CN115048825B - Thin shell curved surface simulation method, device, equipment and medium - Google Patents
Thin shell curved surface simulation method, device, equipment and medium Download PDFInfo
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Abstract
The application discloses a method, a device, equipment and a medium for simulating a curved surface of a thin shell, which relate to the technical field of simulation and comprise the following steps: determining a vertex angle and determining the curvature of each vertex based on the side lengths of all triangles in the curved surface triangular mesh; determining a conformal factor of each vertex meeting a first condition based on a system equation and curvature, and then determining a current vertex angle based on a current side length determined by the conformal factor to obtain a new curvature of the vertex; when the new curvature meets a second condition, mapping the target triangle to the two-dimensional plane according to the current side length and the vertex angle, and re-determining the target triangle until each triangle is mapped to the two-dimensional plane; and generating a block self-adaptive Cartesian grid on the two-dimensional plane after mapping, inversely mapping the block self-adaptive Cartesian grid on the three-dimensional curved surface, and finally simulating a physical field on the thin shell curved surface. The block adaptive Cartesian grid in the application meets the construction requirement of a high-order format so as to overcome the defect of the traditional grid in the aspect of thin shell numerical simulation.
Description
Technical Field
The invention relates to the technical field of simulation, in particular to a method, a device, equipment and a medium for simulating a curved surface of a thin shell.
Background
The thin shell is a shell with the maximum thickness far smaller than the curvature radius of the middle surface and the sizes of the other two directions, has the advantages of light weight and high strength, and is widely applied to the industrial fields of aviation, aerospace, navigation, buildings and the like. In order to perform high-precision numerical simulation on an unsteady physical field on a thin shell, a user needs to generate a high-quality computational grid on a spatial Riemann curved model.
The traditional structural mesh is difficult to maintain good orthogonality on a complex curved surface, and meanwhile, local adaptive encryption is difficult to realize along with the change of a physical field. Although the traditional unstructured grid can flexibly realize the geometric approximation of a complex curved surface, a high-order discrete system of a control equation is difficult to construct on the traditional unstructured grid.
Therefore, how to simply construct a control equation satisfying the high-order construction requirement to overcome the deficiency of the conventional grid in the aspect of thin-shell numerical simulation is an urgent problem to be solved in the art.
Disclosure of Invention
In view of this, the present invention provides a method, an apparatus, a device and a medium for simulating a curved surface of a thin shell, which can simply construct a control equation satisfying a high-order construction requirement to overcome the deficiency of the conventional grid in the aspect of thin shell numerical simulation, and the specific scheme is as follows:
in a first aspect, the application discloses a method for simulating a curved surface of a thin shell, comprising:
acquiring a triangular mesh of a curved surface, determining vertex angles of all triangles based on the side lengths of all triangles in the triangular mesh, and then determining the current curvature of each vertex in all the triangles based on the vertex angles;
determining a conformal factor of each vertex in all the triangles under the condition of meeting a first constraint condition based on a preset linear system equation and the current curvature, determining the current side length of all the triangles based on the conformal factor, and then determining a current vertex angle based on the current side length so as to determine a new current curvature of each vertex according to the current vertex angle;
when the new current curvature meets a second constraint condition, determining a target triangle from the triangular mesh, mapping the target triangle into a two-dimensional plane based on the current side length and the current vertex angle of the target triangle, and then re-executing the step of determining the target triangle from the triangular mesh until each triangle in the curved surface is mapped into the two-dimensional plane;
generating a block self-adaptive Cartesian grid on the mapped two-dimensional plane according to a grid encryption criterion, inversely mapping the block self-adaptive Cartesian grid on the two-dimensional plane to be a block self-adaptive Cartesian grid on a three-dimensional curved surface, and simulating a target physical field on a thin shell curved surface based on the block self-adaptive Cartesian grid on the three-dimensional curved surface.
Optionally, the determining, based on the preset linear system equation and the current curvature, a conformal factor of each vertex in all the triangles under a condition that a first constraint condition is satisfied includes:
based on
Determining that each vertex in all the triangles satisfies
A conformal factor of lower;
wherein, for the curved surface triangle mesh
，
，
Is the vertex of any triangle; matrix of
Is a Laplace-Beltrami operator,
，
，
is that it is
Edge of (1)
The weight of the excess trimming;
is the conformal factor at the x-th iteration,
；
in order to target the curvature of the object,
in order to be the current curvature of the object,
，
is at the vertex
The current curvature of the beam at (a),
is a triangle
To Chinese
Is the internal angle of the vertex;
is the sum of the conformal factors of all vertices in the triangular mesh.
Optionally, the second constraint condition is:
and the absolute value of the difference value between the target curvature and the current curvature of each vertex in all the triangles is smaller than the preset error precision.
Optionally, determining the current side lengths of all the triangles based on the conformal factor, and then determining the current vertex angle based on the current side lengths, further includes:
based on the current vertex angle pair
Edge of (1)
And updating the corresponding weight of the overcut edge.
Optionally, after determining vertex angles of all triangles based on the side lengths of all triangles in the triangle mesh, and then determining the current curvature of each vertex in all triangles based on the vertex angles, the method further includes:
judging that
Edge of (1)
Whether the corresponding single-side cotangent values are not more than zero or not;
if it is said
Edge of (1)
If the corresponding single-side cotangent value is not greater than zero, then the side is aligned
Performing edge swapping operation on the two public triangles, and determining a conformal factor of each vertex in all the triangles under the condition of meeting a first constraint condition based on a preset linear system equation and the current curvature;
if it is said
Edge of (1)
And if the corresponding single-side cotangent value is greater than zero, executing the step of determining the conformal factor of each vertex in all the triangles under the condition of meeting a first constraint condition based on the preset linear system equation and the current curvature.
Optionally, determining the current side lengths of all the triangles based on the conformal factor, and then determining the current vertex angle based on the current side length, so as to determine a new current curvature of each vertex according to the current vertex angle, further including:
and when the new current curvature does not meet the second constraint condition, re-executing the step of determining the vertex angles of all the triangles based on the side lengths of all the triangles in the triangular mesh, and then determining the current curvature of each vertex in all the triangles based on the vertex angles until the current curvature meets the second constraint condition.
Optionally, the inversely mapping the block-adaptive cartesian grid on the two-dimensional plane to the block-adaptive cartesian grid on the three-dimensional curved surface includes:
determining coordinate points of the block adaptive Cartesian grid on the two-dimensional plane;
determining barycentric coordinates of the coordinate points, and determining the coordinate points of the block adaptive Cartesian grid on the three-dimensional curved surface based on the barycentric coordinates;
and connecting the coordinate points of the block adaptive Cartesian grid on the three-dimensional curved surface to generate the block adaptive Cartesian grid on the three-dimensional curved surface.
In a second aspect, the present application discloses a thin shell curved surface simulation apparatus, comprising:
the system comprises a current curvature determining module, a shape calculating module and a shape calculating module, wherein the current curvature determining module is used for acquiring a triangular mesh of a curved surface, determining vertex angles of all triangles based on side lengths of all triangles in the triangular mesh, and then determining the current curvature of each vertex in all the triangles based on the vertex angles;
the new current curvature determining module is used for determining a conformal factor of each vertex in all the triangles under the condition that a first constraint condition is met based on a preset linear system equation and the current curvature, determining the current side length of all the triangles based on the conformal factor, and then determining a current vertex angle based on the current side length so as to determine the new current curvature of each vertex according to the current vertex angle;
a mapping module, configured to determine a target triangle from the triangle mesh when the new current curvature meets a second constraint condition, map the target triangle into a two-dimensional plane based on a current side length and a current vertex angle of the target triangle, and then re-execute the step of determining the target triangle from the triangle mesh until each triangle in the curved surface is mapped to the two-dimensional plane;
and the inverse mapping and simulation module is used for generating a block self-adaptive Cartesian grid on the mapped two-dimensional plane according to a grid encryption standard, inversely mapping the block self-adaptive Cartesian grid on the two-dimensional plane into a block self-adaptive Cartesian grid on a three-dimensional curved surface, and simulating a target physical field on a thin shell curved surface based on the block self-adaptive Cartesian grid on the three-dimensional curved surface.
In a third aspect, the present application discloses a thin shell curved surface simulation device, comprising:
a memory for storing a computer program;
and the processor is used for executing the computer program to realize the thin shell curved surface simulation method disclosed in the foregoing.
In a fourth aspect, the present application discloses a thin shell curved surface simulation medium for storing a computer program; wherein the computer program is executed by a processor to implement the thin shell surface simulation method disclosed in the foregoing.
Therefore, the application provides a thin shell curved surface simulation method, which comprises the following steps: acquiring a triangular mesh of a curved surface, determining vertex angles of all triangles based on the side lengths of all triangles in the triangular mesh, and then determining the current curvature of each vertex in all the triangles based on the vertex angles; determining a conformal factor of each vertex in all the triangles under the condition of meeting a first constraint condition based on a preset linear system equation and the current curvature, determining the current side length of all the triangles based on the conformal factor, and then determining a current vertex angle based on the current side length so as to determine a new current curvature of each vertex according to the current vertex angle; when the new current curvature meets a second constraint condition, determining a target triangle from the triangular mesh, mapping the target triangle into a two-dimensional plane based on the current side length and the current vertex angle of the target triangle, and then re-executing the step of determining the target triangle from the triangular mesh until each triangle in the curved surface is mapped into the two-dimensional plane; generating a block self-adaptive Cartesian grid on the mapped two-dimensional plane according to a grid encryption criterion, inversely mapping the block self-adaptive Cartesian grid on the two-dimensional plane to be a block self-adaptive Cartesian grid on a three-dimensional curved surface, and simulating a target physical field on a thin shell curved surface based on the block self-adaptive Cartesian grid on the three-dimensional curved surface. Therefore, the method maps the curved surface to the two-dimensional plane, generates the block self-adaptive Cartesian grid on the mapped two-dimensional plane, and inversely maps the block self-adaptive Cartesian grid on the two-dimensional plane to the block self-adaptive Cartesian grid on the three-dimensional curved surface; the generalized space block self-adaptive Cartesian grid can meet the construction requirement of a high-order format, so that the method overcomes the defects of the traditional grid in the aspect of thin shell numerical simulation; further, the block adaptive cartesian grid generation process in the present application is simple because the block adaptive cartesian grid inverse on the two-dimensional plane is relatively easy to construct.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the provided drawings without creative efforts.
FIG. 1 is a flow chart of a thin shell surface simulation method disclosed in the present application;
FIG. 2 is a schematic diagram of an initial grid structure disclosed herein;
fig. 3 is a schematic structural diagram of a block adaptive cartesian grid on a two-dimensional plane according to the present disclosure;
FIG. 4 is a flow chart of a specific thin shell surface simulation method disclosed in the present application;
FIG. 5 is a schematic diagram of a structure of a triangular mesh on a two-dimensional plane according to the present disclosure;
FIG. 6 is a schematic structural diagram of a triangular mesh on a three-dimensional curved surface according to the present disclosure;
FIG. 7 is a flow chart of a block adaptive Cartesian grid generation disclosed herein;
FIG. 8 is a schematic view of a thin shell curved surface simulation apparatus according to the present disclosure;
fig. 9 is a structural diagram of a thin shell curved surface simulation device disclosed in the present application.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be obtained by a person skilled in the art without making any creative effort based on the embodiments in the present invention, belong to the protection scope of the present invention.
In order to perform high-precision numerical simulation on an unsteady physical field on a thin shell, a user needs to generate a high-quality computational grid on a spatial Riemann curved model. The traditional structural mesh is difficult to maintain good orthogonality on a complex curved surface, and meanwhile, local adaptive encryption is difficult to realize along with the change of a physical field. Although the traditional unstructured grid can flexibly realize the geometric approximation of a complex curved surface, a high-order discrete system of a control equation is difficult to construct on the traditional unstructured grid.
Therefore, the embodiment of the application provides a thin shell curved surface simulation scheme, which can simply construct a control equation meeting the high-order construction requirement to overcome the defects of the traditional grid in the aspect of thin shell numerical simulation.
The embodiment of the application discloses a method for simulating a curved surface of a thin shell, which is shown in figure 1 and comprises the following steps:
step S11: obtaining a triangular mesh of a curved surface, determining vertex angles of all triangles based on the side lengths of all triangles in the triangular mesh, and then determining the current curvature of each vertex in all the triangles based on the vertex angles.
In this embodiment, the triangular mesh of the curved surface is an unstructured mesh, for example, an stl file.
In this embodiment, first, the side lengths of all the triangles are determined based on the coordinates of all the triangles, the vertex angles of all the triangles are determined based on the side lengths of all the triangles, and then, the current curvature of each vertex in all the triangles is determined based on the vertex angles of all the triangles. In particular, for vertices
The current curvature is:
wherein the content of the first and second substances,
is a triangle
To Chinese
The internal angle of the vertex.
Step S12: determining a conformal factor of each vertex in all the triangles under the condition of meeting a first constraint condition based on a preset linear system equation and the current curvature, determining the current side length of all the triangles based on the conformal factor, and then determining the current vertex angle based on the current side length so as to determine a new current curvature of each vertex according to the current vertex angle.
It should be noted that the determining a conformal factor of each vertex in all the triangles under the condition of satisfying the first constraint condition based on the preset linear system equation and the current curvature includes: based on
Determining that each vertex in all the triangles is satisfied
A lower conformal factor;
wherein, for curved surface triangular mesh
Said
Including all of the triangles;
，
is the vertex of any triangle of the curved surface,
，
possibly in different triangles, possibly in the same triangle, and possibly also recombined into one vertex; hesse matrix
For the Laplace-Beltrami operator,
，
，
is that the
Edge of (1)
The weight of the excess trimming;
is the conformal factor at the x-th iteration,
；
in order to target the curvature of the object,
is the current curvature;
is the sum of the conformal factors of all vertices in the triangular mesh.
In this embodiment, the reason for
Edge of (1)
The corresponding weight of the overcut edge is calculated according to the vertex angle, so that after the current vertex angle of each vertex in all the triangles is determined, the current vertex angle needs to be matched with the vertex angle
Edge of (1)
And updating the corresponding weight of the trimming edge. After the update, determining the
Edge of (1)
Whether the corresponding single-side cotangent values are not more than zero or not; if it is said
Edge of (1)
If the corresponding single-side cotangent value is not more than zero, then the corresponding side is matched
Performing edge swapping operation on the two public triangles, and determining a conformal factor of each vertex in all the triangles under the condition of meeting a first constraint condition based on a preset linear system equation and the current curvature; if it is said
Edge of (1)
And if the corresponding single-side cotangent value is greater than zero, executing the step of determining the conformal factor of each vertex in all the triangles under the condition of meeting a first constraint condition based on the preset linear system equation and the current curvature.
In this embodiment, before determining vertex angles of all triangles in the triangle mesh based on the side lengths of all triangles, and then determining the current curvature of each vertex in all triangles based on the vertex angles, the target curvature, the conformal factor, and the metric need to be measured
Initializing and updating the metric to
. And then determining the current side lengths of all the triangles based on the conformal factor, the current measurement and the side length obtained by previous calculation, and then determining the current vertex angle based on the current side length so as to determine a new current curvature of each vertex according to the current vertex angle, wherein the measurement is an expression form of side length calculation.
Step S13: when the new current curvature meets a second constraint condition, determining a target triangle from the triangular mesh, mapping the target triangle into a two-dimensional plane based on the current side length and the current vertex angle of the target triangle, and then re-executing the step of determining the target triangle from the triangular mesh until each triangle in the curved surface is mapped into the two-dimensional plane.
In this embodiment, the second constraint condition is that an absolute value of a difference between the target curvature and the current curvature of each vertex in all the triangles is smaller than a preset error precision.
It should be noted that, when the new current curvature does not satisfy the second constraint condition, the step of determining vertex angles of all the triangles based on the side lengths of all the triangles in the triangular mesh is executed again, and then determining the current curvature of each vertex in all the triangles based on the vertex angles is executed again until the current curvature satisfies the second constraint condition.
Step S14: generating a block self-adaptive Cartesian grid on the mapped two-dimensional plane according to a grid encryption criterion, inversely mapping the block self-adaptive Cartesian grid on the two-dimensional plane to be a block self-adaptive Cartesian grid on a three-dimensional curved surface, and simulating a target physical field on a thin shell curved surface based on the block self-adaptive Cartesian grid on the three-dimensional curved surface.
In this embodiment, an initial grid is first generated on the mapped two-dimensional plane, the initial grid is shown in fig. 2, then a block adaptive cartesian grid is generated on the mapped two-dimensional plane according to a grid encryption criterion, and the block adaptive cartesian grid on the two-dimensional plane is shown in fig. 3, so that the self-adaptation process of the grid spatial scale can be flexibly implemented by the present application; in addition, because the deformation of the spatial discrete surface is equivalent to the change of the scale factor of the grid point, and the process of mapping the triangular grid of the surface to the plane is continuous, the method is also suitable for the generation requirement of the deformed grid.
Therefore, the application provides a thin shell curved surface simulation method, which comprises the following steps: acquiring a triangular mesh of a curved surface, determining vertex angles of all triangles based on the side lengths of all triangles in the triangular mesh, and then determining the current curvature of each vertex in all the triangles based on the vertex angles; determining a conformal factor of each vertex in all the triangles under the condition of meeting a first constraint condition based on a preset linear system equation and the current curvature, determining the current side length of all the triangles based on the conformal factor, and then determining a current vertex angle based on the current side length so as to determine a new current curvature of each vertex according to the current vertex angle; when the new current curvature meets a second constraint condition, determining a target triangle from the triangular mesh, mapping the target triangle into a two-dimensional plane based on the current side length and the current vertex angle of the target triangle, and then re-executing the step of determining the target triangle from the triangular mesh until each triangle in the curved surface is mapped into the two-dimensional plane; and generating a block self-adaptive Cartesian grid on the mapped two-dimensional plane according to a grid encryption criterion, inversely mapping the block self-adaptive Cartesian grid on the two-dimensional plane to a block self-adaptive Cartesian grid on a three-dimensional curved surface, and simulating the target physical field on the thin shell curved surface based on the block self-adaptive Cartesian grid on the three-dimensional curved surface. Therefore, the curved surface is mapped to the two-dimensional plane, the block self-adaptive Cartesian grid is generated on the mapped two-dimensional plane, and then the block self-adaptive Cartesian grid on the two-dimensional plane is inversely mapped to the block self-adaptive Cartesian grid on the three-dimensional curved surface; the generalized space block self-adaptive Cartesian grid can meet the construction requirement of a high-order format, so that the method overcomes the defects of the traditional grid in the aspect of thin shell numerical simulation; further, the block adaptive cartesian grid generation process in the present application is simple because the block adaptive cartesian grid inverse on the two-dimensional plane is relatively easy to construct.
The embodiment of the application discloses a specific thin shell curved surface simulation method, and compared with the previous embodiment, the embodiment further explains and optimizes the technical scheme. As shown in fig. 4, the method specifically includes:
step S21: obtaining a triangular mesh of a curved surface, determining vertex angles of all triangles based on the side lengths of all triangles in the triangular mesh, and then determining the current curvature of each vertex in all the triangles based on the vertex angles.
Step S22: determining a conformal factor of each vertex in all the triangles under the condition of meeting a first constraint condition based on a preset linear system equation and the current curvature, determining the current side length of all the triangles based on the conformal factor, and then determining the current vertex angle based on the current side length so as to determine a new current curvature of each vertex according to the current vertex angle.
Step S23: when the new current curvature meets a second constraint condition, determining a target triangle from the triangular mesh, mapping the target triangle into a two-dimensional plane based on the current side length and the current vertex angle of the target triangle, and then re-executing the step of determining the target triangle from the triangular mesh until each triangle in the curved surface is mapped into the two-dimensional plane.
Step S24: generating a block self-adaptive Cartesian grid on the mapped two-dimensional plane according to a grid encryption criterion, and determining a coordinate point of the block self-adaptive Cartesian grid on the two-dimensional plane; barycentric coordinates of the coordinate points are then determined.
In this embodiment, the block adaptive cartesian grid coordinate points on the three-dimensional curved surface are solved through invariance of the area coordinate (barycentric coordinate), which is specifically implemented as follows:
in a two-dimensional plane (parameter domain)
、
、
And points on curved surfaces
、
And
and (7) correspondingly.
The barycentric coordinates of the triangular mesh in which the block adaptive cartesian grid coordinate points are located are calculated based on the coordinate points of the block adaptive cartesian grid on the two-dimensional curved surface. Fig. 5 is a triangle on a two-dimensional plane, in which,
for a block adaptive Cartesian grid coordinate point (known) falling within the triangular region, based on
The coordinates of the points and the coordinates of the triangular grid points on the two-dimensional parameter domain can be calculated
Barycentric coordinates of points
. The relationship is as follows:
the solution of the barycentric coordinates is equivalent to the solution of a linear equation system and can be solved by a Newton iteration method.
Step S25: and determining a coordinate point of the block adaptive Cartesian grid on the three-dimensional curved surface based on the barycentric coordinates, connecting the coordinate points of the block adaptive Cartesian grid on the three-dimensional curved surface to generate the block adaptive Cartesian grid on the three-dimensional curved surface, and then simulating a target physical field on the thin shell curved surface based on the block adaptive Cartesian grid on the three-dimensional curved surface.
In this example, the weights of coordinate points according to a block-adaptive Cartesian grid are determinedThe center coordinates calculate a block adaptive cartesian grid coordinate point corresponding to the three-dimensional curved surface. Such as calculating block adaptive Cartesian grid coordinate points on a three-dimensional curved surface
Referring to fig. 6, the relationship is as follows:
for more specific working processes of step S21, step S22 and step S23, reference is made to the foregoing disclosed embodiments, and details are not repeated herein.
Therefore, the application provides a thin shell curved surface simulation method, which comprises the following steps: acquiring a triangular mesh of a curved surface, determining vertex angles of all triangles based on the side lengths of all triangles in the triangular mesh, and then determining the current curvature of each vertex in all the triangles based on the vertex angles; determining a conformal factor of each vertex in all the triangles under the condition of meeting a first constraint condition based on a preset linear system equation and the current curvature, determining the current side length of all the triangles based on the conformal factor, and then determining a current vertex angle based on the current side length so as to determine a new current curvature of each vertex according to the current vertex angle; when the new current curvature meets a second constraint condition, determining a target triangle from the triangular mesh, mapping the target triangle into a two-dimensional plane based on the current side length and the current vertex angle of the target triangle, and then re-executing the step of determining the target triangle from the triangular mesh until each triangle in the curved surface is mapped into the two-dimensional plane; generating a block self-adaptive Cartesian grid on the mapped two-dimensional plane according to a grid encryption criterion, and determining a coordinate point of the block self-adaptive Cartesian grid on the two-dimensional plane; then determining barycentric coordinates of the coordinate points; determining a coordinate point of the block adaptive Cartesian grid on the three-dimensional curved surface based on the barycentric coordinates, connecting the coordinate points of the block adaptive Cartesian grid on the three-dimensional curved surface to generate the block adaptive Cartesian grid on the three-dimensional curved surface, and then simulating a target physical field on a thin shell curved surface based on the block adaptive Cartesian grid on the three-dimensional curved surface, so that the application can be seen; the generalized space block self-adaptive Cartesian grid can meet the construction requirement of a high-order format, so that the method overcomes the defects of the traditional grid in the aspect of thin shell numerical simulation; further, the block adaptive cartesian grid generation process in the present application is simple because the block adaptive cartesian grid inverse on the two-dimensional plane is relatively easy to construct.
FIG. 7 is a flow chart of a block adaptive Cartesian grid generation disclosed herein, (1) inputting a triangular grid of a curved surface; (2) And performing Ricci flow parameterization on the triangular mesh, wherein the specific process of the Ricci flow parameterization is as follows: determining vertex angles of all triangles in the triangular mesh based on the side lengths of all triangles, and then determining the current curvature of each vertex in all triangles based on the vertex angles; determining a conformal factor of each vertex in all the triangles under the condition of meeting a first constraint condition based on a preset linear system equation and the current curvature, determining the current side length of all the triangles based on the conformal factor, and then determining a current vertex angle based on the current side length so as to determine a new current curvature of each vertex according to the current vertex angle; when the new current curvature meets a second constraint condition, determining a target triangle from the triangular mesh, mapping the target triangle into a two-dimensional plane based on the current side length and the current vertex angle of the target triangle, and then re-executing the step of determining the target triangle from the triangular mesh until each triangle in the curved surface is mapped into the two-dimensional plane; (3) And generating a block self-adaptive Cartesian grid on the mapped two-dimensional plane according to a grid encryption criterion, and inversely mapping the block self-adaptive Cartesian grid on the two-dimensional plane into the block self-adaptive Cartesian grid on the three-dimensional curved surface.
It should be noted that the Ricci flow parameterization in the present application can also be implemented with curved harmonic mapping.
For example, when mapping a triangular mesh of a curved surface onto a two-dimensional plane, taking embedding into a circle as an example:
(1) Firstly, a point on the boundary of the curved surface is given
Coordinates of (A) such as
Based on the point adjacent to the boundary point
Length of side of
And the vertex angles of the target triangles where the two points are located to obtain the points
The coordinates are
Re-determining points based on side length and vertex angle
，
Another point in the target triangle
The coordinates of (a). According to
，
，
And calculating the normal direction of the target triangle by the three-point coordinates.
(2) Finding a triangle from the adjacent triangles of the target triangle, judging whether the three vertexes of the triangle are embedded into the plane, and continuing to obtain the next adjacent triangle if the three vertexes are completely embedded. If there are vertices that are not embedded, assume that
Then at this time
，
Is already embedded. To be provided with
，
Is used as the center of a circle,
，
circles of radii intersect at two points and the normal direction of the triangle is the same as the normal direction of the first embedded triangle, whereby the points can be determined
. And (3) repeating the step (2) until all points are embedded into the plane.
In this way, the present application maps the triangular mesh of the curved surface into the circular domain, and since the inverse of the block-adaptive cartesian mesh on the circular domain is relatively easy to construct, the generation process of the block-adaptive cartesian mesh in the present application is simple and the orthogonality is maintained well.
Correspondingly, the embodiment of the present application further discloses a thin shell curved surface simulation device, as shown in fig. 8, the device includes:
a current curvature determining module 11, configured to obtain a triangular mesh of a curved surface, determine vertex angles of all triangles based on side lengths of all triangles in the triangular mesh, and then determine a current curvature of each vertex in all triangles based on the vertex angles;
a new current curvature determining module 12, configured to determine a conformal factor of each vertex in all the triangles under a condition that a first constraint is satisfied based on a preset linear system equation and the current curvature, determine a current side length of all the triangles based on the conformal factor, and then determine a current vertex angle based on the current side length, so as to determine a new current curvature of each vertex according to the current vertex angle;
a mapping module 13, configured to determine a target triangle from the triangle mesh when the new current curvature meets a second constraint condition, map the target triangle into a two-dimensional plane based on a current side length and a current vertex angle of the target triangle, and then re-execute the step of determining the target triangle from the triangle mesh until each triangle in the curved surface is mapped into the two-dimensional plane;
the inverse mapping and simulation module 14 is configured to generate a block adaptive cartesian grid on the mapped two-dimensional plane according to a grid encryption criterion, inversely map the block adaptive cartesian grid on the two-dimensional plane into a block adaptive cartesian grid on a three-dimensional curved surface, and simulate the target physical field on the thin shell curved surface based on the block adaptive cartesian grid on the three-dimensional curved surface.
For more specific working processes of the modules, reference may be made to corresponding contents disclosed in the foregoing embodiments, and details are not repeated here.
Therefore, the application provides a thin shell curved surface simulation method, which comprises the following steps: acquiring a triangular mesh of a curved surface, determining vertex angles of all triangles based on the side lengths of all triangles in the triangular mesh, and then determining the current curvature of each vertex in all the triangles based on the vertex angles; determining a conformal factor of each vertex in all the triangles under the condition of meeting a first constraint condition based on a preset linear system equation and the current curvature, determining the current side length of all the triangles based on the conformal factor, and then determining a current vertex angle based on the current side length so as to determine a new current curvature of each vertex according to the current vertex angle; when the new current curvature meets a second constraint condition, determining a target triangle from the triangular mesh, mapping the target triangle into a two-dimensional plane based on the current side length and the current vertex angle of the target triangle, and then re-executing the step of determining the target triangle from the triangular mesh until each triangle in the curved surface is mapped into the two-dimensional plane; generating a block self-adaptive Cartesian grid on the mapped two-dimensional plane according to a grid encryption criterion, inversely mapping the block self-adaptive Cartesian grid on the two-dimensional plane to be a block self-adaptive Cartesian grid on a three-dimensional curved surface, and simulating a target physical field on a thin shell curved surface based on the block self-adaptive Cartesian grid on the three-dimensional curved surface. Therefore, the method maps the curved surface to the two-dimensional plane, generates the block self-adaptive Cartesian grid on the mapped two-dimensional plane, and inversely maps the block self-adaptive Cartesian grid on the two-dimensional plane to the block self-adaptive Cartesian grid on the three-dimensional curved surface; the generalized space block self-adaptive Cartesian grid can meet the construction requirement of a high-order format, so that the defects of the traditional grid in the aspect of thin shell numerical simulation are overcome; further, since the inverse of the block-adaptive cartesian grid on the two-dimensional plane is relatively easy to construct, the generation process of the block-adaptive cartesian grid in the present application is simple.
Furthermore, the embodiment of the application also provides thin shell curved surface simulation equipment. FIG. 9 is a block diagram illustrating a thin shell curved surface simulation device 20 according to an exemplary embodiment, the contents of which should not be considered as limiting the scope of use of the present application in any way.
Fig. 9 is a schematic structural diagram of a thin-shell curved surface simulation device 20 according to an embodiment of the present application. The thin shell curved surface simulation device 20 may specifically include: at least one processor 21, at least one memory 22, a display 23, an input output interface 24, a communication interface 25, a power supply 26, and a communication bus 27. The memory 22 is used for storing a computer program, and the computer program is loaded and executed by the processor 21 to implement the relevant steps in the thin shell curved surface simulation method disclosed in any of the foregoing embodiments. In addition, the thin shell curved surface simulation device 20 in the present embodiment may be specifically an electronic computer.
In this embodiment, the power supply 26 is configured to provide operating voltages for the hardware devices on the thin-shell curved surface simulation device 20; the communication interface 25 can create a data transmission channel between the thin shell curved surface simulation device 20 and an external device, and the communication protocol followed by the communication interface is any communication protocol applicable to the technical solution of the present application, and is not specifically limited herein; the input/output interface 24 is configured to obtain external input data or output data to the outside, and a specific interface type thereof may be selected according to specific application requirements, which is not specifically limited herein.
In addition, the memory 22 is used as a carrier for resource storage, and may be a read-only memory, a random access memory, a magnetic disk or an optical disk, etc., and the resource stored thereon may include the computer program 221, and the storage manner may be a transient storage or a permanent storage. The computer program 221 may further include a computer program that can be used to perform other specific tasks in addition to the computer program that can be used to perform the thin shell curved surface simulation method performed by the thin shell curved surface simulation apparatus 20 disclosed in any of the foregoing embodiments.
Furthermore, the embodiment of the application also discloses a thin shell curved surface simulation medium which is used for storing a computer program; wherein the computer program is executed by a processor to implement the thin shell curved surface simulation method disclosed in the foregoing.
For the specific steps of the method, reference may be made to corresponding contents disclosed in the foregoing embodiments, and details are not repeated here.
The embodiments in the present application are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same or similar parts among the embodiments are referred to each other, that is, for the apparatus disclosed in the embodiments, since the apparatus corresponds to the method disclosed in the embodiments, the description is simple, and for the relevant parts, the method is referred to the method part.
Those of skill would further appreciate that the various illustrative components and algorithm steps described in connection with the embodiments disclosed herein may be implemented as electronic hardware, computer software, or combinations of both, and that the components and steps of the various examples have been described above generally in terms of their functionality in order to clearly illustrate this interchangeability of hardware and software. Whether such functionality is implemented as hardware or software depends upon the particular application and design constraints imposed on the implementation. Skilled artisans may implement the described functionality in varying ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the present application.
The steps of a method or algorithm described in connection with the embodiments disclosed herein may be embodied directly in hardware, in a software module executed by a processor, or in a combination of the two. A software module may reside in Random Access Memory (RAM), memory, read-only memory (ROM), electrically programmable ROM, electrically erasable programmable ROM, registers, hard disk, a removable disk, a CD-ROM, or any other form of medium known in the art.
Finally, it should also be noted that, herein, relational terms such as first and second, and the like may be used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Also, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrases "comprising a," "8230," "8230," or "comprising" does not exclude the presence of additional like elements in a process, method, article, or apparatus that comprises the element.
The above detailed description is provided for the method, apparatus, device and medium for simulating the curved surface of the thin shell, and the specific examples are applied in this document to explain the principle and implementation of the present application, and the description of the above embodiments is only used to help understand the method and core ideas of the present application; meanwhile, for a person skilled in the art, according to the idea of the present application, the specific implementation manner and the application scope may be changed, and in summary, the content of the present specification should not be construed as a limitation to the present application.
Claims (10)
1. A thin shell curved surface simulation method is characterized by comprising the following steps:
acquiring a triangular mesh of a curved surface, determining vertex angles of all triangles based on the side lengths of all triangles in the triangular mesh, and then determining the current curvature of each vertex in all the triangles based on the vertex angles;
determining a conformal factor of each vertex in all the triangles under the condition of meeting a first constraint condition based on a preset linear system equation and the current curvature, determining the current side length of all the triangles based on the conformal factor, and then determining a current vertex angle based on the current side length so as to determine a new current curvature of each vertex according to the current vertex angle;
when the new current curvature meets a second constraint condition, determining a target triangle from the triangular mesh, mapping the target triangle into a two-dimensional plane based on the current side length and the current vertex angle of the target triangle, and then re-executing the step of determining the target triangle from the triangular mesh until each triangle in the curved surface is mapped into the two-dimensional plane;
generating a block self-adaptive Cartesian grid on the mapped two-dimensional plane according to a grid encryption criterion, inversely mapping the block self-adaptive Cartesian grid on the two-dimensional plane to be a block self-adaptive Cartesian grid on a three-dimensional curved surface, and simulating a target physical field on a thin shell curved surface based on the block self-adaptive Cartesian grid on the three-dimensional curved surface.
2. The thin shell surface simulation method of claim 1, wherein the determining the conformal factor of each vertex of all the triangles under the condition of satisfying a first constraint condition based on a preset linear system equation and the current curvature comprises:
based on
Determining that each vertex in all the triangles satisfies
A conformal factor of lower;
wherein, for curved surface triangular mesh
，
，
Is the vertex of an arbitrary triangle; matrix of
Is a Laplace-Beltrami operator,
，
，
is that the
Edge of (1)
The weight of the residual trimming edge;
is the conformal factor at the x-th iteration,
；
in order to target the curvature of the object,
in order to be the current curvature of the object,
，
is at the vertex
The current curvature of the beam at (a),
is a triangle
In the middle to
Is the internal angle of the vertex;
is the sum of the conformal factors of all vertices in the triangular mesh.
3. The thin shell curved surface simulation method of claim 2, wherein the second constraint condition is:
and the absolute value of the difference value between the target curvature and the current curvature of each vertex in all the triangles is smaller than the preset error precision.
4. The thin shell curved surface simulation method of claim 2, wherein after determining the current side lengths of all the triangles based on the conformal factor and then determining the current vertex angles based on the current side lengths, the method further comprises:
based on the current vertex angle pair
Edge of (1)
And updating the corresponding weight of the trimming edge.
5. The thin shell curved surface simulation method of claim 4, wherein after determining the vertex angles of all the triangles in the triangular mesh based on the side lengths of all the triangles, and then determining the current curvature of each vertex in all the triangles based on the vertex angles, further comprising:
judging that
Edge of (1)
Whether the corresponding single-side cotangent values are not more than zero or not;
if it is said
Edge of (1)
If the corresponding single-side cotangent value is not greater than zero, then the side is aligned
Performing edge swapping operation on the two public triangles, and determining a conformal factor of each vertex in all the triangles under the condition of meeting a first constraint condition based on a preset linear system equation and the current curvature;
if it is said
Edge of (1)
And if the corresponding single-side cotangent value is larger than zero, executing the step of determining the conformal factor of each vertex in all the triangles under the condition of meeting the first constraint condition based on the preset linear system equation and the current curvature.
6. The thin shell curved surface simulation method of claim 1, wherein after determining the current side lengths of all the triangles based on the conformal factors and then determining the current vertex angles based on the current side lengths so as to determine the new current curvature of each vertex according to the current vertex angles, the method further comprises:
and when the new current curvature does not meet the second constraint condition, determining vertex angles of all triangles in the triangular mesh based on the side lengths of all triangles, and then determining the current curvature of each vertex in all triangles based on the vertex angles until the current curvature meets the second constraint condition.
7. The thin shell curved surface simulation method of any one of claims 1 to 6, wherein the inverse mapping of the block-adaptive Cartesian grid on the two-dimensional plane to a block-adaptive Cartesian grid on a three-dimensional curved surface comprises:
determining a coordinate point of the block adaptive Cartesian grid on the two-dimensional plane;
determining barycentric coordinates of the coordinate points, and determining the coordinate points of the block adaptive Cartesian grid on the three-dimensional curved surface based on the barycentric coordinates;
and connecting the coordinate points of the block adaptive Cartesian grid on the three-dimensional curved surface to generate the block adaptive Cartesian grid on the three-dimensional curved surface.
8. A thin shell curved surface simulation device is characterized by comprising:
the current curvature determining module is used for acquiring a triangular mesh of a curved surface, determining vertex angles of all triangles based on the side lengths of all triangles in the triangular mesh, and then determining the current curvature of each vertex in all the triangles based on the vertex angles;
the new current curvature determining module is used for determining a conformal factor of each vertex in all the triangles under the condition that a first constraint condition is met based on a preset linear system equation and the current curvature, determining the current side length of all the triangles based on the conformal factor, and then determining a current vertex angle based on the current side length so as to determine the new current curvature of each vertex according to the current vertex angle;
a mapping module, configured to determine a target triangle from the triangle mesh when the new current curvature meets a second constraint condition, map the target triangle into a two-dimensional plane based on a current side length and a current vertex angle of the target triangle, and then re-execute the step of determining the target triangle from the triangle mesh until each triangle in the curved surface is mapped to the two-dimensional plane;
and the inverse mapping and simulation module is used for generating a block self-adaptive Cartesian grid on the mapped two-dimensional plane according to a grid encryption standard, inversely mapping the block self-adaptive Cartesian grid on the two-dimensional plane into a block self-adaptive Cartesian grid on a three-dimensional curved surface, and simulating a target physical field on a thin shell curved surface based on the block self-adaptive Cartesian grid on the three-dimensional curved surface.
9. A thin shell curved surface simulation device, comprising:
a memory for storing a computer program;
a processor for executing the computer program to implement the thin shell curved surface simulation method of any one of claims 1 to 7.
10. A thin shell curved surface simulation medium is characterized in that the medium is used for storing a computer program; wherein the computer program when executed by a processor implements the thin shell surface simulation method of any of claims 1 to 7.
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