Curved honeycomb sandwich panel structure with high thermal buckling strength and its construction and design method

Abstract

A curved-edge honeycomb sandwich panel structure with high thermal buckling strength, its construction and design method, belongs to the field of structural design. It includes two surface panels and a middle core layer structure. The core layer structure consists of vertically arranged plates periodically within the core layer plane. The vertical plates are either vertically straight-edge plates or vertically curved-edge shells. The core layer plane is parallel to the direction of the surface panels, and the vertical direction is the normal direction of the surface panels. A minimum geometrically repeatable pattern in the periodic arrangement is called a periodic cell, which is constructed from a vertical plate through geometric operations such as rotation and translation. Under uniform high-temperature load, this invention can increase the thermal buckling load by more than 50% compared to a straight-edge honeycomb sandwich panel structure of the same mass. Under extreme high-temperature load, the maximum out-of-plane deformation amplitude of thermal buckling can be reduced by more than 20%. It can realize the design of curved-edge honeycomb sandwich panels with arbitrary smooth curve shapes, allowing other mechanical responses besides thermal buckling to be used as design targets, and ensuring that the designed structure meets processing requirements, equipment requirements, etc.

Description

Technical Field

[0001] This invention belongs to the field of structural design, and in particular relates to a novel curved honeycomb sandwich panel structure with high thermal buckling bearing capacity under high temperature load, as well as its construction and design method. Background Technology

[0002] Sandwich panel structures consist of two surface panels and an intermediate core layer. Due to their high specific strength, high specific stiffness, waterproofing, thermal insulation, and sound insulation, sandwich panel structures are widely used as primary load-bearing or multifunctional components in engineering structures such as spacecraft and automobiles. Common core layer structures include corrugated core structures, foam core structures, grid core structures, truss core structures, folded core structures, and honeycomb core structures. Among these, the core layer of a honeycomb sandwich panel structure consists of vertical panels arranged periodically in triangular, quadrilateral, or hexagonal patterns within the core layer structure.

[0003] In various applications, such as the skin surfaces of hypersonic vehicles, honeycomb sandwich panel structures fail due to extreme high-temperature loads on one side. Specifically, the vertical plates in the core layer restrict the thermal expansion and deformation of the surface plates under high-temperature loads, inducing in-plane compressive stress. When this compressive stress reaches the buckling critical value, the surface plates undergo out-of-plane thermal buckling failure, reducing structural stiffness and causing turbulence or even flutter due to altered aerodynamic shapes, thus decreasing the structure's load-bearing capacity. Improving the thermal buckling load-bearing capacity of honeycomb sandwich panel structures and reducing the out-of-plane deformation amplitude at the onset of thermal buckling has significant engineering value.

[0004] There are two common methods to improve the thermal buckling load-bearing capacity of honeycomb sandwich panel structures. The first method is to reduce the temperature load on the structure. The main methods include: using materials with a large specific heat capacity as heat sink structures, relying on their own heat capacity to absorb heat and stabilize the temperature applied to the structure; covering the surface with an ablation structure, which removes heat through vaporization, thereby reducing the temperature load acting on the structure; and using active cooling structures, such as sweating cooling, which allow coolant to be sprayed from the porous surface to reduce the temperature.

[0005] The second approach is to increase the bending stiffness of the surface panel, such as by thickening it. However, this strategy increases the weight of the honeycomb sandwich panel structure, thus increasing its cost. Another strategy is to prepare the surface panel using composite materials such as silicon carbide ceramics or sandwich fiberboard, but this requires more complex processing techniques to achieve high-quality fabrication, increasing processing costs.

[0006] How to design a novel honeycomb sandwich panel structure with excellent thermal buckling bearing capacity and small post-thermal buckling deformation amplitude while keeping the total mass constant is a key problem that needs to be solved in the aerospace and other fields to achieve breakthroughs in the structural innovation design of major equipment and improve its operational capabilities and performance in extreme temperature environments. Summary of the Invention

[0007] This invention provides a honeycomb sandwich panel structure with a vertical curved shell in the core layer, and a design method for the curved honeycomb sandwich panel structure to achieve high thermal buckling load capacity. Compared with existing straight-edge honeycomb sandwich panel structures, the curved honeycomb sandwich panel structure designed in this invention has a higher critical thermal buckling load and thermal buckling load capacity under the same mass, and the maximum bending deflection caused by the back buckling of the surface plate is also significantly reduced under extreme high-temperature loads.

[0008] To achieve the above objectives, the technical solution adopted by this invention is as follows:

[0009] A curved honeycomb sandwich panel structure with high thermal buckling strength is disclosed. The curved honeycomb sandwich panel structure 1 consists of two surface plates 2 and an intermediate core layer structure 3. The core layer structure 3 is composed of vertical plates arranged periodically within the core layer plane 6. The shape of the vertical plates can be a vertical straight-edge plate 4 or a vertical curved-edge shell 5. The core layer plane 6 is parallel to the direction of the surface plates 2, and the vertical direction is the normal direction of the surface plates. The periodic arrangement includes, but is not limited to, arrangements in the form of regular quadrilaterals, regular hexagons, and equilateral triangles within the core layer plane. A minimum geometrically repeatable shape in the periodic arrangement is called a periodic cell 7. The periodic cell 8 in the regular quadrilateral arrangement is a regular quadrilateral, the periodic cell 9 in the regular hexagonal arrangement is a regular hexagon, and the periodic cell 10 in the equilateral triangle arrangement consists of six equilateral triangles of the same size, sharing a common vertex, and not overlapping each other.

[0010] To describe the geometric configuration of the sandwich structure 3, a right-handed rectangular coordinate system O'-ξηζ is established as the reference coordinate system. A vertical curved shell 5 in the sandwich structure 6 is a shell with its mid-surface being a curved surface formed by stretching a curve along the positive ζ-axis in the ξO′η plane. One endpoint of the curve coincides with the origin O', and the other endpoint lies on the positive half-axis of ξ. The shape of the curve can be described by, but is not limited to, multi-segment straight lines, trigonometric function curves, polynomial curves, interpolation curves, spline curves, etc. The spline curves include, but are not limited to, Bézier curves, B-spline curves, non-uniform rational B-spline curves, T-spline curves, etc. All the curve description methods describe the geometric shape by adjusting a finite number of parameters, and under reasonable parameter settings, the vertical straight-edge plate 4 can be reproduced.

[0011] To describe the relative positions of the sandwich layer structure 3 and the honeycomb sandwich panel structure 1, a right-handed rectangular coordinate system O-xyz is established as the overall coordinate system. The centroid of the inner surface of one side of the honeycomb sandwich panel structure 1 coincides with the origin O. The long side of this surface panel is parallel to the x-axis, the wide side is parallel to the y-axis, and the z-axis coincides with the normal direction of the surface panel. The coordinate system O'-ξηζ and the coordinate system O-xyz satisfy the following conditions: O' coincides with O, the ξ-axis coincides with the x-axis and is in the same positive direction, the η-axis coincides with the y-axis and is in the same positive direction, and the ζ-axis coincides with the z-axis and is in the same positive direction.

[0012] In the sandwich structure 3, a periodic cell 7 can be constructed from a vertical plate through geometric operations such as rotation and translation.

[0013] A complete sandwich structure 3 can be obtained by periodically arranging a periodic cell 7 in the ξO′η plane. The construction methods for different types of sandwich structures are described below:

[0014] To construct a sandwich structure 3 composed of periodic quadrilateral cells: First, take a vertical straight-sided plate or curved shell 11 located in the coordinate system O'-ξηζ. The vertical plate 11 satisfies the condition that its mid-surface is perpendicular to the ξO′η plane, and one endpoint of the intersection line between the mid-surface and the ξO′η plane coincides with the origin O', while the other endpoint is located on the positive half-axis of the ξ axis. Second, rotate the vertical plate 11 90° clockwise around the vertical centerline 15 of its vertical side 16 to obtain a vertical plate 12. Translate the vertical plate 11 along the negative η axis to obtain a vertical plate 13. The translation distance is the distance between the two endpoints of the intersection line between the mid-surface of the vertical plate 12 and the ξO′η plane. Vertical plate 12 is translated along the positive ξ-axis to obtain vertical plate 14. The translation distance is the distance between the two endpoints of the intersection line between the mid-surface of vertical plate 11 and the ξO′η plane. Vertical plates 11, 12, 13, and 14 constitute all the vertical plates of a regular quadrilateral periodic cell 8. Finally, the obtained periodic cells 8 are linearly periodically arrayed in the ξO′η plane along both the ξ-axis and η-axis. The array spacing in both directions is the distance between the two endpoints of the intersection line between the mid-surface of vertical plate 11 and the ξO′η plane. The number of arrays is defined by the user, but there should be a sufficient number of periodic cells to completely fill the sandwich layer structure. The reference coordinate system is placed in the global coordinate system according to the aforementioned relative positional relationship. The structural portion not covered by the surface plate is removed to obtain the sandwich layer structure composed of regular quadrilateral periodic cells.

[0015] To construct a sandwich structure 3 composed of regular hexagonal periodic cells: First, take a vertical straight-edge plate or curved shell 19 located in the coordinate system O'-ξηζ. The vertical plate 19 satisfies the condition that its mid-surface is perpendicular to the ξO′η plane, and one end of the intersection line of the mid-surface and the ξO′η plane coincides with the origin O', while the other end is located on the positive half-axis of the ξ axis. Second, rotate the vertical plate 19 clockwise by 120° around the vertical centerline 25 of its vertical side 26 to obtain a vertical plate 20. Rotate the vertical plate 20 clockwise by 120° around the vertical centerline 27 of its vertical side 28 to obtain a vertical plate 21. Rotate the vertical plate 21 clockwise by 120° around the vertical centerline 29 of its vertical side 30. Vertical plate 22 is obtained. Vertical plate 22 is rotated 120° clockwise around the vertical centerline 31 of its vertical side surface 32 to obtain vertical plate 23. Vertical plate 23 is rotated 120° clockwise around the vertical centerline 33 of its vertical side surface 34 to obtain vertical plate 24. Vertical plates 19, 20, 21, 22, 23, and 24 constitute all the vertical plates of a periodic cell 9 arranged in a regular hexagon. Finally, the obtained periodic cells 9 are arranged in a linear periodic array in the ξO′η plane along the ξ axis and a straight line with an angle of 30° to the ξ axis. The array spacing is three times the distance between the two endpoints of the intersection line between the mid-surface of vertical plate 19 and the ξO′η plane. The number of array elements is user-defined, but there should be a sufficient number of periodic cells to completely fill the sandwich structure. By placing the reference coordinate system in the global coordinate system according to the aforementioned relative positional relationship, and removing the structural portion not covered by the surface plate, a sandwich structure composed of regular hexagonal periodic cells can be obtained.

[0016] To construct a sandwich structure 3 composed of periodic cells of an equilateral triangle: First, take a vertical straight-edge plate or curved shell 37 located in the coordinate system O'-ξηζ. The vertical plate 37 satisfies the condition that its mid-surface is perpendicular to the ξO′η plane, and one end of the intersection line of the mid-surface and the ξO′η plane coincides with the origin O', while the other end is located on the positive half-axis of the ξ axis. Second, rotate the vertical plate 37 clockwise by 120° around the vertical centerline 44 of its vertical side 45 to obtain a vertical plate 38. Rotate the vertical plate 38 clockwise by 120° around the vertical centerline 46 of its vertical side 47 to obtain a vertical plate 39. Rotate the vertical plate 39 clockwise by 120° around the vertical centerline 48 of its vertical side 49 to obtain a vertical plate 40. Rotate the vertical plate 40 clockwise by 120° around the vertical centerline 50 of its vertical side 51 to obtain a vertical plate 41. Vertical plate 41 is rotated 120° clockwise around the vertical centerline 52 of its vertical side 53 to obtain vertical plate 42. Vertical plate 37 is rotated 60° clockwise around the vertical centerline 44 of its vertical side 45 to obtain vertical plate 54. Vertical plates 54 are arranged in an equidistant circular array with the vertical centerline 55 of the vertical side 56 as the central axis, with a total array size of 6, to obtain vertical plate combination 43. Vertical plates 37, 38, 39, 40, 41, 42 and vertical plate combination 43 constitute all the vertical plates of the periodic cell 10 in an equilateral triangle arrangement. Finally, the obtained periodic cell 10 is arranged in a linear periodic array in the ξO′η plane along the ξ axis and a straight line with an angle of 30° with the ξ axis. The interval distance of the array is 3 times the distance between the two endpoints of the intersection line between the mid-surface of vertical plate 37 and the ξO′η plane. The number of array elements is user-defined, but there should be a sufficient number of periodic cells to completely fill the sandwich structure. By placing the reference coordinate system in the global coordinate system according to the aforementioned relative positional relationship, and removing the structural portion not covered by the surface plate, a sandwich structure composed of equilateral triangular periodic cells can be obtained.

[0017] The geometric description parameters of the honeycomb sandwich panel structure are as follows: the two surface panels 2 have the same dimensions and a thickness of t. surface The length is a, the width is b; the distance between the planes of the two surface plates is h; the vertical plates in the sandwich structure 3 have a uniform thickness t. core In the sandwich structure 3, for performance comparison, the sandwich structure composed of the vertical curved shell 5 and the corresponding sandwich structure composed of the vertical straight plate 4 must maintain the same mass. This means that the distance between adjacent corner points of the periodic cell is different in the two designs. The adjacent corner points are the two closest vertices on the boundary of a polygon, which is formed by the intersection of the mid-surface of the vertical plate of the periodic cell 7 and the ξO′η plane. The distance between adjacent corner points of the periodic cell composed of the vertical curved shell 5 is L. curve The distance between adjacent corner points of the periodic cells formed by the vertical straight-edge plate 4 is L. straight Satisfying kLstraight =L curve , where k is the ratio of the length of the intersection line between the mid-surface of the vertical curved shell 5 and the plane ξO′η to the distance between the two endpoints of the intersection line.

[0018] Furthermore, the aforementioned curved honeycomb sandwich panel structure can be prepared using processes such as autoclave manufacturing, molding, vacuum bag manufacturing, and 3D printing. The matrix material can be, but is not limited to, high-temperature resistant metals such as aluminum alloys, titanium alloys, and stainless steel.

[0019] An optimized design method for designing curved-edge honeycomb sandwich panel structures with high thermal buckling capacity. It includes the following steps:

[0020] First, a curve description method is selected to describe the vertical curved shell 5 in the sandwich layer 3. The vertical curved shell 5 is a shell with a uniform thickness, formed by stretching the selected curve vertically in the plane of the sandwich layer along the curved surface as the mid-surface.

[0021] Secondly, an optimization design model is established, using the control point coordinates in the curve description method as design variables, the edge length and maximum curvature as constraints, and maximizing the first-order thermal buckling characteristic value of the honeycomb sandwich panel structure as the design objective.

[0022] Next, uniform temperature loads were applied to the two surface plates of the honeycomb sandwich panel structure, and its nonlinear thermodynamic response was numerically calculated using the finite element method.

[0023] Finally, an optimization algorithm was selected to optimize the shape of the vertical curved plate by iteratively updating the coordinates of the control points, thereby obtaining the shape of the vertical curved shell with the maximum thermal buckling load under the constraint conditions, and thus obtaining a curved honeycomb sandwich panel structure with optimal thermal bearing capacity.

[0024] Furthermore, the optimization algorithms mentioned include, but are not limited to, various intelligent optimization algorithms, such as genetic algorithms, multi-island genetic algorithms, particle swarm optimization, simulated annealing, etc., as well as gradient algorithms such as the descent simplex method, sequential quadratic programming method, and moving asymptote method. When a gradient algorithm is selected, the sensitivity of the response function (including the objective function and constraint function) to the control point coordinates can be obtained through the finite difference method. That is, first calculate the response function value J0 under the current coordinate variable, and then increase the i-th coordinate variable by no more than 1 / 1000 of the original value, denoted as Δx. i While keeping other coordinate variables constant, calculate the response function value J at this time. i Finally, the derivative of the response function with respect to the i-th coordinate variable is calculated as (J i -J0) / Δx i This method allows us to obtain the numerical derivatives of the response function with respect to all coordinate variables.

[0025] Furthermore, when performing linear thermal buckling eigenvalue analysis on the honeycomb sandwich panel structure using the finite element method, the finite element algorithms employed include, but are not limited to, the Lanzos method, the subspace method, and the inverse iteration method. The thermal buckling bearing capacity is obtained using the finite element method considering geometric nonlinearity and material nonlinearity: first, linear buckling analysis is performed on the honeycomb sandwich panel structure; second, the low-order modes obtained from the analysis are introduced into the finite element model as initial geometric defects, and the nodal coordinates are modified; finally, a nonlinear finite element method is used to solve for the thermal deformation, thermal buckling deformation, and physical responses such as thermal stress and thermal strain of the structure under a specified temperature load.

[0026] Furthermore, the optimization design method can also design honeycomb sandwich panel structures of other shapes (such as trapezoids, parallelograms, circles, etc.) with high thermal buckling load-bearing capacity.

[0027] Compared with the prior art, the present invention has the following beneficial effects:

[0028] (1) The curved honeycomb sandwich panel structure provided by the present invention can increase the thermal buckling load by more than 50% compared with the straight honeycomb sandwich panel structure of the same mass under uniform high temperature load, and can reduce the maximum out-of-plane deformation amplitude of thermal buckling by more than 20% under extreme high temperature load.

[0029] (2) Compared with traditional design methods based on the experience of designers, the structural optimization method provided by the present invention has at least three advantages: First, the method can realize the design of sandwich layer curved honeycomb panels with arbitrary smooth curve shapes, and the order, continuity and smoothness of the curve can be controlled by the order of the approximate function and the number of control points; Second, the method allows other mechanical responses besides thermal buckling as design objectives, such as maximizing the overall stiffness of the structure and maximizing the structural strength; Finally, the method can also add necessary geometric and mechanical response constraints during the design process, such as maximum curvature, maximum length, and the movable range of control points, to ensure that the designed structure meets the processing requirements, equipment requirements, etc. Attached Figure Description

[0030] Figure 1 is a schematic diagram of a honeycomb sandwich panel structure containing a hexagonal core layer. Among them, Figure 1(a) is a schematic diagram of the honeycomb sandwich panel structure and the overall coordinate system; Figure 1(b) is a schematic diagram of the straight-edge core layer structure; and Figure 1(c) is a schematic diagram of the curved-edge core layer structure.

[0031] Figure 2 is a schematic diagram of a sandwich layer structure composed of curved square cells. In Figure 2(a), the construction process of the curved square cells is shown; and in Figure 2(b), the schematic diagram of the sandwich layer structure composed of curved square cells is shown.

[0032] Figure 3 is a schematic diagram of a sandwich layer structure composed of curved hexagonal cells. In particular, Figure 3(a) shows the construction process of the curved hexagonal cells; Figure 3(b) is a schematic diagram of the sandwich layer structure composed of curved hexagonal cells.

[0033] Figure 4 is a schematic diagram of a sandwich layer structure composed of curved equilateral triangular cells. In particular, Figure 4(a) shows the construction process of the curved equilateral triangular cells; Figure 4(b) is a schematic diagram of the sandwich layer structure composed of curved equilateral triangular cells.

[0034] Figure 5 is a schematic diagram of the geometric dimensions of the honeycomb sandwich panel structure. Figure 5(a) shows the overall dimensions of the honeycomb sandwich panel structure; Figure 5(b) shows the cell dimensions of the curved-edge sandwich structure and the reference coordinate system used to describe the geometric configuration of the sandwich structure; Figure 5(c) shows the cell dimensions of the straight-edge sandwich structure and the reference coordinate system used to describe the geometric configuration of the sandwich structure. The dashed line represents the intersection of the vertical mid-surface of the panel and the ξO′η plane.

[0035] Figure 6 This is a schematic diagram of a third-order Bézier curve and a design curve describing the shape of a curved cell. Solid lines represent third-order Bézier curves, dashed lines represent design curves, and dotted lines represent broken lines connecting control points. This represents the control points and their spatial coordinates of a third-order Bézier curve. This represents the control points of the design curve and their spatial coordinates.

[0036] Figure 7 is a schematic diagram of the curved edge shape of the periodic cell controlled by Bézier curves. Among them, Figure 7(a) is a top view of the regular hexagonal cell obtained by Bézier curves; Figure 7(b) is a top view of the regular quadrilateral cell obtained by Bézier curves; and Figure 7(c) is a top view of the equilateral triangle cell obtained by Bézier curves.

[0037] Figure 8 shows the thermodynamic response results of a honeycomb sandwich panel structure with equilateral triangular curved-edge core layers and a honeycomb sandwich panel structure with equilateral triangular straight-edge core layers under uniform temperature load. Figure 8(a) is the buckling mode diagram of the honeycomb sandwich panel structure with equilateral triangular straight-edge core layers; Figure 8(b) is the buckling mode diagram of the honeycomb sandwich panel structure with equilateral triangular curved-edge core layers, where the grid lines are the intersection lines of the vertical plates and the surface plates of the sandwich panel structure; Figure 8(c) shows the maximum displacement of the honeycomb sandwich panel structure with equilateral triangular curved-edge core layers and the honeycomb sandwich panel structure with equilateral triangular straight-edge core layers under uniform temperature load as a function of temperature load.

[0038] Figure 9 shows the thermodynamic response results of a honeycomb sandwich panel structure with a regular quadrilateral curved-edge core layer and a regular quadrilateral straight-edge core layer under uniform temperature load. Figure 9(a) is a modal deformation diagram of the honeycomb sandwich panel structure with a regular quadrilateral straight-edge core layer, and Figure 9(b) is a modal deformation diagram of the honeycomb sandwich panel structure with a regular quadrilateral curved-edge core layer. The lines in the surface plate in the modal diagrams are the intersection lines of the vertical plates of the core layer and the surface plate. Figure 9(c) shows the maximum displacement of the honeycomb sandwich panel structure with a regular quadrilateral curved-edge core layer and the honeycomb sandwich panel structure with a regular quadrilateral straight-edge core layer under uniform temperature load as a function of temperature load.

[0039] Figure 10 shows the thermodynamic response results of a honeycomb sandwich panel structure with a regular hexagonal curved-edge core layer and a regular hexagonal straight-edge core layer under uniform temperature load. Figure 10(a) is a modal deformation diagram of the honeycomb sandwich panel structure with a regular hexagonal straight-edge core layer, and Figure 10(b) is a modal deformation diagram of the honeycomb sandwich panel structure with a regular hexagonal curved-edge core layer. The lines in the surface plate in the modal diagrams are the intersection lines of the vertical plates of the core layer and the surface plate. Figure 10(c) shows the maximum displacement of the honeycomb sandwich panel structure with a regular hexagonal curved-edge core layer and the honeycomb sandwich panel structure with a regular hexagonal straight-edge core layer under uniform temperature load as a function of temperature load.

[0040] In the figure: 1. Honeycomb sandwich panel; 2. Honeycomb sandwich panel surface panel (including two surface panels); 3. Honeycomb sandwich panel core layer structure; 4. Vertical straight edge panel in a straight edge panel type core layer structure; 5. Vertical curved edge shell in a curved edge shell type core layer structure; 6. Core layer plane; 7. Periodic cell (smallest unit) of the core layer structure; 8. Curved square cell; 9. Curved hexagonal cell; 10. Curved equilateral triangle cell; 11, 12, 13, 14. Vertical plates constituting the curved square cell; 15. The centerline of the vertical side surface 16 of vertical plate 11; 16. One vertical side surface of vertical plate 11; 17. The line segment connecting the endpoints of the intersection line between the mid-surface of vertical plate 11 and the ξO′η plane; 18. Vertical The line segment connecting the endpoints of the intersection line between the mid-surface of plate 13 and the plane ξO′η; 19, 20, 21, 22, 23, 24 forming the vertical plate of the curved regular hexagonal cell; 25 a midline of the vertical side surface 26 of vertical plate 19; 26 a vertical side surface of vertical plate 19; 27 a midline of the vertical side surface 28 of vertical plate 20; 28 a vertical side surface of vertical plate 20; 29 a midline of the vertical side surface 30 of vertical plate 21; 30 a vertical side surface of vertical plate 21; 31 a midline of the vertical side surface 32 of vertical plate 22; 32 a vertical side surface of vertical plate 22; 33 a midline of the vertical side surface 34 of vertical plate 23; 34 vertical plate 2 3. A vertical side surface; 35. The line segment connecting the endpoints of the intersection of the mid-surface of vertical plate 19 and the plane ξO′η; 36. The line segment connecting the endpoints of the intersections of the mid-surfaces of vertical plates 19 and 20 and the plane ξO′η; 37, 38, 39, 40, 41, 42, and 43. Vertical plates forming a curved equilateral triangle cell; 44. A midline of the vertical side surface 45 of vertical plate 37; 45. A vertical side surface of vertical plate 37; 46. A midline of the vertical side surface 47 of vertical plate 38; 47. A vertical side surface of vertical plate 38; 48. A midline of the vertical side surface 49 of vertical plate 39; 49. A vertical side surface of vertical plate 39; 50. A midline of the vertical side surface 50 of vertical plate 40. Centerline; 51 A vertical side of vertical plate 40; 52 A centerline of vertical side 53 of vertical plate 41; 53 A vertical side of vertical plate 41; 54 The vertical plate obtained by rotating vertical plate 37 60° clockwise around the vertical centerline 44 of its vertical side 45; 55 A centerline of vertical side 56 of vertical plate 54; 56 A vertical side of vertical plate 54; 57 The line segment connecting the endpoints of the intersection of the mid-surface of vertical plate 37 and the ξO′η plane; 58 The line segment connecting the endpoints of the intersection of the mid-surfaces of vertical plates 37 and 38 and the ξO′η plane; 59 A third-order Bezier curve describing the vertical curved shell configuration of the periodic cell; 60 A design curve that determines the parameters of curve 59. Detailed Implementation

[0041] To fully illustrate the present invention, further detailed description is provided below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the scope of the invention.

[0042] Referring to Figures 1-7, the present invention provides a curved honeycomb sandwich panel structure with high thermal buckling load capacity. The curved honeycomb sandwich panel structure 1 is composed of upper and lower surface plates 2 and a core layer structure 3.

[0043] To describe the geometry of the sandwich structure, a right-handed rectangular coordinate system O'-ξηζ is established as the reference coordinate system. The sandwich structure 3 can be, but is not limited to, a shell structure composed of periodically arrayed curved hexagonal cells, curved equilateral triangular cells, and curved quadrilateral cells. Preferably, a third-order Bézier curve is used to describe the shape of the vertical curved shell constituting the cell; the coordinates of any point on the Bézier curve can be expressed as:

[0044]

[0045] Where n is the order of the Bézier curve, P ξi P ηi C represents the coordinates of the control points used to describe the Bézier curve. ξ C η Let B be the coordinates of a point on the curve, t be a parameter variable, and B be the coordinates of a point on the curve. i，n This can be expressed as:

[0046]

[0047] One of the vertical curved shells in the sandwich structure is a shell with a mid-surface formed by stretching a curve 59 along the positive ζ-axis in the ξO′η plane. Curve 59 is a third-order Bézier curve, with one endpoint coinciding with the origin O' and the other endpoint located on the positive ξ-axis. The correspondence between the geometric configuration of the curved quadrilateral cell and curve 59 is shown in Figure 7(a), the correspondence between the geometric configuration of the curved equilateral triangle cell and curve 59 is shown in Figure 7(b), and the correspondence between the geometric configuration of the curved hexagonal cell and curve 59 is shown in Figure 7(c).

[0048] To describe the relative positions of the core layer structure and the honeycomb sandwich panel structure, a right-handed rectangular coordinate system O-xyz is established as the overall coordinate system. Preferably, the honeycomb sandwich panel structure is a cuboid shape. The centroid of the inner surface of one side of the honeycomb sandwich panel structure coincides with the origin O. The long side of the surface panel is parallel to the x-axis, the wide side is parallel to the y-axis, and the z-axis coincides with the normal direction of the surface panel. The coordinate system O'-ξηζ and the coordinate system O-xyz satisfy the following conditions: O' coincides with O, the ξ-axis coincides with the x-axis and is in the same positive direction, the η-axis coincides with the y-axis and is in the same positive direction, and the ζ-axis coincides with the z-axis and is in the same positive direction.

[0049] After obtaining the periodic cells, a linear periodic array of the periodic cells is performed in the ξO′η plane according to the method described above. The number of array cells is defined by the user, but there should be a sufficient number of periodic cells to completely fill the sandwich structure. The reference coordinate system is placed in the global coordinate system according to the relative position relationship described above. The structural part not covered by the surface plate is removed to obtain the sandwich structure composed of the corresponding periodic cells.

[0050] To ensure that the resulting sandwich structure composed of a vertically curved shell has the same weight as the straight-plate sandwich structure, the distance between the two endpoints of curve 59 needs to be adjusted. The method is as follows: Draw a design curve 60 in the ξO′η plane. This design curve 60 is a third-order Bézier curve, and the control point is... The coordinates of the first and last control points Q0 and Q3 are Q0(0, 0) and Q3(L, 0) respectively. straight The coordinates of Q1 and Q2 remain unchanged during the optimization process (0); by changing the coordinates of Q1 and Q2... The shape of the design curve 60 can be changed. Given coordinates Q1 and Q2, the length of the design curve 60 is s. The curve length s is related to L. straigh The ratio of t is k = s / L straight ; Scale the coordinates of all control points in design curve 60 by a factor of k to obtain curve 59, whose control points are: The coordinates of the control points of the two curves satisfy when When k=1, curve 59 becomes a straight line, and the cell side length can be obtained as L. straight The vertical straight-edge sandwich structure.

[0051] The aforementioned design of a curved-edge honeycomb sandwich panel structure with high thermal buckling capacity refers to the structural optimization design of the honeycomb sandwich structure under uniform temperature loads applied to the upper and lower surface plates. Fixed, simply supported, and free displacement boundary conditions can be applied to the upper and lower surface plates and the perimeter of the core layer structure. The optimization design process is as follows:

[0052] (1) Select two control points in the middle of the design curve 60. coordinates These are design variables, and their initial values ​​are set by the designers.

[0053] (2) Establish a curved honeycomb sandwich panel structure model and use the finite element method to perform linear thermal buckling analysis on the current configuration to obtain the linear buckling characteristic value of the model. As the preferred method, the subspace iteration method is selected to calculate the critical buckling characteristic value of the structure.

[0054] (3) Preferably, the multi-island genetic optimization algorithm is used to update the design variables, and the linear buckling characteristic value under different design variable values ​​is calculated using the method described in step 2), and the structure with the maximum critical buckling characteristic value is selected as the optimal design.

[0055] (4) Numerical experiments were conducted on the optimally designed curved honeycomb sandwich panel structure to analyze its nonlinear mechanical response under extreme high-temperature loads. As a preferred method, the first five buckling modes of the curved honeycomb sandwich panel structure were calculated using the subspace method and introduced into the finite element model as initial geometric defects. The nodal coordinates were modified, and the amplitude of the initial geometric defects was one-thousandth of the thickness of the surface plate of the curved honeycomb sandwich panel structure. Subsequently, the thermal displacement of the curved honeycomb sandwich panel structure under uniform temperature load on the upper surface was calculated using the nonlinear finite element method, and the physical responses such as thermal buckling deformation, thermal stress, and thermal strain were calculated. As a preferred method, the Newton-Raphson method was used for nonlinear finite element analysis, and the load-displacement curves and stress cloud diagrams were output.

[0056] As a preferred option, the following optimization parameters were set in the optimization iteration, and numerical experiments were conducted to compare the optimal curved-edge honeycomb sandwich panel structure design with the straight-edge honeycomb sandwich panel structure design under the same weight:

[0057] (1) Preferably, the surface plate of the curved honeycomb sandwich panel structure composed of equilateral triangular cells has a length of a = 200.0 mm, a width of b = 200.0 mm, a distance between the mid-surfaces of the surface plate of h = 10.0 mm, and a thickness of t. surface =2.0mm, the thickness of the vertical plate in the sandwich structure is t core = 2.0mm. Parameter L in design curve 60 straight =25.0mm, the range of coordinate values ​​for intermediate control points Q1 and Q2: The variation range is 0.0 to 25.0 mm; The variation range is -50.0 to 50.0 mm, and the boundary condition is that the four boundaries of the honeycomb sandwich panel structure are fixed.

[0058] Using the above structural optimization method, the coordinates of the control points of curve 59 describing the optimal curved edge configuration are P0(0.0,0.0), P1(7.3,16.5), P2(9.2,-13.3), and P3(32.2,0.0). Figures 8(a)-(b) show a comparison of the thermal buckling modes of the optimal curved edge configuration and a straight-edge honeycomb sandwich panel structure of equal mass under the same boundary conditions and loads. Figure 8(c) shows the curve of the maximum displacement of the structure versus temperature in the nonlinear finite element analysis. The numerical experimental results show that the critical thermal buckling load of the optimal curved edge design is 1777℃, while that of the corresponding straight edge design is 1142℃, with the former being 55% higher than the latter. The critical thermal buckling mode of the optimal curved edge design is the co-occurrence of overall thermal buckling of the honeycomb sandwich structure and local thermal buckling of the high-temperature side surface plate, while the corresponding straight edge design uses local thermal buckling of the high-temperature side surface as the critical buckling mode. In the post-buckling nonlinear analysis, when the temperature of the high-temperature side surface plate reaches 1700℃, the maximum out-of-plane deflection of the optimal curved edge design is 0.4mm, while the maximum out-of-plane displacement of the corresponding straight edge design is 3.2mm, with the former being 82% lower than the latter.

[0059] (2) Preferably, the surface plate of the curved honeycomb sandwich panel structure composed of regular quadrilateral cells has a length of a = 200.0 mm, a width of b = 200.0 mm, a distance between the mid-surfaces of the surface plate of h = 10.0 mm, and a thickness of t. surface =2.0mm, the thickness of the vertical plate in the sandwich structure is t core = 2.0mm. Parameter L in design curve 60 straight =15mm, the range of coordinate values ​​for intermediate control points Q1 and Q2: The variation range is 0.0–15.0 mm. The variation range is -30.0 to 30.0 mm, and the boundary condition is that the four boundaries of the honeycomb sandwich panel structure are fixed.

[0060] Using the above structural optimization method, the coordinates of the control points of curve 59 describing the optimal curved edge configuration are P0(0.0,0.0), P1(11.8,-2.5), P2(11.3,7.5), and P3(17.1,0.0). Figures 9(a)-(b) show a comparison of the thermal buckling modes of the optimal curved edge configuration and a straight-edge honeycomb sandwich panel structure of equal mass under the same boundary conditions and loads; Figure 9(c) shows the curve of the maximum displacement of the structure versus temperature in the nonlinear finite element analysis. The numerical experimental results show that the critical thermal buckling load of the optimal curved edge design is 1590℃, while that of the corresponding straight edge design is 1364℃, with the former being 17% higher than the latter. The critical thermal buckling mode of the optimal curved edge design is the co-occurrence of overall thermal buckling of the honeycomb sandwich structure and local thermal buckling of the high-temperature side surface plate, while the corresponding straight edge design uses local thermal buckling of the high-temperature side surface as the critical buckling mode. In the post-buckling nonlinear analysis, when the temperature of the high-temperature side surface plate reaches 1600℃, the maximum out-of-plane deflection of the optimal curved edge design is 4.5mm, while the maximum out-of-plane displacement of the corresponding straight edge design is 6.0mm, with the former being 25% lower than the latter.

[0061] (3) Preferably, the surface plate of the curved honeycomb sandwich panel structure composed of regular hexagonal cells has a length of a = 200.0 mm, a width of b = 200.0 mm, a distance between the mid-surfaces of the surface plate of h = 10.0 mm, and a thickness of t. surface =2.0mm, the thickness of the vertical plate in the sandwich structure is t core = 2.0mm. Parameter L in design curve 60 straight =10.0mm, the range of coordinate values ​​for intermediate control points Q1 and Q2: The variation range is 0.0–10.0 mm. The variation range is -20.0 to 20.0 mm, and the boundary condition is that the four boundaries of the honeycomb sandwich panel structure are fixed.

[0062] Using the above structural optimization method, the coordinates of the control points of curve 59 describing the optimal curved edge configuration are P0(0.0,0.0), P1(8.0,4.1), P2(4.5,4.8), and P2(11.0,0.0). Figures 10(a)-(b) show a comparison of the thermal buckling modes of the optimal curved edge configuration and a straight-edge honeycomb sandwich panel structure of equal mass under the same boundary conditions and loads; Figure 10(c) shows the curve of the maximum displacement of the structure versus temperature in the nonlinear finite element analysis. The numerical experimental results show that the critical thermal buckling load of the optimal curved edge design is 1532℃, while that of the corresponding straight edge design is 1344℃, with the former being 14% higher than the latter. The critical thermal buckling mode of the optimal curved edge design is the co-occurrence of overall thermal buckling of the honeycomb sandwich structure and local thermal buckling of the high-temperature side surface plate, while the corresponding straight edge design uses local thermal buckling of the high-temperature side surface as the critical buckling mode. In the post-buckling nonlinear analysis, when the temperature of the high-temperature side surface plate reaches 1600℃, the maximum out-of-plane deflection of the optimal curved edge design is 5.6mm, while the maximum out-of-plane displacement of the corresponding straight edge design is 6.7mm, with the former being 20% ​​lower than the latter.

[0063] The curved honeycomb sandwich panel structure described in this embodiment is made of aluminum alloy and can be manufactured using 3D printing technology.

[0064] The embodiments described above are merely illustrative of implementation methods of the present invention and should not be construed as limiting the scope of the present invention. Those skilled in the art can make other modifications and improvements within the scope of the present invention, and these all fall within the protection scope of the present invention. All components not explicitly stated in this embodiment can be implemented using existing technology.

Claims

1. A curved honeycomb sandwich panel structure having high hot bend strength, characterized by, The curved honeycomb sandwich panel structure (1) includes two surface panels (2) and a core layer structure (3) in the middle; the core layer structure (3) is composed of vertical panels arranged periodically in the plane (6) of the core layer. The vertical plate shape is a vertical curved shell (5); the sandwich layer plane (6) is parallel to the direction of the surface plate (2), and the vertical direction is the normal direction of the surface plate; the smallest geometrically repeatable pattern in the periodic arrangement is called a periodic cell (7); The geometric configuration of the sandwich layer structure (3) and its relative position to the honeycomb sandwich panel structure (1) are as follows: Geometric configuration of sandwich structure (3): Establishing a right-handed rectangular coordinate system As a reference coordinate system; a vertical curved shell (5) in the sandwich structure (3) is based on... A curved surface formed by stretching a curve along the positive ζ-axis in a plane is a shell of mid-surface, where one endpoint of the curve is perpendicular to the origin. The two ends coincide, with the other end located on the positive half of the ξ-axis. Relative positions of the sandwich layer structure (3) and the honeycomb sandwich panel structure (1): Establish a right-handed spatial rectangular coordinate system As a global coordinate system; the centroid of the inner surface of one side of the honeycomb sandwich panel structure (1) is parallel to the origin. The surface plate's long side is parallel to the x-axis, its wide side is parallel to the y-axis, and its z-axis coincides with the direction of the surface plate's normal; coordinate system. With coordinate system satisfy and The ξ-axis coincides with the x-axis and has the same positive direction; the η-axis coincides with the y-axis and has the same positive direction; the ζ-axis coincides with the z-axis and has the same positive direction. A complete sandwich structure (3) is obtained from a periodic cell (7) in a planar periodic array; The periodic arrangement specifically refers to the arrangement in the sandwich layer plane in the form of a regular square, a regular hexagon, or an equilateral triangle, wherein: the periodic cells in the regular square arrangement are regular squares, the periodic cells in the regular hexagon arrangement are regular hexagons, and the periodic cells in the equilateral triangle arrangement are six equilateral triangles of the same size, with a common vertex and not overlapping each other. The optimized design method for the curved honeycomb sandwich panel structure with high thermal buckling strength includes the following steps: S1 First, a curve description method is selected to describe the vertical curved shell (5) in the honeycomb sandwich panel structure, wherein the vertical curved shell (5) is a shell with a uniform thickness, formed by stretching the selected curve vertically in the sandwich layer plane along the curved surface as the mid-surface. S2 Secondly, an optimization design model is established, using the coordinates of the control points in the curve description method as design variables, the length of the curved edge and the maximum curvature as constraints, and maximizing the first-order thermal buckling characteristic value of the honeycomb sandwich panel structure as the design objective. S3 Again, uniform temperature loads are applied to the two surface plates of the honeycomb sandwich panel structure, and its nonlinear thermodynamic response is numerically calculated using the finite element method. Finally, in S4, an optimization algorithm is selected to optimize the shape of the vertical curved plate by iteratively updating the coordinates of the control points. This yields the vertical curved shell shape with the maximum thermal buckling load under the constraint conditions, and thus obtains a curved honeycomb sandwich panel structure with optimal thermal bearing capacity.

2. A method of constructing the curved edge honeycomb sandwich panel structure having high thermal buckling strength according to claim 1, characterized by, The construction methods for different types of sandwich layer structures are as follows: To construct a sandwich structure composed of periodic quadrilateral cells: First, take a line located in the coordinate system The vertical curved shell, the first vertical plate (11) satisfies the condition that the mid-surface is perpendicular to the surface of the shell. The plane is perpendicular and the mid-plane is One endpoint of the line of intersection of the planes and the origin Overlapping, the other end is located The positive half-axis; next, the first vertical plate (11) is rotated 90° clockwise around the vertical centerline of its vertical side to obtain the second vertical plate (12), and the second vertical plate (12) is then moved along... The third vertical plate (13) is obtained by translating in the positive direction of the axis, and the translation distance is the distance between the mid-surface of the first vertical plate (11) and the mid-surface of the third vertical plate (13). The distance between the two endpoints of the intersection line of the planes is used to translate the first vertical plate (11) along the negative direction of the η axis to obtain the fourth vertical plate (14). The translation distance is the distance between the mid-surface of the second vertical plate (12) and the... The distance between the two endpoints of the intersection line of the plane, the first vertical plate (11), the second vertical plate (12), the third vertical plate (13), and the fourth vertical plate (14) constitute all the vertical plates of a regular quadrilateral periodic cell (8); finally, the obtained periodic cell (8) is arranged along... In the two directions of the axis and the η-axis, A linear periodic array is constructed in the plane, with the array spacing in both directions being the distance between the mid-surface of the first vertical plate (11) and... The distance between the two endpoints of the intersection line of the plane and the number of arrays are determined according to the actual situation, and finally a sandwich structure composed of regular quadrilateral periodic cells is obtained. To construct a sandwich structure composed of regular hexagonal periodic cells: First, take a line located in the coordinate system The vertical curved shell, the fifth vertical plate (19) satisfies the condition that the mid-surface is perpendicular to the surface. Plane perpendicular, and mid-plane with One endpoint of the line of intersection of the planes and the origin Overlapping, the other end is located The positive half-axis; next, the fifth vertical plate (19) is rotated 120° clockwise around the vertical centerline of its vertical side to obtain the sixth vertical plate (20), the sixth vertical plate (20) is rotated 120° clockwise around the vertical centerline of its vertical side to obtain the seventh vertical plate (21), the seventh vertical plate (21) is rotated 120° clockwise around the vertical centerline of its vertical side to obtain the eighth vertical plate (22), and the eighth vertical plate (22) is rotated clockwise around the vertical centerline of its vertical side. A ninth vertical plate (23) is obtained by rotating 120° clockwise around the vertical centerline of its vertical side to obtain a tenth vertical plate (24). The fifth vertical plate (19), the sixth vertical plate (20), the seventh vertical plate (21), the eighth vertical plate (22), the ninth vertical plate (23), and the tenth vertical plate (24) constitute all the vertical plates of a periodic cell (9) arranged in a regular hexagon. Finally, the obtained periodic cell (9) is arranged along... shaft and with A straight line with an included angle of 30° to the axis, in A linear periodic array is constructed in the plane, with the array spacing being the mid-surface of the fifth vertical plate (19) and... Three times the distance between the two endpoints of the line of intersection of the planes The number of arrays is determined based on actual conditions, and the final result is a sandwich structure composed of regular hexagonal periodic cells. To construct a sandwich structure composed of periodic cells of an equilateral triangle: First, take a line located in the coordinate system The vertical curved shell, the eleventh vertical plate (37) satisfies the condition of the mid-surface and The plane is perpendicular and the mid-plane is One endpoint of the line of intersection of the planes and the origin Overlapping, the other end is located The positive half-axis; next, the eleventh vertical plate (37) is rotated 120° clockwise around the vertical centerline of its vertical side to obtain the twelfth vertical plate (38), the twelfth vertical plate (38) is rotated 120° clockwise around the vertical centerline of its vertical side to obtain the thirteenth vertical plate (39), the thirteenth vertical plate (39) is rotated 120° clockwise around the vertical centerline of its vertical side to obtain the fourteenth vertical plate (40), the fourteenth vertical plate (40) is rotated 120° clockwise around the vertical centerline of its vertical side to obtain the fifteenth vertical plate (41), and the fifteenth vertical plate (41) is rotated 120° clockwise around the vertical centerline of its vertical side to obtain the sixteenth vertical plate. To obtain the seventeenth vertical plate (54), rotate the sixteenth vertical plate (37) 60° clockwise around the vertical centerline of its vertical side to obtain the seventeenth vertical plate (54). Arrange the seventeenth vertical plate (54) in an equidistant circular array with the vertical centerline of its vertical side as the central axis, with a total array size of 6, to obtain the vertical plate combination (43). The eleventh vertical plate (37), twelfth vertical plate (38), thirteenth vertical plate (39), fourteenth vertical plate (40), fifteenth vertical plate (41), sixteenth vertical plate (42), and vertical plate combination (43) constitute all the vertical plates of a periodic cell (10) arranged in an equilateral triangle. Finally, arrange the obtained periodic cell (10) along... Axis and A straight line with an included angle of 30° to the axis, in A linear periodic array is constructed in the plane, with the array spacing being the mid-surface of the eleventh vertical plate (37) and... Three times the distance between the two endpoints of the line of intersection of the planes The number of arrays is determined based on actual conditions, ultimately resulting in a sandwich structure composed of equilateral triangular periodic cells. The geometric description parameters of the honeycomb sandwich panel structure are as follows: the two surface plates (2) have the same size, and the vertical plates in the sandwich layer structure have a uniform thickness; the distance between adjacent corner points of the periodic cells formed by the vertical curved shell (5) is... The distance between adjacent corner points of the periodic cell formed by the vertical straight-edge plate (4) is ,satisfy Where k is the mid-surface of the vertical curved shell (5) and The ratio of the length of the line of intersection of two planes to the distance between the two endpoints of the line of intersection.

3. A method of constructing a curved honeycomb sandwich panel structure having high buckling strength according to claim 2, wherein The curved honeycomb sandwich panel structure is prepared by autoclave process, molding process, vacuum bag process or 3D printing technology; the matrix material is selected from aluminum alloy, titanium alloy or stainless steel.

4. An optimized design method for a curved honeycomb sandwich panel structure with high thermal buckling strength as described in claim 1, characterized in that, Includes the following steps: S1 First, a curve description method is selected to describe the vertical curved shell (5) in the honeycomb sandwich panel structure, wherein the vertical curved shell (5) is a shell with a uniform thickness, formed by stretching the selected curve vertically in the sandwich layer plane along the curved surface as the mid-surface. S2 Secondly, an optimization design model is established, using the coordinates of the control points in the curve description method as design variables, the length of the curved edge and the maximum curvature as constraints, and maximizing the first-order thermal buckling characteristic value of the honeycomb sandwich panel structure as the design objective. S3 Again, uniform temperature loads are applied to the two surface plates of the honeycomb sandwich panel structure, and its nonlinear thermodynamic response is numerically calculated using the finite element method. Finally, in S4, an optimization algorithm is selected to optimize the shape of the vertical curved plate by iteratively updating the coordinates of the control points. This yields the vertical curved shell shape with the maximum thermal buckling load under the constraint conditions, and thus obtains a curved honeycomb sandwich panel structure with optimal thermal bearing capacity.

5. The optimization design method according to claim 4, characterized in that, The curve shape in step S1 is described by a multi-segment straight line, trigonometric function curve, polynomial curve, interpolation curve or spline curve, and can reproduce the vertical curved shell (5) under reasonable parameter settings.

6. The method of optimizing design of claim 4, wherein, The optimization algorithm in step S4 is selected from genetic algorithm, particle swarm optimization, simulated annealing algorithm, descent simplex method, sequential quadratic programming method or moving asymptote method.

7. The method of optimizing design of claim 4, wherein, When performing linear thermal buckling eigenvalue analysis on the honeycomb sandwich panel structure using the finite element method, the finite element algorithm used is selected from the Lanzos method, the subspace method, or the inverse iteration method.

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