DE102011056677A1 - Optimization method for determining optimized component shape of fiber composite component, involves calculating load behavior of component shape depending on predetermined boundary conditions in pre-defined installation space - Google Patents

Abstract

The optimization method involves calculating a load behavior of a component shape (23) depending on the predetermined boundary conditions (21,22) in a pre-defined installation space (20). The component shape is changed in the pre-defined installation space depending on the predetermined optimization strategies, the calculated load behavior of the component shape and the predetermined border conditions. A fiber course (24) of the changed component shape is considered depending on the predetermined border conditions. An independent claim is included for a computer program with a program code unit for performing the optimization method on a computer.

Description

The invention relates to an optimization method for determining an optimized component shape of a fiber composite component within a predefined installation space with respect to a predetermined boundary condition and predetermined optimization criteria.

Due to the special property to have a high stiffness or strength at a low weight, fiber composite components find more and more use in a variety of areas. In particular, where it comes down to a low weight of the components used, such as in the automotive sector or in aircraft, find complex fiber composite components in load-bearing structures application. However, especially in the case of complex component shapes, the manufacturing costs are higher than those of other conventional materials, since much has to be done by hand.

The production of a fiber composite component is carried out by draping a semi-finished fiber product (dry or pre-soaked) in a forming tool having the later shape of the desired component. Subsequently, the semifinished fiber product is infiltrated in the mold with a matrix resin, if this is not done sufficiently and then cured, so that the matrix resin reacts with the semi-finished fiber product and forms a solid component.

Another difference to conventional, in particular isotropic materials (such as iron or steel) is that fiber composites have a direction-dependent material behavior, which is characterized in particular by the fiber profile of the fiber composite component underlying semifinished fiber. Thus, fiber composite components along their fiber direction usually their greatest stability and strength, while orthogonal to the fiber plane, the fiber composite component, the stability is relatively weak. Not least because of this fiber composite components are usually formed in a flat form in order to make use of the direction-dependent material behavior.

Although the weight / stiffness ratio of fiber composite components over conventional materials is particularly favorable, there are still efforts to optimize the subsequent component shape of a fiber composite component with respect to certain optimization criteria. Such optimization criteria may be, for example, the reduction of the weight, the reduction of the materials used or the like. Prerequisite here, however, is always that the optimized component shape is chosen so that a later, based on this fiber composite component the set boundary conditions, such as clamping, forces, bearing points, loads and load direction is sufficient. First and foremost, the later fiber composite component must meet the requirements of the respective field of application and intended use. The optimization of the component form is also called topology optimization.

There are topology optimizers available for isotropic materials, i. For materials that have the same material properties and strength in all directions, find the optimum component shape in any three-dimensional design space. An optimization strategy here is to use mathematical or heuristic methods to determine a truss construction from tensile and compression bars which, with regard to the given optimization criteria and the given boundary conditions, find the optimal design within the given three-dimensional design space.

However, such a topology optimization is usually unsuitable for fiber composite components, since the directional material properties remain unconsidered. If one were to use such an optimized component form for the production of a fiber composite component and replace the isotropic material with a fiber composite material with directional material properties, then one would again move away from the actual optimum, since the conventional topology optimizers based on isotropic materials do not take this directional material behavior into account ,

It is therefore an object of the present invention to provide an improved topology optimization method with which an optimal component shape for a fiber composite component with respect to predetermined boundary conditions and optimization criteria can be determined within any three-dimensional design space.

• a) Berechnen eines Lastverhaltens einer Bauteilform in Abhängigkeit von den vorgegebenen Randbedingungen innerhalb des vordefinierten Bauraumes,
• b) Verändern der Bauteilform innerhalb des vordefinierten Bauraumes in Abhängigkeit von vorgegebenen Optimierungsstrategien, dem berechneten Lastverhalten der Bauteilform und den vorgegebenen Randbedingungen unter Berücksichtigung eines Faserverlaufes der Bauteilform derart, dass die Optimierungskriterien durch die veränderte Bauteilform angenähert werden, und
• c) Ermitteln eines angepassten Faserverlaufes der in Schritt b) veränderten Bauteilform in Abhängigkeit von den vorgegebenen Randbedingung und Wiederholen der Schritte a) bis c) auf Basis der veränderten Bauteilform und des hieran angepassten Faserverlaufes entsprechend.

The object is achieved with the optimization method of the type mentioned in the present invention with the iteration steps:

• a) calculating a load behavior of a component shape as a function of the predetermined boundary conditions within the predefined installation space,
• b) changing the component shape within the predefined installation space depending on predetermined optimization strategies, the calculated load behavior of the component form and the given boundary conditions taking into account a fiber profile of the component form such that the optimization criteria are approximated by the changed component shape, and
• c) Determining an adapted fiber profile of the component form changed in step b) as a function of the predetermined boundary condition and repeating the steps a) to c) on the basis of the changed component shape and the fiber shape adapted thereto.

According to the invention, it is proposed that first of all a load behavior of a component form within the predefined installation space be calculated as a function of the predetermined boundary conditions, such as predetermined forces and force points, advantageously also taking into account a possible fiber progression. The calculated load behavior then finds its way into the topology optimization in step b), where the component shape is changed or adapted within the predefined installation space as a function of optimization strategies, depending on the previously calculated load behavior and with respect to the given boundary conditions taking into account one Fiber course of the component form.

By changing the component shape, the optimization criteria set, for example, reduction of weight or increased stability, are approximated accordingly. By taking into account the course of the fibers, in particular the direction-dependent material behavior defined by the fiber progression, the adaptation of the component form for optimization can specifically address the problems with respect to fiber composite components.

Subsequently, a fiber shape adapted to this changed component shape is determined in step c), again in dependence on the given boundary conditions, so that an optimum fiber profile results in the component with respect to the changed component shape, the steps being repeated thereafter to approximate the optimal component shape and the optimal fiber shape.

Advantageously, the steps a) to c) are repeated until the component shape and the fiber profile required for the production of the fiber composite component have approximated so that a stable state has been found and / or the corresponding optimization criteria have been substantially achieved. The state in which a change in the component shape in step b) no longer achieves any improvement in the optimization criteria is regarded as a stable state. The steps are thus repeated with the appropriate specifications until an optimal component shape and fiber course has been found.

The iteration steps are carried out by a calculating machine, whereby step a) can be carried out by a load calculation module, step b) by a form finding module and step c) by a fiber progression module of the calculating machine.

The predetermined optimization strategies can be based, for example, on a mathematical approach in which the optimal component shape is approximated by calculations, in particular by means of the finite element method. Advantageously, however, a heuristic approach is preferred in which parts within the component space are added to the component form or corresponding parts of the component form are removed. Thus, the change in the component shape depending on the optimization strategies carried out such that determined in relation to the given boundary conditions taking into account the fiber flow of the force flow or the load behavior and are added at locations with a high tensile and / or compressive stress parts of the component form, while parts of the component form are removed at points of the component form with low tensile and / or pressure loads. With this heuristic approach to topology optimization, it is possible to find an optimal component shape, taking the fiber orientation into account.

The calculated load behavior of the component form therefore quantitatively describes the stress due to the predetermined loads (boundary conditions) at each position in the component, so that the tensile and / or compressive loading within the component can be determined at any desired position.

The determination of an adapted fiber profile to the component shape changed in step b) can furthermore be determined as a function of a draping property of a semifinished fiber product to be used for the fiber composite component, on the basis of which ultimately the fiber profile is based. The draping property of a semifinished fiber product essentially describes the property of the semifinished fiber product with regard to displacement, distortion and / or shear properties. This ensures that the course of the fiber within the component form is actually chosen such that the component can be produced later with such a fiber course.

Advantageously, the material properties of a semifinished fiber product are also used as the basis for the steps, in particular direction-dependent material properties such as tensile and compressive loading of the material and the rigidity of the material. On the basis of the direction-dependent material property, the optimal component shape can thus be found with regard to the boundary conditions taking into account the fiber profile.

It is particularly advantageous if a flat component shape is determined, since this is the Direction-dependent material behavior of fiber composites particularly accommodates. Thus, it is particularly advantageous if the changing of the component form in step b) is always carried out against the background that the changed component shape has essentially a flat shape.

In order to determine the starting conditions, it is advantageous if a starting configuration with a starting component shape and an initial fiber profile of this starting component form is specified. The starting component shape and the relevant initial fiber course are then used as the basis for the first iteration step. In the further iteration steps, the changed component shape or the adapted fiber profile is recursively used.

It is also conceivable, however, that the starting component shape and the initial fiber profile are determined in an initialization step before the first iteration as a function of the predetermined optimization strategies and the predetermined boundary conditions. This determination can be carried out by an initialization module of the arithmetic unit.

The invention will be described by way of example with reference to the accompanying drawings. Show it:

1 Flowchart of the present iteration method;

2a to 2c - Exemplary result representation for a selected optimization example.

1 schematically shows the flow of the present optimization method. Starting from a startup configuration 1 with a startup part shape and an initial fiber flow is in the module 2 calculated the load behavior of the start configuration with respect to the given boundary conditions. In a module 3 Then, the component shape is adjusted within a predefined installation space using predetermined optimization strategies as a function of the load behavior, in order to approach the optimum of the component shape defined by the optimization criteria. It can by the startup configuration 1 also the necessary boundary conditions, optimization criteria and optimization strategies are given.

According to the method according to the invention, the change of the component form takes place in step 3 taking into account a fiber flow in the component form, so as to take into account the directional material behavior in determining the optimal design with. Such a fiber course can also be done by the start configuration 1 be specified.

The in step 3 changed component shape is then the module 4 so that on the basis of this a matched fiber profile can be determined. In order to determine the adapted fiber profile, the boundary conditions necessary for the development of the component are taken into account, such as, for example, clamping, loads and load direction. This results in a corresponding energy favorable fiber flow for in step 2 found component form, in which case additionally the draping properties of a possible semifinished fiber product can be taken into account. The determination of the adapted fiber profile can be carried out, for example, by means of a simulated draping of the semi-finished fiber products as a function of the changed component shape.

In a verification step 5 The found component shape is then checked for optimization criteria to determine if the found part shape meets the optimization criteria and the method can be terminated. In the verification step 5 can also be checked whether a stable state of the component form was found. In this case, a stable state is understood as meaning that further iteration steps through the method no longer lead to any change in the component or the optimization criteria can no longer be approximated. If a stable state is found or if the optimization criteria are sufficiently approximate, then the found component shape, together with the fiber shape adapted thereto, becomes the final result 6 output. Otherwise, the process goes to the step 2 Repeated on the basis of the previously changed component shape and the adapted fiber profile, until shape and fiber shape have sufficiently approximated and led to an optimal result.

2a to 2c show by way of example the results during a complete run of the optimization process. In 2a is a predefined space 20 shown, within which a fiber composite component to be found with an optimal shape. The defined boundary conditions are on the one hand the given on the left side clamping 21 to which the later component is then actually attached, and the load defined on the right 22 which can act as force in the directions shown by the arrow. The maximum limit of the force is also given by the boundary conditions.

In the installation space 20 extends from the clamping 21 until the load is taken up 22 an initial component shape 23 with a given fiber path 24 , Through the fiber path 24 is the directional material behavior of the component form 23 Are defined.

During an iteration step, the initial part shape becomes 23 changed, using the given optimization strategies. The optimization strategy sees in the embodiment of 2a suggest that in the areas in which the component form has high tensile and / or compressive stresses, corresponding parts of the component form 23 to be added. The added parts are with 25 characterized.

The tensile and / or compressive stress of the component form takes place in dependence on the given boundary conditions (clamping, loads) taking into account the fiber profile 24 , which specifies the directional material behavior. Thus, tensile and / or compressive stresses are above an upper limit for the addition of parts 25 used, while tensile and / or compressive stress below a lower limit are used to parts of the component form at these positions 23 to remove.

In the subsequent step then the fiber flow 24 to the changed component shape 23 , which are now from the original component form 23 and the added parts 25 results, adjusted. By adjusting the fiber flow, the directional material behavior will also change, thereby changing the tensile and compressive stresses within the component.

2 B shows a component shape 33 , which is made up of the initial component shape of the 2a after a few iteration steps of the present method.

It can be seen that both the shape of the component and the course of the fibers 34 an optimal design, as in 2c shown, approximates. In addition, it should also be noted that the component form basically has a flat shape, which accommodates the production of fiber composite components.

The optimization strategies for determining the optimum design are thus chosen such that, in addition to an approximation to the optimization criteria, a planar shape is always preferred. The change of the component form within the predefined installation space as a function of the given optimization strategies and the given boundary conditions, taking into account a fiber progression, thus takes place in such a way that the optimization criteria are approximated by the changed component form in a planar form.

2c finally shows the found optimal component shape 43 , By adding parts and removing parts, a flat shape has been found that has a continuous grain 44 and thus optimally carries the loads, the flat shape particularly accommodating in the manufacture of the fiber composite component. The optimum component shape and the considered fiber profile have come close to giving an optimum component shape with regard to the optimization criteria, such as, for example, weight reduction or material reduction. The component form in 2c In addition, it has the lowest energy fiber path 44 for this component.

In addition, taking into account a draping property of a semifinished fiber product to be used, the fiber course can also be determined in such a way that afterwards a physically physically producible component results, without further adaptations being necessary. Since semifinished fiber products can only be shortened to a limited extent without causing defects in the later component, by taking into account the draping property not only a component form can be found which is optimized with regard to the optimization criteria, but also with regard to production.

The embodiment of 2a to 2c shows a simplified procedure for illustrative purposes. Basically, topology optimization in any 3D construction space and any boundary conditions is possible with the present method.

Claims (9)

Optimization method for determining an optimized component shape of a fiber composite component within a predefined installation space ( 20 ) with regard to given boundary conditions ( 21 . 22 ) and given optimization criteria, with the iteration steps: a) calculating a load behavior of a component shape ( 23 ) depending on the given boundary conditions ( 21 . 22 ) within the predefined installation space ( 20 ), b) changing the component shape ( 23 ) within the predefined installation space ( 20 ) as a function of given optimization strategies, the calculated load behavior of the component form ( 23 ) and the given boundary conditions taking into account a fiber course ( 24 ) of the component form ( 23 ) such that the optimization criteria are approximated by the changed component shape, and c) determining an adapted fiber profile ( 24 ) of the component shape changed in step b) as a function of the predetermined boundary condition and repeating the steps a) to c) on the basis of the changed component shape and the fiber shape adapted thereto. Optimization method according to claim 1, characterized by repeating steps a) to c) until the optimization criteria in Substantially achieved and / or a stable state of the component form was found. Optimization method according to claim 1 or 2, characterized by predetermining or determining a start configuration with a starting component shape ( 23 ) and an initial fiber course ( 24 ) and performing the first iteration with the startup configuration. Optimization method according to one of the preceding claims, characterized by determining the fiber profile of the modified component shape further in dependence on a Drapiereigenschaft a to be used for the fiber composite component semi-finished fiber product. Optimization method according to one of the preceding claims, characterized by changing the component shape in step b) and / or determining an adapted fiber profile in step c) further in dependence on a material property of a semi-finished fiber to be used for the fiber composite component. Optimization method according to one of the preceding claims, characterized in that changing the component shape in step b) such that the component form is a substantially flat shape. Optimization method according to one of the preceding claims, characterized by changing the component shape as a function of the given optimization strategies by adding parts ( 25 ) to the component shape ( 23 ) and / or removing parts from the component mold. Computer program with program code means set up for carrying out the method according to one of claims 1 to 7, when the computer program is executed on a computer. Computer program with program code means stored on a machine-readable carrier, set up for carrying out the method according to one of Claims 1 to 7, when the computer program is executed on a computer.

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