Orthotropic sandwich structure

Abstract

The present invention relates to an orthotropic sandwich structure (1) with differentiated bending stiffnesses, comprising a first membrane (21) and a second membrane (22) spaced apart by a distance H, as well as a shearing structure (3) connecting them and made up of a plurality of shearing elements (4) each having a generatrix (G) of curvilinear length L. The ends (I1, I2) of the generatrix are positioned at a distance d1 from the first membrane (21) and at a distance d2 from the second membrane (22), respectively. According to the invention, the generatrix (G) has a curvilinear length L at least equal to 1.25*(H-(d1+d2)), and the straight line (D) passing respectively through the orthogonal projections (J1, J2) of the ends (I1, I2) on the membranes (21, 22) forms, with a direction (ZZ') perpendicular to the mean surface (Sm) of the shearing structure (3), an angle (B) at most equal to 45°.

Description

Orthotropic sandwich structure

[0001] The present invention relates to an orthotropic sandwich structure with differentiated bending rigidities, in two directions perpendicular to each other.

[0002] Usually a one-dimensional structure, such as a beam, or a two-dimensional structure, such as a shell, is subjected to tension / compression and / or bending. These stresses locally generate stresses and deformations.

[0003] Generally, a beam or a shell, in the case where it is mainly stressed in bending, is used either as a static structural part, for example in a building or civil engineering structure, or as a subassembly of a structure in motion within a fluid, for example a helicopter blade, a wind turbine blade, an aircraft wing. In the first case of a static structural part, the bending deformations are generally very low, typically at most equal to 0.5%. In the second case of a subassembly of a structure in motion, the bending deformations, resulting from interactions with the fluid environment are higher, but remain limited, typically within the interval [1%; 2%]. By definition, the bending deformation, at a point, is the ratio between the relative displacement between the two membranes and the distance between the two membranes.

[0004] A sandwich-type structure, more simply called a sandwich structure, is commonly used for a beam or a shell. A sandwich structure is classically made up of two thin structures, or membranes, spaced from each other, and an intermediate structure connecting them, or a shear structure. During bending of the sandwich structure, the membranes are mainly subjected to tensile or compressive stresses, while the intermediate structure is mainly subjected to shear stresses, hence its name shear structure.

[0005] A structure can also be characterized by its isotropy or its anisotropy. A structure is said to be isotropic when its mechanical properties, in particular its stiffness characteristics, are independent of the direction considered within the structure. A structure is said to be anisotropic when its stiffness characteristics vary according to the direction considered within the structure. More specifically, a A structure is said to be orthotropic when its rigidity characteristics vary in two directions perpendicular to each other.

[0006] The inventors set themselves the objective of designing an orthotropic sandwich structure with differentiated bending rigidities, such that a first bending rigidity, around a first direction, is at least equal to 5 times a second bending rigidity, around a second direction perpendicular to the first direction, the bending deformation around this second direction being at least equal to 10%.

[0007] This objective was achieved by an orthotropic sandwich structure comprising a first membrane, a second membrane and a shear structure connecting the first and second membranes, -the orthotropic sandwich structure having an average surface equidistant from the first and second membranes, -the shear structure being constituted by a plurality of shear elements distributed in a first direction tangent to the average surface, - any shear element having a section having, in any plane perpendicular to the mean surface and containing the first direction, a generator, not perpendicular to the mean surface and extending between a first and a second end, -the generator having a curvilinear length L measured between the first and second ends, -the first and second ends having respectively a first orthogonal projection on the first membrane, positioned at a distance dl from the first end, and a second orthogonal projection on the second membrane, positioned at a distance d2 from the second end, -the first and second orthogonal projections being spaced by a distance H, -the generator of the section of the shear element having a curvilinear length L at least equal to 1.25*(H-(dl+d2)) -and the straight line, passing respectively through the first and second orthogonal projections, forming, with a third direction perpendicular to the average surface, an angle at most equal to 45°.

[0008] The orthotropic sandwich structure comprises a first membrane, a second membrane and a shear structure connecting the first and second membranes. By convention, a mean surface of the orthotropic sandwich structure is defined as equidistant from the first and second membranes. By definition, a membrane is a three-dimensional structure with a smallest dimension, small compared to its other two dimensions and called thickness. A membrane is mainly subjected to tensile-compressive forces in its thickness. The first and second membranes are not necessarily parallel to each other and can therefore be separated by a variable space.

[0009] The shear structure of an orthotropic sandwich structure according to the invention essentially comprises a distribution, in a first direction, of a plurality of shear elements distributed according to a pitch that is not necessarily constant. The shear structure can be continuous, when each shear element is connected at each of its ends to an adjacent shear element, or discontinuous, when the shear elements are distributed discretely, without connection between them. Such a shear structure makes it possible to limit the mass of the orthotropic sandwich structure.

[0010] In any plane perpendicular to the mid-surface of the orthotropic sandwich structure and containing the first direction, any shear element, i.e. any elementary pattern, of the plurality of shear elements, has a section having a mid-line, called a generator, not perpendicular to the mid-surface and of curvilinear shape. This generator extends between a first end and a second end. The first and second ends respectively have a first orthogonal projection onto the first membrane, positioned at a distance dl from the first end, and a second orthogonal projection onto the second membrane, positioned at a distance d2 from the second end.This implies that the first and second ends are not necessarily positioned respectively on the first membrane and on the second membrane, and that there may therefore be a transition zone interfacing between said section of the shear element and respectively the first and second membranes. Furthermore, the distances dl and d2 are not necessarily constant either in the first direction or in a second direction perpendicular to the first direction. Furthermore, it should be noted that the shape of the. generator is an open curve and not closed on itself: thus, for example, the generator cannot have a closed circular shape.

[0011] According to the invention, the generatrix of the section of the shear element must have a curvilinear length L, measured along this generatrix between its two ends, at least equal to 1.25*(H-(dl+d2)), H being the distance H between the first and second orthogonal projections respectively. Such a generatrix is ​​therefore non-rectilinear, which guarantees geometric flexibility of the shear element.

[0012] Still according to the invention, the straight line, passing through the first and second orthogonal projections respectively, forms, with a third direction perpendicular to the average surface, an angle at most equal to 45°.

[0013] These two essential characteristics give the generator a shape that guarantees optimization of the stresses generated in the shear element, under bending stresses, around a second direction, perpendicular to the first direction. Indeed, compared to simpler structures such as straight beams, this generator shape makes it possible either to have a longer effective working length of the shear element, for a given distance H, or to have interfaces with the first and second membranes that are thick enough to move the maximum stresses and deformations to the core of the shear element and not at the level of said interfaces.

[0014] Furthermore, the shape of the generator, in combination with the thickness characteristics of the shear element and the modulus of elasticity of the material(s) constituting said shear element, makes it possible to optimize the mechanical rigidity characteristics of the orthotropic sandwich structure, with a view to distributing the stresses in said structure.

[0015] In addition, the shear stiffness of the orthotropic sandwich structure, along the first direction, must also be adapted to ensure, in particular, an optimal distribution of shear stresses. This shear stiffness is mainly provided by the shear structure connecting the first and second membranes respectively. The shear of such a shear structure generates, in each shear element, local bending causing deformation of this shear element.

[0016] On the other hand, the bending rigidity of the orthotropic sandwich structure around the first direction is typically at least equal to 5 times the bending rigidity of the orthotropic sandwich structure around the second direction.

[0017] An orthotropic sandwich structure according to the invention is thus very flexible and deformable, in a first direction, with bending deformations at least equal to 10%, without damage to the structure. Adapting the shape and length of the generatrix of the shear elements makes it possible to guarantee a level of stresses and deformations compatible with the properties of resistance to rupture and / or fatigue limit of the material constituting said shear elements.

[0018] Advantageously, the distance dl between the first end and the first orthogonal projection is at most equal to 0.5 times the distance H between the first and second orthogonal projections.

[0019] Advantageously, the distance dl between the first end and the first orthogonal projection is equal to 0. This implies that there is no transition zone interfacing between the section of the shear element and the first membrane.

[0020] Advantageously, the distance d2 between the second end and the second orthogonal projection is at most equal to 0.5 times the distance H between the first and second orthogonal projections.

[0021] Advantageously, the distance d2 between the second end and the second orthogonal projection is equal to 0. This implies that there is no transition zone interfacing between the section of the shear element and the second membrane.

[0022] Advantageously, the tangent to the generator at its first end forms, with the third direction perpendicular to the average surface, an angle at least equal to 45°.

[0023] Still advantageously the tangent to the generator at its second end forms, with the third direction perpendicular to the average surface, an angle at least equal to

[0024] Advantageously, the generator of the section of any shear element has a shape having a single inversion of its direction of curvature, such as, for example, an S shape.

[0025] Advantageously, the section of any shear element has a non-constant thickness E0. This variation in thickness makes it possible to optimize the distribution of stresses and strains in this shear element. The thickness E0, measured in a given plane, can also vary between two distinct planes, according to the second direction.

[0026] Preferably, the shear elements are distributed with a constant pitch, according to the first direction.

[0027] More preferably, any shear element of the plurality of shear elements is made of a material having a modulus of elasticity in extension at 4% elongation at least equal to 20 MPa, preferably at least equal to 30 MPa. This modulus of elasticity in extension is measured statically. More precisely, it is the modulus of elasticity of the material measured, on a standardized test piece, during a uniaxial tensile experiment, at an elongation value of 0.04 (i.e. 4% elongation, expressed as a percentage). A constant uniaxial tensile speed is imposed on a test piece of the material, and its elongation and the corresponding force are measured. The measurement is carried out using an INSTRON type tensile machine, at a temperature of 23°C, and a relative humidity of 50% (ISO 23529 standard). The conditions for measuring and using the results to determine elongation and stress are described in standard NF ISO 37: 2012-03.The stress is determined for an elongation of 0.04 and the secant modulus of elasticity at 4% elongation is calculated by dividing this stress value by the elongation value.

[0028] The shape of the generatrices of the shear elements means that the stresses generated by the shearing of the orthotropic sandwich structure, resulting from bending stresses around the first direction, are sufficiently low to allow the use of materials having higher moduli of elasticity than those of the commonly used elastomeric materials. Generally, the material of the first and second membranes is identical to that of the shear elements.

[0029] Using materials with a high modulus of elasticity makes it possible either to lighten the orthotropic sandwich structure by reducing the effective sections of the shear elements, in a given plane, or to stiffen it.

[0030] The characteristics of the invention are illustrated by schematic figures 1 to 3, not shown to scale: -Figure 1: Overview of an orthotropic sandwich structure with parallel membranes, according to a first embodiment of the invention, -Figure 2: Sectional view, in a plane perpendicular to the average surface and containing the first direction, of a shear element, according to a first variant of the first embodiment of the invention (with dl and d2 non-zero), -Figure 3: Sectional view, in a plane perpendicular to the average surface and containing the first direction, of a shear element, according to a second variant of the first embodiment of the invention (with dl and d2 zero). -Figure 4: Overview of an orthotropic sandwich structure with non-parallel membranes, according to a second embodiment of the invention.

[0031] Figure 1 is an overall view of an orthotropic sandwich structure 1 with parallel membranes (21, 22), according to a first embodiment of the invention. The orthotropic sandwich structure 1 comprises a first membrane 21, a second membrane 22 and a shear structure 3 connecting the first and second membranes (21, 22). The orthotropic sandwich structure 1 has a mean surface Sm equidistant from the first and second membranes (21, 22). The shear structure 3 is constituted by a plurality of shear elements 4 distributed along a first direction XX' tangent to the mean surface Sm. Each shear element 4 has a section 40 having, in any plane XZ perpendicular to the mean surface Sm and containing the first direction XX', a generatrix G, not perpendicular to the mean surface Sm and extending between a first and a second end (II, 12).The first direction XX', the second direction YY' and the third direction ZZ' define an orthogonal coordinate system. The XZ plane contains the first direction XX' and the second direction YY and is perpendicular to the third direction ZZ'.

[0032] Figure 2 is a sectional view, in a plane XZ perpendicular to the mean surface Sm and containing the first direction XX', of a shear element 4, according to a first variant of the first embodiment of the invention (with dl and d2 non-zero). Any shear element 4 has a section 40 having, in any plane XZ perpendicular to the mean surface Sm and containing the first direction XX', a generatrix G, not perpendicular to the mean surface Sm and extending between a first and a second end (II, 12). The generatrix G has a curvilinear length L measured between the first and second ends (II, 12). The first and second ends (II, 12) respectively have a first orthogonal projection J1 on the first membrane 21, positioned at a distance dl from the first end II, and a second orthogonal projection J2 on the second membrane 22, positioned at a distance d2 from the second end 12. The first and second orthogonal projections (JI, J2) are spaced apart by a distance H.According to the invention, the generatrix G of the section 40 of the shear element 4 has a curvilinear length L at least equal to 1.25*(H-(dl+d2)) and the straight line D, passing respectively through the first and second orthogonal projections (JI, J2), forms, with a third direction ZZ' perpendicular to the mean surface Sm, an angle B at most equal to 45°. In the embodiment variant shown, the distance dl from the first end II of the generatrix G to the first orthogonal projection J1 and the distance d2 from the second end 112 of the generatrix G to the second orthogonal projection J2 are less than 0.5 times the mean radial distance H and non-zero. Furthermore, the tangent Tl to the generator G at its first end It forms, with the third direction ZZ' perpendicular to the mean surface Sm, an angle Al at least equal to 45° and even close to 90°.Similarly, the tangent T2 to the generator G at its second end 12 forms, with the third direction ZZ' perpendicular to the mean surface Sm, an angle A2 at least equal to 45° and even close to 90°. Finally, the generator G of the section 40 of the shear element 4 has an S shape and the section 40 of the shear element 45 has a constant thickness E0.

[0033] Figure 3 is a sectional view, in a plane XZ perpendicular to the average surface and containing the first direction XX', of a shear element 4, according to a second variant of the first embodiment of the invention (with dl and d2 zero). This shear element 4 differs from that of Figure 2 by a generator shape G with more marked curvatures, a longer generator length L G and a smaller section thickness E0. Furthermore, in the embodiment variant shown, the distance dl from the first end II of the generator G to the first orthogonal projection J1 and the distance d2 from the second end 12 of the generator G to the second orthogonal projection J2 are zero. In other words, the section 40 is in direct interface with the first and second membranes (21, 22).

[0034] Figure 4 is an overall view of an orthotropic sandwich structure 1 with non-parallel membranes (21, 22), according to a second embodiment of the invention. The membranes (21, 22) being non-parallel, the average surface Sm is not flat. In this embodiment, the shear structure 3 is discontinuous and constituted by a discrete distribution of shear elements 4, two by two disjoint and of different shapes.

[0035] The inventors have more particularly studied this invention according to two variants RI and R2 of the first embodiment.

[0036] In the first RI variant, the modulus of elasticity in extension at 4% elongation of the material constituting a shear element is equal to 150 MPa, corresponding to a thermoplastic elastomer (TPE).

[0037] In the second variant R2, the modulus of elasticity in extension at 4% elongation and at -200°C of the material constituting a shear element is equal to 5800 MPa, corresponding to a thermoplastic of the poly etheretherketone (PEEK) type or to a polyimide.

[0038] Table 1 below shows the respective characteristics of the two embodiment variants RI and R2: [Table 1]

Claims

Claims 1. Orthotropic sandwich structure (1) comprising a first membrane (21), a second membrane (22) and a shear structure (3) connecting the first and second membranes (21, 22), -the orthotropic sandwich structure (1) having an average surface (Sm) equidistant from the first and second membranes (21, 22), -the shear structure (3) being constituted by a plurality of shear elements (4) distributed in a first direction (XX') tangent to the average surface (Sm), - any shear element (4) having a section (40) having, in any plane (XZ) perpendicular to the mean surface (Sm) and containing the first direction (XX'), a generator (G), not perpendicular to the mean surface (Sm) and extending between a first and a second end (II, 12), -the generator (G) having a curvilinear length L measured between the first and second ends (II, 12), -the first and second ends (II, 12) having respectively a first orthogonal projection (Jl) on the first membrane (21), positioned at a distance dl from the first end (II), and a second orthogonal projection (J2) on the second membrane (22), positioned at a distance d2 from the second end (12), -the first and second orthogonal projections (Jl, J2) being spaced apart by a distance H, characterized in that the generatrix (G) of the section (40) of the shear element (4) has a curvilinear length L at least equal to 1.25*(H-(dl+d2)) and in that the straight line (D), passing respectively through the first and second orthogonal projections (Jl, J2), forms, with a third direction (ZZ') perpendicular to the average surface (Sm), an angle (B) at most equal to 45°.

2. Orthotropic sandwich structure (1) according to claim 1, wherein the distance dl between the first end (II) and the first orthogonal projection (Jl) is at most equal to 0.5 times the distance H between the first and second orthogonal projections (Jl, J2).

3. Orthotropic sandwich structure (1) according to one of claims 1 or 2, in which the distance dl between the first end (II) and the first orthogonal projection (Jl) is equal to 0.

4. Orthotropic sandwich structure (1) according to any one of claims 1 to 3, in which the distance d2 between the second end (12) and the second orthogonal projection (J2) is at most equal to 0.5 times the distance H between the first and second orthogonal projections (J1, J2).

5. Orthotropic sandwich structure (1) according to any one of claims 1 to 4, wherein the distance d2 between the second end (12) and the second orthogonal projection (J2) is equal to 0.

6. Orthotropic sandwich structure (1) according to any one of claims 1 to 5, in which the tangent (Tl) to the generator (G) at its first end (II) forms, with the third direction (ZZ') perpendicular to the average surface (Sm), an angle (Al) at least equal to 45°.

7. Orthotropic sandwich structure (1) according to any one of claims 1 to 6, in which the tangent (T2) to the generator (G) at its second end (12) forms, with the third direction (ZZ') perpendicular to the average surface (Sm), an angle (A2) at least equal to 45°.

8. Orthotropic sandwich structure (1) according to any one of claims 1 to 7, in which the generatrix (G) of the section (40) of any shear element (4) has a shape having a single inversion of its direction of curvature.

9. Orthotropic sandwich structure (1) according to any one of claims 1 to 8, in which the section (40) of any shear element (4) has a non-constant thickness E0.

10. Orthotropic sandwich structure (1) according to any one of claims 1 to 9, in which the shear elements (4) are distributed with a constant pitch, in the first direction (XX').

11. Orthotropic sandwich structure (1) according to any one of claims 1 to 10, wherein any shear element (4) of the plurality of shear elements is made of a material having a modulus of elasticity in extension at 4% elongation at least equal to 20 MPa, preferably at least equal to 30 MPa.

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