coordinate system generation step may include:
Transforming a position vector in an orthogonal coordinate system having a control point and a fixed base vector of the Nursk data into a position vector of a curved surface coordinate system;
Obtaining a covariance basis vector of the surface coordinate system;
Wherein the step of normalizing the isomorphic analytical model is performed by the isomorphic analytical model normalization section,
From the covariance base vector, the following equation
Figure 112016010070403-pat00127

[here,
Figure 112016010070403-pat00128
Represents a covariance basis vector of a curved surface coordinate system, x represents a position vector of a curved surface coordinate system,
Figure 112016010070403-pat00129
Represents a basal basis function,
Figure 112016010070403-pat00130
Represents a control point. CP = the total number of control points]
To obtain a baseband function,
Using the obtained NLBF and the control point, the following equation
Figure 112016010070403-pat00131

[S represents the specified NURBS surface,
Figure 112016010070403-pat00132
And
Figure 112016010070403-pat00133
Represents surface coordinates]
And defining a surface of the NURBS by the method. The method of claim 3,
The step of analyzing the curved surface may include:
Using the Nursing basis function and the response coefficient of the control point,
Figure 112015041752201-pat00134

[
Figure 112015041752201-pat00135
Represents the response coefficient of the control point, and d represents the displacement]
And obtaining a displacement by means of the first and second sensors. The method of claim 4, wherein
The step of analyzing the design sensitivity of the curved surface shape may include:
Using the position vector of the curved surface coordinate system and the position vector of the neutral plane of the shell,
Figure 112015041752201-pat00136

[x represents the position vector of the curved coordinate system,
Figure 112015041752201-pat00137
Represents the position vector of the neutral plane of the shell,
Figure 112015041752201-pat00138
Represents the unit normal vector for a given plane,
Figure 112015041752201-pat00139
Represents the thickness coordinate of the shell]
Obtaining a unit normal vector for a given plane;
Using the NURBS basis function, the design change amount of the control point, and the unit normal vector, the following equations
Figure 112015041752201-pat00140
,
Figure 112015041752201-pat00141

[V represents the design speed field,
Figure 112015041752201-pat00142
Represents the design variation of the control point]
Acquiring a design speed field by means of a control unit; And
Using the velocity fields and displacements,
Figure 112015041752201-pat00143

[z represents displacement,
Figure 112015041752201-pat00144
Represents the amount of change in the shape of the design variable direction,
Figure 112015041752201-pat00145
Represents the design sensitivity of the displacement field]
And obtaining a design sensitivity of the displacement field by the second step.
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Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN107563016A (en) * 2017-08-15 2018-01-09 西北工业大学 A kind of wing box section Parameter Sensitivity Analysis method based on ellipsoidal model
CN108763658A (en) * 2018-05-07 2018-11-06 长安大学 Based on etc. methods of geometry combination thin-wall construction intrinsic frequency design method
CN112419254A (en) * 2020-11-16 2021-02-26 重庆长安汽车股份有限公司 Method for analyzing visual continuity among uniform parting curved surfaces based on human visual limit

Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20090024370A1 (en) 2007-07-19 2009-01-22 Scott Michael A Method and System for Performing T-Spline Based Isogeometric Analysis

Patent Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20090024370A1 (en) 2007-07-19 2009-01-22 Scott Michael A Method and System for Performing T-Spline Based Isogeometric Analysis

Non-Patent Citations (3)

* Cited by examiner, † Cited by third party
Title
"고주파수 파워흐름 문제의 아이소-지오메트릭 형상 최적설계", 한국전산구조공학회논문집 제27권 제3호(페이지 155-162), 2014년 06월
"아이소-지오메트릭 형상 최적설계의 실험적 검증", 한국전산구조공학회논문집 제27권 제5호(페이지 345-352), 2014년 10월
"일반 곡면 좌표계에서 구현된 아이소-지오메트릭 형상 설계민감도 해석", 한국전산구조공학회논문집 제25권 제6호(페이지 497-504), 2012년 12월*

Cited By (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN107563016A (en) * 2017-08-15 2018-01-09 西北工业大学 A kind of wing box section Parameter Sensitivity Analysis method based on ellipsoidal model
CN107563016B (en) * 2017-08-15 2020-07-21 西北工业大学 Method for analyzing sensitivity of structural parameters of wing box of wing based on ellipsoid model
CN108763658A (en) * 2018-05-07 2018-11-06 长安大学 Based on etc. methods of geometry combination thin-wall construction intrinsic frequency design method
CN108763658B (en) * 2018-05-07 2022-05-20 长安大学 Combined thin-wall structure natural frequency design method based on isogeometric method
CN112419254A (en) * 2020-11-16 2021-02-26 重庆长安汽车股份有限公司 Method for analyzing visual continuity among uniform parting curved surfaces based on human visual limit
CN112419254B (en) * 2020-11-16 2024-02-09 重庆长安汽车股份有限公司 Method for analyzing visual sense continuous sense between uniform parting curved surfaces based on human eye visual limit

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