WO2004109559A2 - Procede de simulation d'une liaison d'assemblage - Google Patents

Procede de simulation d'une liaison d'assemblage Download PDF

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Publication number
WO2004109559A2
WO2004109559A2 PCT/EP2004/005776 EP2004005776W WO2004109559A2 WO 2004109559 A2 WO2004109559 A2 WO 2004109559A2 EP 2004005776 W EP2004005776 W EP 2004005776W WO 2004109559 A2 WO2004109559 A2 WO 2004109559A2
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layer
point
finite element
elements
finite
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German (de)
English (en)
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WO2004109559A3 (fr
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Christophe Ageorges
Reiner Jost
Matthias Martin
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Mercedes Benz Group AG
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DaimlerChrysler AG
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    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]

Definitions

  • the invention relates to a method for automatically establishing an equation system for describing a physical behavior of a given system according to the finite element method.
  • finite elements The method of finite elements is from "Dubbel - Taschenbuch für den Maschinenbau", 20th edition, Springer-Verlag, 2001, C 48 to C 50, and from TR Chandrupalta & AD Documentation: "Introduction to Finite Element in Engineering” , Prentice-Hall, 1991.
  • strength tasks of all kinds e.g. B. for stress distribution or stability
  • numerically solved For example, it is determined how a system of rigid bodies deforms and bends under external loads and how the bodies move relative to one another.
  • Finite elements are the surface or solid elements that are formed with the help of the nodes as their corners. Curved surfaces or bodies, which are approximately as Surfaces treated, eg sheet metal of a body of a motor vehicle, are often broken down into shell elements.
  • the nodes form a network in the construction, which is why the process of defining nodes and creating finite elements is called "meshing" of the construction.
  • the displacements of these nodes are Te and / or rotations of the finite elements in these nodes or the stresses in these finite elements are introduced as unknowns. Equations are set up that describe the displacements, rotations or stresses within a finite element approximately. Further equations result from dependencies between different finite elements, e.g. B. from the fact that the principle of virtual work in the nodes must be fulfilled and the calculated displacements must be constant and must meet the boundary condition that in reality there are no gaps or penetrations.
  • Different bodies in the construction of a system are often networked independently of one another.
  • the system is part of the body of a motor vehicle to be constructed, and the bodies are subsystems that are constructed in parallel by different suppliers without the networks being adapted to one another.
  • the bodies are networked independently of one another, the nodes on adjoining surfaces of the bodies often do not lie on one another, but are e.g. B. shifted against each other or belong to finite elements of different sizes and different orientations in space.
  • Such cross-links of adjoining bodies are referred to as incompatible cross-links.
  • a realistic finite element simulation must take into account the interactions and dependencies between different bodies, which are caused by the adjacent surfaces. In the case of a system with a body and a layer, the interactions and dependencies between the body and layer must be taken into account. Finite element simulations are desired that take these interactions and dependencies into account even with independent and therefore generally incompatible networking of body and layer. Because if a compatible network were necessary for the establishment of the system of equations and the implementation of the simulations, the bodies could not be networked independently of each other.
  • a method for finite element simulation of an adhesive connection is known from G. Tokar: "Spot welding adhesive - properties and calculation method for linear body stiffness", VDI reports No. 1559, pp. 549-575, 2000.
  • the system comprises two bodies and a layer that connects the two bodies.
  • the two bodies are two sheets that are connected by a layer in the form of an adhesive seam. Due to external loads, shifts between the sheets and deformations of the two sheets occur.
  • the sheets are approximately represented by areas in the middle of the sheet.
  • a number of shell elements are created in the sheet center plane.
  • the displacements of the nodes of these shell elements act as unknowns in a finite element simulation.
  • the networks of the two sheets can have been created independently of each other, a compatible network is not required.
  • a so-called interpolation surface is created on the surface of each sheet that faces the adhesive seam.
  • the adhesive seam is limited in the construction by these interpolation surfaces and also in finite Disassembled elements with nodes.
  • nodes of the shell elements are mapped onto the interpolation surface and interpolations are carried out in the interpolation surface.
  • the invention has for its object to provide a method by which an equation system for a realistic finite element simulation is automatically generated such that the set-up and the numerical solution of the equation system are associated with less computational effort than when using known methods.
  • the simulation should relate to a system that includes a body and an adjacent layer.
  • the automatically generated system of equations refers to nodes of a construction that includes a body and an adjacent layer. Finite elements for the body are created.
  • the layer is automatically broken down into volume elements, using geometric information about the layer and specifications for networking the layer become.
  • For at least one node that belongs to a volume element of the layer a finite element of the body lying next to the node and a closest point on this finite element are determined.
  • a function for a physical relationship between the value that the physical quantity takes on the closest point and the values that this value takes on the nodes of the closest finite element is generated.
  • the physical quantity is, for example, a mechanical, kinematic, electrical or thermodynamic quantity. Their values can be scalars or vectors.
  • the value of the physical quantity in a point is: the spatial displacement of the point in a three-dimensional coordinate system, the rotation angle in the point of the finite element to which the point belongs in a three-dimensional coordinate system and the temperature in the point.
  • the physical behavior of the layer can only be predicted realistically if the physical dependencies and interactions between the body and the adjacent layer are taken into account.
  • such points in finite elements of the body are determined as further points which are closest to the nodes of finite elements of the layer. Between nodes of the layer and the nearest points of the finite elements of the body there are physical, e.g. B. mechanical, kinematic or electrical, dependencies.
  • the node for which the closest finite element and the closest point are determined can lie both on a boundary surface and inside the layer.
  • the boundary surfaces can be flat or curved surfaces. They can be parallel to one another or inclined relative to one another.
  • the invention shows a way to adequately take into account the dependencies between body and layer, without additional degrees of freedom occurring and thereby increasing the system of equations due to additional unknowns. Thanks to the invention, no additional unknowns occur. By taking additional unknowns into account, the usually very extensive system of equations would be even larger.
  • a function for a physical relationship is generated between the value that the physical quantity assumes in the closest point and the values that this dimension assumes in the nodes of the closest finite element. This function expresses the physical relationship with sufficient accuracy. In all generated equations, the value of the physical quantity in the closest point is given by the Function replaced.
  • the unknowns that result from the degrees of freedom of the closest point do not appear in the system of equations, but are calculated after the system of equations has been solved using the function for the physical relationship.
  • An example of such an equation, in which the function is used, is an equation that results from a dependency described above between node points of the layer and the closest points of the body and which is taken into account in the simulation.
  • the advantage that unknowns are saved in the equation system is particularly evident in the case of extensive systems, e.g. B. part of a body of a motor vehicle, weight.
  • the equation system then often includes hundreds of thousands or even millions of unknowns. Its solution requires considerable computing capacity and computing time.
  • the advantage is even more significant if the system of equations is changed during the construction of the system and therefore has to be solved and evaluated several times. This is e.g. B. necessary if different possible constructions of a technical system are to be compared or if different design levels are run through and a finite element simulation is carried out for each variant or each design status and the physical behavior of the variant or the design status is to be predicted.
  • the advantage of the unknowns saved is particularly significant when deformations and / or tensions in the technical system occur under a external stress should be predicted.
  • discretization of the time axis defines many points in time or time intervals. An unknown is generated for each node and each of these times, namely the value of the physical quantity at this node and at this time. If, for example, the discretization delivers 1000 points in time, the method according to the invention saves N * 1000 unknowns in a single application, where N is the number of degrees of freedom of the entire system.
  • the advantage of the saved nodes is particularly significant if the system of equations comprises nonlinear equations and is therefore solved approximately, namely iteratively by solving a linear system of equations several times. Often, several dozen iterations, in each of which a linear system of equations is solved, are required to determine a sufficiently accurate approximation solution for a nonlinear system of equations. Thanks to the invention, unknowns are saved for each iteration step.
  • the method according to the invention can also be used if the body and the adjacent layer are crosslinked independently of one another and therefore have incompatible crosslinks. Therefore, the body and the layer can be constructed in parallel, e.g. B. from different agents who do not have to coordinate the networking. Because parallel design and parallel networking are made possible and no coordination about the networking is required, time is saved and a simultaneous product design is made possible.
  • the method can be used for a construction with a body and an adjacent layer, e.g. B. use a sheet with a layer of paint. It can also be applied to a construction with two bodies and a layer connecting the bodies, e.g. B. apply an adhesive surface or adhesive seam or insulating layer. It is possible to network the bodies independently of one another and, first of all, Perform simulations for each body independently of other bodies. For the finite element simulation according to the invention of the entire construction, the networks of the individual bodies that have been generated once can be reused.
  • the method according to the invention does not require a compatible crosslinking of the body and the adjacent or connecting layer.
  • the generation of the nodes for the layer does not depend on the networking of the bodies and can therefore be adapted well to the particular task that is to be dealt with by means of the solution of the system of equations generated according to the invention.
  • the adjacent or connecting layer is broken down into many small or a few large finite elements.
  • the thickness of the layer is taken into account - even if the layer has different thicknesses at different points.
  • the layer is treated mechanically in the system of equations.
  • mechanical parameters of the layer can be taken into account in equations of the system of equations. Is the layer z.
  • B. an adhesive seam mechanical parameters of the adhesive used can be taken into account.
  • the mechanical behavior of the connecting layer in the case of displacements of the body relative to the adjacent layer or in the case of relative displacements of two bodies which are connected by the layer can be predicted.
  • Another advantage of the method is that it is not necessary to set up a replacement model. Setting up and validating a replacement model requires working time and is prone to errors. The advantage of doing without a replacement model is particularly significant when different constructions of a technical system are to be compared using the finite element method.
  • volume elements for the layer are generated automatically. Because the layer is broken down into volume elements, a continuum-mechanical behavior of the layer can be predicted by solving the system of equations and the solution is analyzed. The complete layer is included in the system of equations. Only by including the entire layer is it possible to carry out at least one or more of the following calculations for the construction of the system: geometric displacements due to external loads,
  • Direction and speed of a three-dimensional flow e.g. B. an electrical flow, that of a liquid or a gas.
  • the values of the corresponding physical quantity in the nodes are determined by numerically solving the system of equations.
  • the value of the size in the at least one node is determined by inserting the values in the nodes into the function for the connection.
  • the solution is evaluated using known methods to predict the mechanical behavior sought.
  • volume elements For practical applications, e.g. B. for more complex subsystems of a motor vehicle, it is not possible in a reasonable time to generate volume elements by hand in such a way that simulations based on these volume elements are realistic Lead results. This applies in particular if the networking with volume elements has to be carried out several times, e.g. B. with volume elements of different edge lengths for different physical sizes.
  • the invention shows a way of networking the layer with volume elements automatically, quickly, systematically, comprehensibly and in a short time.
  • volume elements are generated that are perpendicular to the layer thickness, i.e. perpendicular to the boundary surfaces of the layer, an edge length of 0 , 4 mm.
  • the networking of the layer is controlled by a few, clear parameters. These parameters can be selected so that networking provides the best results for the respective task.
  • the volume elements are preferably cuboids, but other shapes of volume elements are also possible.
  • the method according to the invention is preferably carried out for each node of the layer which lies on that boundary surface of the layer which is adjacent to the body (claim 2).
  • This allows mechanical dependencies between the nodes on the adjacent boundary surface of the layer and the closest points of the body to be taken into account when setting up the system of equations, without generating additional unknowns.
  • the mechanical behavior in the transition area between layer and body has to be taken into account.
  • the method steps according to the invention are carried out for each node on the adjacent boundary surface of the layer, in particular the determination of the nearest finite element and the closest point on this finite element, the generation of the function and the replacement of the value in the determined point by means of the function.
  • equations for mechanical relationships between nodes of the layer and determined points of the body are preferably generated, and mechanical dependencies between layer and body are thereby taken into account in an advantageous manner (claim 3).
  • finite elements of the form "RBE2" are used. These dependencies often result from kinematic interactions that can be described by a linear approximation.
  • the method according to the invention delivers particularly realistic results because by determining the points in the body, the effects, which the layer exerts on the body are taken into account, without additional unknowns being generated and used.
  • the body is approximated by a surface in the simulation.
  • the approximating surface is preferably its central surface.
  • Surface elements are created as finite elements of the surfaces. The surface and the surface elements replace the body and the finite elements of the body in the networking and simulation.
  • finite elements in surfaces generally have fewer nodes than finite elements in bodies, this configuration saves further unknowns. This creates systems of equations with fewer unknowns, which can be generated more quickly and with less required computing capacity and which can be solved numerically.
  • At least one of the following requirements is used for the automatic decomposition of the adjacent layer into volume elements - it is possible that several requirements are combined:
  • volume elements e.g. B. cuboids, hexahedra or pentagons.
  • the projection is specified as the default, the finite elements of the body are projected onto the boundary surface of the layer adjacent to the body.
  • the boundary surfaces of the volume elements are specified by the projection.
  • the crosslinking of the layer is generally not compatible with the crosslinking of the other body.
  • the adjacent view is a lacquer layer
  • the layer is a zinc coating, which is applied to a sheet as the body, or an organic coating, e.g. B. with polymers that protect the body against corrosion, or a heat or cold insulation or a layer that protects against moisture.
  • an organic coating e.g. B. with polymers that protect the body against corrosion, or a heat or cold insulation or a layer that protects against moisture.
  • adjacent layer comprises a layer that isolates the body from the surroundings of the system, for example a lacquer layer on a sheet metal or an insulating layer on a cable.
  • adjacent layer is also understood to mean a layer, which is between two bodies of the system and is adjacent to both bodies. The layer has the function, for example, of connecting the two bodies or a minimum distance between the bodies. to create or dampen collisions between the bodies Examples of such a layer are an adhesive bond between a sheet and a plastic part, an insulating layer between two cables and a rubber seal between two sheets.
  • the method according to the invention is carried out for each node of the layer which lies on a boundary surface of the layer (claim 15).
  • the layer is broken down into volume elements.
  • the following process steps are carried out: the determination of the closest finite element and the closest point, the generation of the function for the connection and the elimination of the value in the determined point.
  • the body that is adjacent to the boundary surface is determined as the closer body.
  • the method steps according to the invention are carried out for each node on a boundary surface of the layer, in particular the determination of the nearest finite element and the closest point on this finite element, the generation of the function and the replacement of the value in the determined point by means of the function.
  • the embodiment according to claim 15 shows a way to generate an equation system for a construction with two bodies and an adhesive connection between them, without generating additional unknowns and thereby increasing the system of equations.
  • the adhesive bond is treated as a continuum and is not approximately replaced by individual adhesive points.
  • mechanical parameters of the adhesive connection and acting forces e.g. B. by clamping in a clamping device during production to be predetermined.
  • the bodies need not yet have been physically produced, so the prediction can be made at an early stage in product development.
  • the layer that connects the two bodies is z. B. an adhesive connection.
  • Adhesive connections are e.g. B. increasingly used in automotive engineering because a welded connection is not technically feasible, the surfaces to be connected are difficult to access for welders or welding machines or because the welded connection cannot withstand the loads and forces that occur.
  • a welded joint in particular, is often not possible or uneconomical if the two bodies are made of different materials, e.g. As aluminum and steel or aluminum and magnesium, or if at least one of the boundary surfaces of the body is made of plastic.
  • the equation system generated according to the invention is preferably solved numerically (claim 17). As a result, at least approximately the values are determined which the physical size assumes in the nodes of the construction. Further calculations are then preferably carried out in order to determine the mechanical behavior of the system. If, for example, the value of the physical quantity in a point is the displacement of the point, the displacements of all nodes are determined by solving the system of equations. For each finite element, the stress or stress tensor to which the finite element is exposed due to the displacements is then determined depending on the displacements of its nodes. The stress tensor is determined and evaluated with a predetermined criterion. For example, the maximum voltage is Finite elements are compared with a predetermined upper bound.
  • Fig. 3. the check for parallelism in the example of Fig. 2;
  • Fig. 5 bilinear interpolation in a quadrangular finite element with four nodes in one plane;
  • Fig. 7 bilinear interpolation in a triangular finite element.
  • the embodiment relates to a body of a motor vehicle as a technical system.
  • the body includes various sheets and other bodies.
  • the aim is to determine how the body deforms under a given load.
  • finite elements are generated.
  • the spatial displacements of all nodes due to the loads are sought.
  • These shifts are the unknowns of the system of equations to be generated.
  • Each node has six degrees of freedom. Six unknowns are generated per node, namely one unknown per degree of freedom:
  • Fig. 1 a section of this construction is shown.
  • This section comprises a sheet and a voluminous body K.I.
  • the sheet is approximated by a surface F.1 in the middle of the sheet, that is to say by a central surface.
  • the construction gives the thickness d_l of the sheet which is approximated by F.l.
  • the body K.l comprises a boundary surface F.6 pointing towards the sheet.
  • F.6 consists of the two partial areas F.6a and F.6b.
  • the distance between the surface F.l and the body K.l as well as the different orientations of the sheet and the body K.l in space are greatly exaggerated in FIG. 1 for clarification.
  • the sheet and the body Kl are connected by an adhesive connection.
  • this adhesive connection K 1 acts as the “adjacent layer”.
  • the construction to be examined includes the body K 1, the area F 1 and the Adhesive connection Kl.
  • This adhesive connection Kl covers only a part of the sheet and only a part of the body Kl and therefore only the partial area F.6a of the boundary surface F.6 of the body Kl.
  • the partial area F.6b lies on the boundary surface F.6 of the bordering area of the adhesive connection Kl Body Kl
  • the covered part of the sheet is represented by a partial area F.la of the approximating area Fl.
  • the adhesive connection Kl which connects the sheet and the body Kl, completely fills the space between the surfaces F.lb and F.6c.
  • a distance between the adhesive connection Kl and the body Kl is entered in FIG. 1.
  • F.6a and F.6c coincide in the design.
  • the area F.lb lies on the surface of the sheet adjacent to the adhesive connection Kl and not shown in FIG. 1 and thus also on a boundary surface of the adhesive connection Kl.
  • F.lb is parallel to F.6c, because an adhesive connection with two parallel boundary surfaces is easier to construct than one with non-parallel boundary surfaces.
  • the areas F.la and F.6a are approximately parallel.
  • the distance between F.la and F.lb is 0.5 * d_l (half the thickness of the sheet).
  • the two surfaces F.lb and F.6a and the adhesive connection Kl are networked independently of one another and broken down into finite elements.
  • the networks can be incompatible with each other.
  • the two surfaces F.lb and F.6a are broken down into surface elements, the adhesive connection Kl into volume elements, e.g. B. Hexahedron.
  • Networking of the adhesive connection Kl is carried out automatically.
  • the following information is taken from the computer-available design of the system: the spatial position of the two surfaces Fl and F.6 and the thickness of the sheet, which is approximated by the area Fl - in this example, the sheet has a constant thickness over the entire extent , but a variable thickness is also possible.
  • the thickness of the adhesive bond Kl is 0.8 mm.
  • the thickness and the spatial extent of the overlap area of Fl and F.6 and thus of the adhesive connection Kl are automatically obtained from this geometric information about the surfaces. It is also possible to specify the two delimiting partial areas F.lb and F.6b instead.
  • the following predetermined parameters are also used for networking the adhesive connection Kl: a lower and / or upper limit for the edge length of a volume element of the adhesive connection Kl parallel to the boundary surface of the adhesive connection Kl, the geometric shape of the volume elements, eg. As cuboids, hexahedra or pentagons, the number of finite elements perpendicular to the thickness of the adhesive bond Kl, a crosslinking process, for. B. "paving” or “free messing", the finite elements of the body are projected onto the boundary surface of the layer adjacent to the body.
  • the boundary surfaces of the volume elements are predetermined by the projection and the geometric shape of the volume elements, eg. B. cuboids, hexahedra or pentagons.
  • the finite elements of the surface F1 onto the boundary surface F.lb of the adhesive connection Kl adjacent to the sheet.
  • the boundary surfaces of the volume elements of the adhesive bond Kl are predetermined.
  • the networking of the area Fl and thus that of the adhesive The connection Kl is generally not compatible with the networking of the surface F1.
  • All volume elements preferably have the shape of cuboids or at least hexahedra.
  • B. also finite elements in the form of pentagons.
  • the number of volume elements perpendicular to the thickness of the adhesive bond is Kl 2.
  • Perpendicular to the thickness two volume elements lying next to each other should be created.
  • an edge length parallel to the boundary surface of 5 mm in flat areas of the adhesive connection K 1 and 4 mm in curved areas is specified.
  • the edge length parallel to the boundary surface is not specified, but a lower and / or upper limit for the ratio of the longest to the shortest edge of a volume element.
  • a ratio of 10 in curved and 12.5 in flat areas of the adhesive connection K1 is specified.
  • Fig. 2 shows a hexahedron 110.1, which belongs to the adhesive connection Kl, and four surface elements 100.1, 100.2, 100.3 and 100.4 of the surface F.la and thus the surface F.l.
  • the following describes how the method according to the invention is carried out for node 201.1 of this hexahedron.
  • the surface element closest to node 201.1 is determined.
  • the boundary surfaces of the hexahedron 110.1 are determined, which point to a surface that is adjacent to the adhesive connection K1.
  • boundary surfaces 111.1 and 111.2 are determined.
  • FIG. 2 A method which can be carried out quickly and is illustrated by FIG. 2 provides for a normal 210.1 to be generated on the boundary surface 111.1 which runs through the node 201.1.
  • This normal 210.1 meets the surface F.la in the surface element 100.2 and there in point 205.1.
  • This intersection 205.1 is determined as the closest point.
  • the Area element 100.2 to which the intersection belongs is determined as the next finite element.
  • the normal to the boundary surface 111.1 is successively shifted into the nodes of the hexahedron 110.1. 2 also shows the normal 210.3 through the node 201.2. This intersects the area Fl. a in point 205.2. For node 201.2, point 205.2 is determined as the closest point and surface element 100.1 is determined as the next finite element.
  • the angle 230.1 between these two standards is determined. In the case of parallel surfaces, the angle is 0. If this angle is less than or equal to a predetermined upper bound, the intersection 205.1 and the surface element 100.2, which were determined as described above, are used as the closest point or subsequent finite element.
  • the method described below is preferably carried out.
  • the node closest to 201.1 in the area F.la is determined. In the example in FIG. 4, this is the node 200.1.
  • all distances between different nodes of the construction are determined in advance and temporarily stored in a table.
  • the node belongs to the four surface elements 100.1, 100.2, 100.3 and 100.4. Are these four surface elements in one plane, a normal 210.4 is determined on the four surface elements by 201.1. This normal intersects the area Fl.a in point 205.3, which belongs to the area element 100.4. This means that 205.3 and 100.4 are determined. If the four surface elements are not in one plane, four normals and four intersection points are determined and the closest intersection point is used as the closest point.
  • Fig. 5 illustrates the bilinear interpolation for any square area element.
  • the surface element has the four nodes 200. a, 200. b, 200. c and 200. d, which lie in one plane, as corners.
  • the shifts P.a, P.b, P.c and P.d of these four nodes appear as four unknowns.
  • the point 205.x of the surface element was determined as the closest point.
  • the displacement P.x of point 205.x is approximately expressed as a linear function of the displacements P.a, P.b, P.c and P.d:
  • P.x g.a * P.a + g.b * P.b + g.c * P.c + g.d * P.d
  • FIG. 6 illustrates the geometric meaning of the two coordinates s and t.
  • the position of each point of the square shown in FIG. 5 is described after a coordinate transformation by two coordinates (x, y).
  • the point 205.x is described by the coordinates (x, y), the intersection 200. m by (x_m, y__m), the corners 200. a, 200. b, 200. c and 200. d by the coordinates
  • the square on the right half of Fig. 6 illustrates the calculation of the coordinates s and t.
  • the point (x, y) has the coordinates (s, t) after the transformation into the natural coordinate system in the square.
  • the point (x_m, y_m) has the coordinates (0, 0), the point (x_a, y_a) (-1, -1), the point (x_b, y_b) (1, -1), the point (x_c, y_c) (-1, 1) and the point
  • the coordinates s and t are preferably calculated according to the following calculation rule:
  • a l B y D x - D y B x
  • a y y_a + y__b + y_c + y_d
  • the displacement P.x is determined by inserting the then known coordinates and displacements.
  • P.x g.a * P.a + g.b * P.b + g.c * P.c.
  • the position of point 205.x in the surface elements with respect to a coordinate system, the axes of which are the distance from 200. a to 200. b and the distance from 200. a to 200. c is determined by two coordinates s and t. The coordinates s and t are determined so that the following applies:
  • the triangle is transformed by a suitable coordinate transformation such that the point 205.x has the coordinates (x, y).
  • the point 200. a has the coordinates (x_a, y_a), the point 200.
  • b the coordinates (x_b, y_b) and 200.
  • c the coordinates (x_c, y__c).
  • the coordinates s and t are determined as follows:
  • the coordinates s and t are not determined with respect to the surface element with the corners 200. a, 200.b, 200. c and 200. d, but with respect to an approximate surface element with the four corners 200. a ⁇ , 200 lying in one plane. b ⁇ , 200. c ⁇ and 200. d x .
  • 200.d is the base of a normal through 20O.d on the plane determined by 200. a, 200.b and 200. c. 0- the four corners are determined so that
  • the second possible step provides that it is automatically decided whether 205.x lies in the triangle with the corners 200. a, 200.b and 200. c or in the triangle with the corners 200.a, 200.b and 200.d .
  • the procedure described above is carried out for triangular surface elements.
  • the solution delivers the value that the physical size assumes in this node.
  • the values of the physical quantity are calculated in the closest points determined.
  • the solution is evaluated to analyze the construction of the system.

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Abstract

L'invention concerne un procédé permettant d'établir automatiquement un système d'équations d'après la méthode des éléments finis. Ce système d'équations se rapporte à des noeuds d'une construction comprenant un corps et une couche (Kl) adjacente. Des éléments finis sont produits pour le corps. La couche (Kl) est automatiquement décomposée en éléments de volume au moyen d'informations géométriques relatives à ladite couche et de spécifications pour le maillage de celle-ci. Pour au moins un noeud (201.1) faisant partie d'un élément de volume de la couche, on détermine l'élément fini (100.2) du corps qui est le plus proche de ce noeud et le point le plus proche (205.1) sur cet élément fini. On génère ensuite une fonction pour une relation physique entre la valeur que prend la grandeur physique au niveau du point le plus proche (205.1) et les valeurs que prend cette grandeur au niveau des noeuds de l'élément fini le plus proche (100.2). Lors de l'établissement du système d'équations, la valeur de la grandeur physique au niveau du point déterminé est éliminée au moyen de la fonction. L'invention permet de supprimer les inconnues dans le système d'équations.
PCT/EP2004/005776 2003-06-11 2004-05-28 Procede de simulation d'une liaison d'assemblage Ceased WO2004109559A2 (fr)

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DE10326229A DE10326229A1 (de) 2003-06-11 2003-06-11 Verfahren zur Simulation einer Fügeverbindung
DE10326229.6 2003-06-11

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WO2004109559A2 true WO2004109559A2 (fr) 2004-12-16
WO2004109559A3 WO2004109559A3 (fr) 2005-03-31

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EP2913202A1 (fr) * 2014-02-26 2015-09-02 Bombardier Transportation GmbH Procédé de conception d'une unité de traction pour véhicule ferroviaire
CN113722823B (zh) * 2021-08-30 2024-02-09 江南造船(集团)有限责任公司 一种适用于船舶结构有限元分析的板缝预处理方法

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DE102021109799A1 (de) 2021-04-19 2022-10-20 Bayerische Motoren Werke Aktiengesellschaft Verfahren zum Prüfen eines virtuellen Modells eines Bauteils, Computerprogramm sowie computerlesbares Medium

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Publication number Priority date Publication date Assignee Title
JP2972654B2 (ja) * 1997-05-27 1999-11-08 日本電気株式会社 有限要素法におけるデータ作成計算装置及びコンピュータ読み取り可能な記録媒体
US6560570B1 (en) * 1999-11-22 2003-05-06 Sandia Corporation Method and apparatus for connecting finite element meshes and performing simulations therewith

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
EP2913202A1 (fr) * 2014-02-26 2015-09-02 Bombardier Transportation GmbH Procédé de conception d'une unité de traction pour véhicule ferroviaire
WO2015128381A1 (fr) * 2014-02-26 2015-09-03 Bombardier Transportation Gmbh Procédé de conception d'une unité de traction de véhicule ferroviaire
CN113722823B (zh) * 2021-08-30 2024-02-09 江南造船(集团)有限责任公司 一种适用于船舶结构有限元分析的板缝预处理方法

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WO2004109559A3 (fr) 2005-03-31

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