JP2005228260A - Distortion distribution calculation method for shaping plate material to objective curved surface - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a calculation method for obtaining distortion distribution required to shape plate material to objective curved surface, while giving a shape when developing a curved surface to a plane. <P>SOLUTION: This method consists of following processes; a. a process which converts a curved surface shape displayed by coordinate of discrete points etc. into a function, b. a process which draws geodesic lines in longitudinal and lateral directions on a curved surface made by the function, c. a process which performs calculation of distribution of the distortion quantity concerning an undevelopable surface formation necessary for curved surface formation from shape change on a curved surface of a domain surrounded by four geodesic lines forming a square on a plane or change of interval on the geodesic lines which satisfies parallel condition on a plane, and d. a process which extracts developable transformation component bringing the difference when difference exists between the undevelopable surface obtained by giving distribution of distortion quantity obtained by each process above mentioned to the plate material and the objective curved surface, and which performs calculation of both of the undevelopable transformation and developable transformation. <P>COPYRIGHT: (C)2005,JPO&NCIPI

Description

  According to the present invention, from a curved surface information given by coordinates of discrete points on a curved surface, the computer system calculates and calculates the strain type and size distribution required to form a flat plate material such as a steel plate into a desired curved surface shape. Regarding the method.

  For example, part of the ship's hull and the outer shell of aircraft, trains, etc. have curved shapes, and when these curved surfaces are formed, conventionally developed views of the curved shape developed on a plane by a specific method have been drawn. Based on the experience and intuition of highly skilled and experienced technicians, for example, curved surface formation by linear heating has been performed.

In recent years, the relationship between additional strain and deformation has been dealt with as an optimization problem by utilizing the fact that the deformation shape after applying strain to a plate material is obtained by numerical simulation. On the other hand, when a flat plate material is formed into a desired curved surface by linear heating, in order to make an accurate cutting to eliminate the need for finishing cutting after bending, the inherent distortion and inherent deformation of each linear heating are previously performed. After creating a linear heating method that performs bending when the desired curved surface shape is given, the intrinsic deformation data of the heating wire is called and the direction of the intrinsic deformation is positive or negative A method is known in which a curved surface is developed into a planar shape by performing an FEM (finite element method) elastic simulation in which a generated inherent strain distribution is added to a target curved surface shape after being reversed and deformed freely (for example, Patent Documents) 1).
JP2000-237826A

  However, the above prior art has a problem that the work is performed without knowing the amount of distortion to be added in order to obtain the desired curved surface shape. In the above prior art, the amount of strain to be added to the plate material depends on the method of developing the curved surface to the plane, but between the method of developing the curved surface to the plane and the method of forming the curved surface. There was no association. Even if a development diagram is drawn according to the above-described prior art and a required plate material is cut out, it is unclear where and how much strain should be applied to the flat plate material. In addition, since the numerical simulation is performed while the strain type and the quantity distribution are unknown, a huge amount of calculation time is required, and finally a rework by a skilled worker is required.

  In order to solve the above-described problems in the prior art, the present invention can provide a shape when a curved surface is developed into a flat surface, and can obtain a strain distribution required for forming the developed flat shape into a target curved surface. It is an object of the present invention to provide a calculation calculation method based on the above.

  The invention described in claim 1 for solving the above-mentioned problems is: a. A step of functionalizing a curved surface shape displayed by coordinates of discrete points, etc. b. On a curved surface functionalized by the above or other methods Process of drawing geodesic lines vertically and horizontally c. Change in distance on geodesic lines that satisfy the parallel condition on the plane, or change of shape on the curved surface of the area surrounded by four geodesic lines forming a square on the plane A process of calculating and calculating the distribution of the strain amount related to the formation of the non-developable surface necessary for forming the curved surface d. The curved surface by the non-deformable deformation obtained by giving the distribution of the strain amount obtained by the above processes to the flat plate material If there is a difference between the target curved surface shape and the target curved surface shape, the process of extracting the deformable deformation component causing the difference and calculating both the non-developable deformation and the deformable deformation is processed by a computer system. The target curved surface is a flat plate material characterized by A strain distribution calculation method of calculating required to molding.

  According to a second aspect of the present invention, the function of converting the curved surface shape displayed with discrete point coordinates or the like into a function assigns the curved surface shape as numeric data, and the numerical data can be decomposed into a plurality of steps with the required accuracy. The strain distribution calculation calculation method required for forming the flat plate material according to claim 1 into a target curved surface, which is functionalized by a network.

  According to a third aspect of the present invention, a geodesic line in an arbitrary direction starts from an arbitrary point on the approximate surface function that is functionalized by the neural network according to the second aspect or on the curved surface function given by another method. This is a flat plate material characterized by recording the trajectory at arbitrary intervals and recording the trajectory corresponding to the grid on the surface developed into a plane vertically and horizontally on the curved surface. This is a computer system for creating a geodesic curve for calculating a strain distribution calculation required to form a target curved surface.

  According to a fourth aspect of the present invention, the change in the distance between the geodesic curves on the curved surface corresponding to the parallel lines on the development map to the plane is obtained from the geodesic trajectory information by the geodesic line creation computer system according to the third aspect. From the change in the quadrilateral shape created by the distance between the intersections of the geodesic curves on the curved surface corresponding to two sets of four straight lines parallel to each other in the development on the plane A strain distribution calculation calculation method required for forming a flat plate material into a target curved surface, which calculates and calculates a distribution of strain amount related to non-deformable deformation necessary for forming.

  According to a fifth aspect of the present invention, there is provided a target curved surface obtained by decomposing a square having a point on the geodesic line as a vertex, which is used in the computer system for calculating and calculating the distribution of the distortion amount according to the fourth aspect, into elements having one unit. On the other hand, this is a computer system for simulation that determines the deformable deformation necessary to obtain the target curved surface shape by simulating the shape change when an arbitrary deformable deformation is applied.

  According to the present invention, since the amount of strain required to form an arbitrary curved surface shape from a flat plate material can be determined, there is no need to perform an operation that relies on intuition. Even if the amount of deformation is different from the planned amount, it is possible to repair by adding an amount of distortion required for correction by performing automatic shape measurement and obtaining the amount of distortion again from geodesic information.

  According to the second aspect of the present invention, the process of functionalizing the curved surface shape displayed with the coordinates of discrete points or the like is performed by a neural network that can be decomposed into a plurality of steps. The weight function is once obtained with a relatively coarse accuracy of about% to obtain a rough approximate expression, and then an error between the correct value and the approximate value is obtained, and a weight for approximating the error is obtained, for example, at 10%, and a sequential error is obtained. By obtaining an approximate expression for eliminating the above, a highly accurate approximate curved surface can be obtained in a short time.

  The curved surface formation can be automated by using a laser that can be easily controlled for adding strain as a linear heating means and combining it with an automatic shape measuring instrument. On the other hand, as a method of giving strain for forming a curved surface, either a method of giving only one direction of orthogonal strain or a method of giving strain in two directions can be selected. For the curved surface formation, it is advantageous in terms of efficiency to employ a working method that imparts a unidirectional strain that is easy to work. The present invention can also be applied to distortion removal work, and can correct an unnecessary curved surface (such as a bulge) to be flat. In this case, swelling and the like can be removed by simultaneously applying strain in two directions.

  When a flat plate material such as a steel plate is formed into a three-dimensional curved surface using the present invention, the size and distribution of non-deformable deformation to be given to the flat plate material can be determined on any curved surface based on information obtained by functionalizing the target curved surface shape. It is obtained from the rate of change of the distance between the geodesic lines and the distance between the intersections of the geodesic lines drawn using a program for generating geodesic lines. On the other hand, for the deformable deformation, a necessary deformable deformation component is obtained by using a simulation program for estimating a curved surface shape obtained by adding the deformable deformation to a deformation state in which only the non-developable deformation is applied to the flat plate material.

  The method of developing the curved surface according to the first aspect of the present invention into a plane is not only a curved surface given in the form of a function but also a curved surface given by discrete numerical data with the accuracy required for the curved surface function. The amount of distortion required for surface expansion can be calculated from the change in geodesic spacing and the distance between intersections of geodesic lines by freely drawing geodesic curves on the obtained function curved surface or the given function curved surface. Calculate the distribution. If the strain distribution obtained in the calculation calculation process is used in reverse, the flat plate material can be formed into a curved surface.

  In order to form a curved surface from a flat plate material, a deformable deformation is necessary in addition to a non-developable deformation. For this purpose, numerical analysis with a strain distribution is performed by a computer system for generating a geodesic curve and a computer system for calculating and calculating a strain distribution, or a shape having the minimum elastic energy is obtained by a computer system for simulation of developable deformation according to claim 5. Predict and determine the amount of deformable deformation that complements the difference from the target curved surface shape. When information on both the non-developable deformation and the developable deformation is obtained, all the distortion amounts necessary for the deformation are determined.

  In the present invention, the process of functionalizing the curved surface shape displayed by the coordinates of discrete points and the like will be described. In this embodiment, the curved surface is functionalized using a neural network. A sigmoid function is used for a node (synapse) using this neural network. FIG. 1 shows a schematic diagram of one node. The sum of values obtained by multiplying the plurality of input values by the weight W is S.

  The function F shown in Formula 2 is a function called a sigmoid function, and a value obtained by multiplying the function value F by the weight W is an output to the next node. In this example network, there are two inputs, x and y, and the final output is one of z. FIG. 2 shows an example of a neural network. A circle in FIG. 2 represents one node, and B represents a constant input value called a bias. Also, there is a weight in the line segment connecting the nodes. When viewed from the input side, the first node group is called the input layer, the last node group is called the output layer, the group between them is called the hidden layer, and the number of nodes in each layer is called the number of nodes. The number of hidden layers depends on the complexity of the problem. The use of a neural network is to determine a weight value so that a target output value can be obtained for an appropriate input value. In this embodiment, the back propagation method is used.

  The prediction error of the neural network is defined by the following equation.

  The subscript k in Equation 3 is a data number, t is a true value, and n is a value predicted by the network. Since the unknown in the error E is only the weight, the weight that minimizes E can be searched. A method of determining the weight correction amount from the error change amount with respect to the weight change amount and repeatedly correcting until the error converges is called a back propagation method.

  Next, a specific example is shown. A bias was used for a torus with a small radius of 10 and a large radius of 20, with a hidden layer of 1 and the number of nodes of 11. Since the sigmoid function region ranges from 0 to 1,

Was used to convert z domain 24.74 <z <30 into domain 0.05 <O ₁ <0.95. The input value (x, y) is

  The area was limited using the, and learning was performed. For learning, in the range of −8 <x <8, −8 <y <8, a total of 81 on the lattice points with an interval of (−8, 8) starting from (−8, 8) and 2 in the x positive direction and 2 in the y positive direction. The point (x, y, z) was used as teacher data. Table 1 shows the weights obtained when the convergence error was set to 3%. The teacher data is shown in Table 2.

  In Table 1, i = 0 is a weight between the input layer and the hidden layer, i = 1 is a weight between the hidden layer and the output layer, j = 1 is a weight corresponding to the input x, and j = 2 is corresponding to the input y. It is a weight, and j = 0 is a bias value. k is the node number of the hidden layer.

  Becomes an approximate value of z.

Next, the process of drawing a geodesic curve on a functionalized curved surface will be described. FIG. 3 shows the geodesic start point. First, as shown in FIG. 3, the starting point is determined as a point S (x, y) on the xy plane. This neural network (x, y) be given the coordinates can be easily know the z-coordinate, which is the starting point of the geodesic a _point G. Point D is the end point of vector SD indicating the direction in which the geodesic line is drawn on the xy plane. Points S ₁ and S ₂ are determined at equal distances across a point S on a straight line on the xy plane perpendicular to SD. A z-coordinate on the curved surface P corresponding to the x and y coordinates of the points S ₁ and S ₂ is obtained using a neural network, and points h ₁ and f ₁ on the curved surface are determined.

Let C ₁ and C ₂ be circles of the same radius that are in a plane perpendicular to the line segment h ₁ f ₁ and have their centers at points h ₁ and f ₁ , respectively. Of the intersections of the circles C ₁ and C ₂ and the curved surface P, the points on the geodesic traveling direction side are defined as h ₂ and f ₂ . Furthermore, among the intersection points of the circle C _1, C ₂ and circle C ₁ at the same _size, a circle centered at point G ₁ in a plane parallel to the C ₂ and the curved surface P, and the point in the traveling direction side of the geodesic and G _2. When the operations previously performed on the line segment h ₁ f ₁ and the point G ₁ are performed on the line segment h ₂ f ₂ and the point G ₂ , the G point is sequentially obtained and its coordinates are recorded. (X, y, z) coordinates obtained by dividing points on the geodesic line at equal intervals can be obtained as discrete coordinates of the geodesic line.

FIG. 4 shows a geodesic start portion perpendicular to the geodesic start point shown in FIG. Once a geodesic line has been drawn as a continuous G point as shown in FIG. 4, the operations previously performed on the line segment h ₁ f ₁ and the point G ₁ are as shown in FIG. Then, it is performed on the line segment G ₁ G ₃ and the point G ₂ , and the point N ₂ is obtained and the N point is repeatedly obtained. When the point N ₂ intersects the previous geodesic line at the point G ₂ (x , Y, z) coordinates can be obtained as discrete coordinates.

  Next, the non-necessity necessary for the curved surface formation from the change in the distance on the geodesic line that satisfies the parallel condition or the change in the shape on the curved surface of the area surrounded by the four geodesic lines forming the square on the plane. A process of calculating and calculating the distribution of the strain amount related to the development of the surface will be described. 5 and 6 show a basic concept of a method of developing a curved surface into a plane. As shown in FIG. 5, an arbitrary geodesic line OB is drawn on the curved surface P, and a geodesic line OA that intersects the geodesic line OB perpendicularly at the point O is drawn. Further, a geodesic line BC perpendicular to the geodesic line OB is drawn at the point B, and a geodesic line AC perpendicular to the geodesic line OA is drawn at the point A. Geodesic line AC and geodesic line BC intersect at point C but do not necessarily intersect perpendicularly.

  FIG. 6 is a diagram when the curved surface shown in FIG. 5 is developed into a plane. O′A ′ in FIG. 6 is obtained by developing the geodesic line OA in FIG. 5 on the plane P ′. Geodesic lines can be developed as straight lines on a plane, and O'A 'is a straight line. This is a locus of contact formed when the plane P ′ is arranged on the curved surface P so as to be in contact with the geodesic line OA and the contact is moved from the point O to the point A. Since geodesic line OA and geodesic line OB intersect perpendicularly at point O, when drawing development line O'B 'of geodesic line OB on plane P', O'A 'and O'B' in the vicinity of point O ' Is vertical and O′B ′ is developed into a straight line, so that O′A ′ and O′B ′ become straight lines that intersect perpendicularly to each other. B′C ″, which is a developed view of the geodesic line BC, is a straight line that intersects the straight line O′B ′ perpendicularly for the same reason. Since O′A ′ is a line copied on OA by a method in which plane P ′ is in contact with curved surface P, the road on OA is copied on O′A ′ as an actual size without expansion and contraction. The road on OB is also moved to O'B 'as actual size.

  A'C 'is a straight line obtained by developing the geodesic line AC on the plane P', and intersects the straight line O'A 'perpendicularly at the point A'. The path of the geodesic line AC in FIG. 5 is moved to the straight line A′C ′ in FIG. 6, and that point is defined as C ′. B′C ″ is a straight line obtained by developing the geodesic line BC on the plane P ′, and intersects the straight line O′B ′ perpendicularly at the point B ′. The path of the geodesic line BC in FIG. 5 is moved to the straight line B′C ″ in FIG. 6, and that point is designated as C ″. When the point C ′ and the point C ″ are the same point, the length of the four sides of the OACB on the curved surface P is the same side as the rectangle O′A′C ′ ″ B ′ on the plane P ′. At this time, there is no distortion anywhere, and only the deformable deformation.

  In the case of non-developable deformation, the length of the path on the curved surface P is changed, so that the point C ′ and the point C ″ are not at the same position. A point where the same path as the geodesic line OA in FIG. 5 is taken from the point B on the geodesic line BC is defined as C ′ ″ ″. At this time, on the curved surface P, the path of the geodesic line starting from the point A and passing through the point C ′ ″ ″ and the amount of change of the geodesic line OB become distortion in the OB direction during this period. When this strain is applied to the plane P ′ shown in FIG. 2, only the strain in the O′B ′ direction is applied, so that the length in the O′A ′ direction does not change before and after the deformation, and the plane P ′. The upper point C ′ ″ appears at C ″ ″ on the curved surface P. In addition, the change rate of the length O′A ′ and the length B′C ″ in FIG. 6 is the strain in the O′A ′ direction, and the change rate of the length O′B ′ and the length A′C ′ is A distortion in the direction of the straight line O′B ′ is given. When the two orthogonal directions of strain are simultaneously applied to the plane P ′, the rectangle O′A′C ′ ″ B ′ on the plane P ′ is moved to the OACB on the curved surface P, and the point C ′ on the plane P ′. '' Can be moved to a point C on the curved surface P.

  FIG. 7 shows a specific method for developing non-developable deformation only by vertical strain in one direction. Let P be a curved surface functionalized by a neural network or the like. A reference geodesic curve is drawn on the curved surface P. This geodesic curve is shown as QM in FIG. This geodesic line is called a trunk line in the present invention. A plurality of points are arranged on the main line at known intervals. The intervals between these points need not be the same as long as they are known, but are easier to process if they are aligned. Two of these points are Q and M shown in FIG. A geodesic line that passes through the point Q and intersects the geodesic line QM perpendicularly is defined as QN. A geodesic line passing through the point M and perpendicular to the geodesic line QM is defined as ML. Geodesic lines that intersect perpendicularly with these trunk lines are called branch lines in the present invention. On these two branch lines, points on the same road from the main line are denoted as N and L, respectively. The rate of change of the road QM and the road NL is the distortion at the position of the point N or the point L. If the road QM is set sufficiently smaller than the size of the curved surface P, the distance QM and the road NL can be substituted by the distance QM and the distance NL. The trunk line and the branch line can be drawn on the curved surface P by the geodesic line creation computer system of the present invention, and the strain distribution can be obtained by the strain distribution calculation calculation method of the present invention. FIG. 8 is a development view of the curved surface shown in FIG.

  FIG. 9 shows a specific method for developing non-deformable deformation by applying vertical strain in two directions to a plate material. In this case, it is necessary to draw a pair of two trunk lines orthogonal to the curved surface P, which is OG and OE in FIG. This operation is performed by the geodesic line creation computer system of the present invention. Further, branch lines are drawn on the curved surface P at known intervals for each trunk line. Two branch lines on each trunk line are selected and indicated by GK, FH, DJ, and EK in FIG. When the distance GF and the distance ED are considered to be minute, the distortion in two directions at an arbitrary position in the curved surface P can be obtained from the change rate of the distance GF and the distance KH and the change rate of the distance ED and the distance KJ. It is also possible to determine the shear strain from the shape change of the quadrangle KHIJ. The strain distribution can be obtained by the strain distribution calculation calculation method of the present invention. FIG. 10 is a development view of the curved surface shown in FIG.

  The strain distribution calculation calculation method required for forming the flat plate material of the present invention into the target curved surface can not only obtain the strain distribution amount required to obtain the target curved surface shape, but also can be obtained from the existing curved surface shape measurement data. The amount of distortion to be obtained can also be obtained. Therefore, when a problem occurs in the curved surface forming process and the target curved surface shape cannot be obtained, the strain amount to be added can be obtained from the difference between the target strain amount and the current strain amount.

  FIG. 11 shows calculation processing steps by a computer system when a strain distribution calculation calculation method required for forming the flat plate material of the present invention into a target curved surface is performed. The process from S1 to S5 is the first step. Step S1 is performed by the curved surface functionalization program using the neural network of the present invention. Step S2 is performed by the geodesic line creation computer system of the present invention. Step S3 is performed by the computer system for calculation of strain amount distribution of the present invention. Steps S4 and S5 are performed by the computer system for the deformable deformation simulation of the present invention described later. When the flat plate material is formed into a curved surface, an implementation process may be performed in step S6, or a preliminary experiment may be performed by numerical simulation. In step S7, the shape is inspected, and if the target curved surface shape is obtained, the processing step is terminated. If the error is large, the distortion amount in the curved surface shape after deformation is calculated, and an excess of the target distortion amount is calculated. The shortage will be added. A thick frame portion in FIG. 11 is a portion executed by the computer system of the present invention.

  In the present invention, even when the same curved surface shape is obtained, the amount of distortion to be given differs depending on how the trunk line position is selected. This is convenient when the processing method is limited. In the case of a processing method such as linear heating, it is difficult to give a tensile strain, and in the case of forging, it is difficult to give a compressive strain. If the portion where the greatest tensile strain is required is selected as the main line from the strain distribution obtained in advance in the region where the flat plate material is formed into a curved surface shape, the processing procedure can be determined under the condition of compressive strain. Conversely, if the portion where the greatest compressive strain is required is selected as the trunk line, the processing procedure can be determined under the conditions of all tensile strains. This is because the distortion is always zero at the main line.

Next, a method for simulating a shape change when a deformable deformation is added to a flat plate material together with a non-developable deformation in order to obtain a target curved surface in the present invention will be described. FIG. 12 shows elements of a region surrounded by four points on a curved surface indicating a geodesic line. In FIG. 12, focusing on one point where four elements share a vertex, only these four elements will be considered first. Let O be the point shared by the four elements. As shown in FIG. 12, the angles θ ₁ to θ ₄ are named. At this time, the angle between the surfaces between the elements has a dependency relationship except when the sum of the apex angles of the adjacent elements is 180 °. First, this relationship is derived.

FIG. 13 shows the relationship between elements that share the point O and are adjacent to each other. In FIG. 13, φ ₁₂ is an angle between elements 1 and 2, and θ ₁ and θ ₂ are apex angles. I is a point at a distance of 1 from the point O on the intersection line of the elements 1 and 2. As shown in FIG. 13, let J and K be points where a perpendicular drawn to the intersection line of element 1 and element 2 passing through point I intersects with the other sides of element 1 and element 2. For the triangle IJK and the triangle OJK, applying the cosine theorem on the side JK,

Than

Get. Since ψ ₁₂ = ψ ₃₄ ψ ₄₁ = ψ ₂₃ , the relationship between the inter-plane angles φ ₁₂ and φ ₃₄ and φ ₄₁ and φ ₂₃ are

Can be obtained as follows. Therefore, then, if Shimese the relationship interplanar angle phi ₁₂ and phi _41, so that the derived all the relationship of these four faces between the angle.

FIG. 14 shows the relationship between the inter-surface angles between elements. As shown in FIG. 14, a point G is placed at a distance 1 from the point O on the intersection line of the elements 1 and 2. A point H is set at a distance 1 from the point O on the intersection line of the elements 3 and 4. When the angle GOH is set to ψ ₄₁ = ψ ₂₃ and attention is paid to the triangle GOH, the cosine theorem

Next, consider a square CBOA on the plane AOE. FIG. 15 shows a square CBOA on the plane AOE. In FIG. 15, since the intersection of the perpendiculars drawn from the point G to the plane AOE is C and the perpendicular drawn from C to OA is CA, the plane GCA is a plane perpendicular to both the plane AOB and the plane GOA. Accordingly, the straight line GA intersects the straight line OA perpendicularly. FIG. 16 shows how to obtain the length OC. As shown in FIG. 16, when applying the x-y coordinates, the coordinates of the point B is _{(cosθ 2 · cosψ 12, cosθ} 2 · sinψ 12). The equation for the straight line OB is

  The formula for the straight line BC is

  When the coordinates of the intersection are obtained,

It becomes.

Is required. Also,

  further,

The coordinates of point F are

In summary, the interplanar angle phi ₁₂ and phi _34, relationship phi ₁₂ and phi ₃₄ in relation to phi ₄₁ and phi ₂₃ are

the relationship of φ ₄₁ and φ ₂₃ is,

It is. the relationship of φ ₁₂ and φ ₄₁ is,

And

Φ ₁₂ and φ ₄₁ from are related. From the above relationship, the dependency relationship of the angle between the quadrangular elements is expressed, so that it is possible to know the deformation of the entire curved surface when the surface angle at one location is changed. Since the deformable deformation is a deformation that changes only the curvature of the curved surface, software that changes only the angle between the surfaces without changing the dimensional shape of the quadrilateral element is convenient.

  FIG. 18 shows a shape called a torus. Centering on this (x, y, z) = (0, 0, 30), a curved surface in a range of −8 <x <8 and −8 <y <8 is set as an object with an interval of 1 on the xy plane. FIG. 19 shows a result obtained by reading discrete data obtained by obtaining z coordinates at lattice points into a computer system that functions by a neural network and approximating a curved surface. The solid line is the theoretical surface, and the plotted points are the points on the approximate surface. Although the result is when the convergence accuracy is 0.3%, they are in good agreement. For a curved surface in the range of −5 <x <5 and −5 <y <5 shown in FIG. 18, the amount of strain required for forming the curved surface is obtained, and the deformation is simulated by a finite element method (FEM). The result of examining the shape of the cut surface in the z plane and the yz plane is shown in FIG. The target shapes are curvature radii R = 10 and R = 30, respectively. As is clear from FIG. 20, they are in good agreement.

  It can be used to create curved surface processing procedures for ships, aircraft, trains, etc., and to determine the method of distortion removal work.

Schematic diagram showing one node (synapse) in a neural network Diagram showing an example of a neural network Diagram showing geodesic starting point Diagram showing the geodesic start portion in a direction perpendicular to the geodesic start portion shown in FIG. Schematic diagram showing the concept of how to draw geodesic lines The top view which shows the state when the curved surface shown in FIG. Schematic diagram showing the method of determining distortion and the geodesic pattern drawn at that time when the distortion necessary for curved surface formation is represented only by vertical distortion in one direction The top view which shows the state when the curved surface shown in FIG. Schematic diagram showing the method of determining the amount of strain when the strain required for curved surface formation is represented by two vertical strain components perpendicular to each other and shear strain, and the geodesic pattern drawn at that time The top view which shows the state when the curved surface shown in FIG. 9 is developed on a plane A flowchart showing a processing process when the present invention is used for feedback. Diagram showing the elements of the area surrounded by four points on the curved surface showing the geodesic line Diagram showing the relationship between adjacent elements sharing point O Diagram showing the relationship between the face angles between elements Diagram showing square CBOA on plane AOE FIG. 15 is a diagram showing a method for obtaining the distance between OCs in FIG. Diagram showing a method for obtaining the distance between CFs in FIG. Diagram showing a shape called a torus FIG. 18 is a graph showing a result when a curved surface is approximated by a neural network from discrete numerical information of the curved surface of the torus shown in FIG. The graph which shows the result of having simulated the amount of distortion required for curved-surface formation calculated | required by this invention by the finite element method, and having investigated the cross-sectional shape in the cut surface in a xz plane and a yz plane

Claims (5)

a. a process of functionalizing the curved surface shape displayed by the coordinates of discrete points, etc. b. a process of drawing geodesic lines vertically and horizontally on the curved surface functionalized by the above or other methods c. a parallel condition on a plane The amount of distortion related to non-developable surface formation required for curved surface formation from the change in the interval on the geodesic line or the change in shape on the curved surface of the area surrounded by four geodesic lines forming a square on the plane D. Calculating and calculating the distribution of d. If there is a difference between the curved surface due to non-deformable deformation obtained by applying the strain distribution obtained by the above process to the flat plate and the target curved surface shape, the difference Of strain distribution required to form a flat plate material into a target curved surface, which is a computer system that processes the process of calculating both non-deformable deformation and deformable deformation by extracting the deformable deformation components Calculation method.   The process of functionalizing the curved surface shape displayed by the coordinates of discrete points, etc. is to assign the curved surface shape as numerical data, and to convert the numerical data into a function by a neural network that can be decomposed into a plurality of steps with the required accuracy. A strain distribution calculation calculation method required for forming the flat plate material according to item 1 into a target curved surface.   A geodesic line is drawn in an arbitrary direction starting from an arbitrary point on an approximate curved surface functionalized by the neural network according to claim 2 or a curved surface function expressed in the form of z = f (xy). A flat plate material characterized in that the geodesic trajectory is recorded at intervals of and the geodesic line corresponding to the grid on the plane developed into a plane is drawn vertically and horizontally on the curved surface and the trajectory is recorded. A geodesic computer system for calculating the strain distribution required for forming a target curved surface.   From the geodesic trajectory information by the calculation calculation computer system for geodesic line creation according to claim 3, the change in the distance between the geodesic curves on the curved surface corresponding to the parallel lines on the development view to the plane is converted into distortion, or The non-development necessary for curved surface formation from the change in the square shape created by the distance between the intersections of the geodesic curves on the curved surface corresponding to two sets of four orthogonal straight lines parallel to each other on the development to the plane and the line connecting the intersections A strain distribution calculation method required for forming a flat plate material into a target curved surface, which calculates and calculates a distribution of strain amount related to deformation. 5. An arbitrary deformable deformation is added to the target curved surface that is decomposed into elements each having a square having a point on the geodesic line as a vertex used in the computer system for calculating and calculating the strain distribution according to claim 4. A computer system for simulation of deformable deformation that determines the deformable deformation necessary to obtain the target curved surface shape by simulating the shape change in the case of the deformation.

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