Interlaced three-dimensional geometric structure of parametric curves for aerospace applications with high structural strength and vibration reduction.

Three-Dimensional Intertwined Geometric Structure: State of the Art and Applications

1. Introduction

The development of lightweight, high-strength structures capable of vibration dissipation has been a central focus in modern aerospace engineering. With increasing demands for performance and efficiency in satellites, drones, aircraft, and space probes, conventional structural solutions such as metallic trusses, honeycomb panels, and composites present significant limitations, particularly regarding stress distribution, mass reduction, and vibration control.

In this context, the study of a three-dimensional intertwined structure based on parametric curves is proposed, integrating high mechanical strength with the efficiency of additive manufacturing, offering innovative solutions for aerospace engineering.

2. State of the Art

Conventional aerospace structures include:

• Metallic trusses: efficient in load transfer, but increase mass and concentrate stresses at critical points.

• Honeycomb panels: lightweight and stiff, but limited in vibration dissipation and geometric adaptability.

• Orthogonal structural grids: easy to model and manufacture, yet perform poorly under multidirectional loading.

• Advanced composites: high strength and low weight, but susceptible to micro-crack propagation and manufacturing complexity.

Organizations such as NASA and the European Space Agency (ESA) have explored alternative geometries, including lattice structures and metamaterials, to reduce mass and improve stress distribution. However, solutions based on three-dimensional intertwined parametric curves, capable of creating multiple spatially distributed intersections, remain largely unexplored.

3. Development of the Proposed Structure

The structure under study consists of a three-dimensional network formed by intertwined parametric curves, where each element follows a continuous trajectory defined by equations of the type:

{x(t)=Acos⁡(t)+Bcos⁡(kt)y(t)=Csin⁡(t)+Dsin⁡(kt)z(t)=Esin⁡(mt)\begin{cases} x(t) = A \cos(t) + B \cos(k t) \\ y(t) = C \sin(t) + D \sin(k t) \\ z(t) = E \sin(m t) \end{cases}⎩⎨⎧x(t)=Acos(t)+Bcos(kt)y(t)=Csin(t)+Dsin(kt)z(t)=Esin(mt)

• A, B, C, D, E: geometric amplitudes defining the curve scale.

• k, m: frequency parameters, determining the degree of intertwining.

The multiple intertwining creates structural intersection points, which act as load transfer elements, increasing the overall stiffness of the network and enabling isotropic stress distribution.

Key features:

• Efficient load distribution across any point of the structure.

• Mechanical vibration dissipation due to multiple interconnections.

• Structural mass reduction compared to traditional solutions.

• Compatibility with additive manufacturing technologies, such as metal 3D printing, selective laser sintering (SLS), and fused filament fabrication (FFF).

4. Applications of the Structure

The structure is directly applicable in aerospace and high-engineering systems, including:

• Satellites: internal structural panels and lightweight load-bearing supports.

• Drones: structural arms and mounts for sensors or cameras.

• Aircraft: lightweight internal components, fuselage reinforcements, and wing supports.

• Space vehicles and probes: internal modules, instrument supports, and vibration damping systems.

Moreover, it can be integrated into modular platforms, reusable spacecraft, and systems where mass reduction and vibration resistance are critical.

5. Conclusion

The proposed three-dimensional intertwined parametric curve structures represent a significant advancement over the state of the art. Their geometry enables:

• Structural mass reduction without compromising strength.

• Isotropic stress distribution in multiple directions.

• Efficient vibration dissipation.

• Flexibility for manufacturing with metals, composites, or advanced polymers.

These features pave the way for the next generation of lightweight, resilient, and adaptable aerospace structures, meeting the growing demands for efficiency and performance in the sector.

Three-dimensional geometric structure interlaced with parametric curves for aerospace applications with high structural strength and vibration reduction.  
Field of the invention  
[001] The present invention falls within the field of aerospace engineering, more specifically in the development of lightweight three-dimensional structures with high mechanical strength intended for application in structural components of aerospace vehicles.  
[002] The invention particularly refers to a three-dimensional interlaced geometric structure formed by parametric curves, capable of distributing structural loads and reducing mechanical vibrations in components used in aircraft, satellites, spacecraft, drones, and other aerospace systems.  
[003] The invention is also related to the fields of structural engineering, additive manufacturing, and advanced materials, being especially suitable for fabrication through three-dimensional printing processes of metals or structural polymers.  
[004] Additionally, the proposed structure may be applied in systems that require a high strength-to-weight ratio, such as structural supports for scientific instruments, internal satellite structures, aircraft structural panels, and structural components of unmanned aerial vehicles.  
[005] Thus, the present invention lies at the intersection of the fields of aerospace engineering, materials engineering, and the design of structures optimized for additive manufacturing, proposing a new geometric architecture intended to improve the structural performance of aerospace components.  

Background of the Invention  
[001] Structures used in the aerospace industry traditionally employ geometric configurations based on linear trusses, honeycomb-type panels, and orthogonal reinforcement structures manufactured from metallic alloys or composite materials. Such structures are widely used in structural components of aircraft, satellites, and spacecraft due to their ability to withstand mechanical loads with a relative reduction in structural mass.  
[002] In recent years, advances in the fields of additive manufacturing and materials engineering have enabled the development of more complex three-dimensional structures, including cellular geometries and structural metamaterials capable of exhibiting mechanical properties superior to traditional structures. These structures seek to optimize the relationship between mechanical strength and structural mass, a fundamental characteristic for aerospace applications.  
[003] However, many of these solutions still present relevant limitations, such as stress concentration at specific structural points, low capacity for dissipating mechanical vibrations, and geometric restrictions related to traditional manufacturing methods. Furthermore, structures based exclusively on linear or repetitive geometries may exhibit anisotropic structural behavior, reducing their efficiency in multidirectional loading situations.  
[004] Additionally, in aerospace environments, structural components are subjected to severe conditions of vibration, acceleration, and thermal variations, especially during launch phases or orbital maneuvers. Under such conditions, conventional structures may exhibit structural fatigue or propagation of undesirable vibrations, compromising the stability of sensitive instruments or onboard systems.  
[005] Thus, there remains a need to develop new structural architectures capable of providing better load distribution, greater vibration dissipation, and a high strength-to-weight ratio, without significantly increasing the structural mass of the system.  
[006] The present invention proposes a three-dimensional geometric structure based on interlaced parametric curves, forming a spatial structural network with multiple intersection points distributed throughout the structural volume. This architecture allows mechanical loads to be distributed more homogeneously throughout the structure, reducing stress concentration and increasing the overall strength of the component.  
[007] Unlike traditional structures based on linear elements, the proposed structure uses continuous curved elements defined by parametric functions, which makes it possible to create more efficient structural paths for load transfer. This configuration also contributes to improving the dissipation of mechanical vibrations, since the multiple structural intersections act as points of redistribution of vibrational energy.  
[008] The structure described in the present invention is particularly suitable for manufacturing through additive manufacturing processes, enabling the production of complex geometries that would be difficult or impossible to obtain through traditional manufacturing methods.  
[009] As a result, the invention presents significant technical advantages compared to the state of the art, including better distribution of structural stresses, greater capacity for dissipating mechanical vibrations, and potential reduction of structural mass in aerospace applications.  
[010] In this way, the present invention offers an innovative technical solution to the problem of developing lightweight and resistant structures for aerospace applications, being particularly suitable for structural components of satellites, spacecraft, aircraft, and unmanned aerial vehicles.

Description of the Invention  
[002] The present invention relates to an interlaced three-dimensional geometric structure formed by parametric curves, intended for application in structural components of aerospace systems. The proposed structure is designed to offer a high strength-to-weight ratio, optimized distribution of mechanical stresses, and greater capacity for dissipating structural vibrations.

[003] The structure is composed of a set of curved structural elements arranged three-dimensionally in space, which interconnect to form a spatial structural network. Each structural element follows a geometric trajectory defined by continuous parametric functions, enabling the creation of an interlaced three-dimensional mesh with multiple points of intersection.

[004] In a preferred embodiment, the structural curves are described by continuous parametric equations of the general form:

x(t) = f(t)  
y(t) = g(t)  
z(t) = h(t)

where *t* represents the curve path parameter and the functions *f(t)*, *g(t)*, and *h(t)* define the spatial coordinates of the structural element.

[005] In a specific configuration, the curves may be described by trigonometric functions, such as:

x(t) = A cos(at)  
y(t) = B sin(bt)  
z(t) = C sin(ct)

where *A*, *B*, and *C* represent geometric amplitudes and the parameters *a*, *b*, and *c* define the spatial periodicity of the curves.

[006] The use of these parametric functions makes it possible to generate continuous three-dimensional structures that interlace to form a spatial structural support network. This configuration allows mechanical forces to be distributed along multiple structural paths, reducing stress concentrations at specific points of the structure.

[007] In one embodiment, the structure may be composed of multiple parametric curves interconnected with each other in different spatial orientations. These curves may intersect or approach one another, forming structural interaction points where redistribution of mechanical loads occurs.

[008] In another embodiment, the density of the structural network may vary along the structure, making it possible to adjust the distance between the structural elements according to specific requirements for mechanical strength or reduction of structural mass.

[009] The proposed structure may be manufactured through different industrial processes, including additive manufacturing methods such as three-dimensional printing of metals or structural polymers, selective laser sintering, selective laser melting, or fused material deposition.

[010] Materials suitable for manufacturing the structure include, but are not limited to:  
aerospace aluminum alloys  
titanium alloys  
carbon fiber–reinforced composite materials  
high-strength structural polymers.

[011] In aerospace applications, the structure may be used in different structural components, such as internal satellite supports, structural arms for sensors, solar panel supports, internal drone structures, and aircraft structural panels.

[012] In one specific application, the structure may be integrated into the internal structure of satellites or spacecraft with the purpose of supporting sensitive scientific instruments. In this case, the interlaced three-dimensional network contributes to reducing structural vibrations generated during launch or operational phases.

[013] In another application, the structure may be used as a structural element of arms or supports in unmanned aerial vehicles, allowing the reduction of total structural weight without compromising the mechanical strength of the system.

[014] The parametric geometry of the structure allows its shape to be adapted for different dimensions and structural requirements, enabling the adjustment of geometric parameters such as amplitudes, periodicity, and the number of structural curves used in the three-dimensional network.

[015] Thus, the structure described in the present invention constitutes a new structural architecture capable of offering better distribution of mechanical stresses, greater structural strength, and improved vibration dissipation compared to conventional structures based on linear elements or orthogonal geometries.

[016] Therefore, the invention provides an efficient technical solution for the development of lightweight and strong structures for aerospace applications, which may be implemented at different scales and geometric configurations according to the specific requirements of each application.