# Static and Dynamic Analysis of Non-Pneumatic Tires Based on Experimental and Numerical Methods
## 1 Introduction  
The tire is one of the most important components of vehicles, being responsible for a large set of functions: connecting the transmission to the ground with the forces necessary for motion, supporting the vehicle loads, ensuring the directionality of the vehicle by enabling steering in the driver's desired trajectory, and improving passengers' comfort by contributing to the vehicle suspension [1]. The pneumatic tire design is the market leader because of four main advantages over the NPT used in the past: lower energy loss on rough surfaces, lower radial stiffness, lower contact pressure, and lower mass [2]. Nevertheless, relying upon the containment of pressurized air, it is susceptible to be punctured and eventual burst may cause fatal accidents. Moreover, the air pressure inside the tire should be kept in a proper range, representing a potential discomfort for its users: the loss of pressure--caused by the leaking around the wheel rim and by the oxygen absorption in rubber--leads the tire to flatten in the contact area, increasing wear and fuel consumption. To overcome these disadvantages, researchers developed an innovative concept, the Non-Pneumatic tire (NPT), that does not require compressed air to work [3, 4]. This concept was designed to own the key characteristics of the pneumatic tire, bringing advantages such as the absence of maintenance for proper internal pressure, a wider range of application in fields where the pneumatic tire struggles--such as the military and agricultural fields, and the recyclability of its components, so its production can be environmentally friendlyand more efficient in the use of resources [5]. A proper definition of the NPT is reported in the code of Federal regulations of the United States of America [6], where it is defined as a mechanical device that transmits the vertical load and tractive forces from the roadway to the vehicle, generates the tractive forces that provide the directional control of the vehicle, and does not rely on the containment of any gas or fluid for providing those functions. Although this definition does not specify a structure, an NPT is generally composed of the following elements: a rigid hub connected to an annular outer ring, called shear band or shear beam, by means of flexible polyurethane elements called spokes and a tread. Since the rigid hub and the tread explicate the exact same functions of the ones in the pneumatic tire, the peculiar elements are the shear beam and spokes. The shear beam is constituted by two inextensible membrane layers separated by a relatively low modulus elastic layer [2]. For what concerns the spokes, researchers and tire makers developed a huge variety of structures that differ from each other in geometries and material characteristics. Several comparative studies were conducted to evaluate the effects of different spokes' structures on performance parameters. [PERSON] et al. [7] compared three different concepts to investigate the influence of spokes structures on the contact pressure, radial stiffness, and stresses. Each concept was also modeled with and without the shear band to highlight its influence. Results showed that the presence of the shear band has a great influence on the deformed shapes of the spokes and on the contact pressure distribution. The objects of the aforementioned work were also modeled using finite element (FE) method by [PERSON] et al. [8] to perform a static radial test with the aim of assessing the effects of different spoke structures on vertical displacement of the rim, deformation shape, stress distribution, and contact pressure. [PERSON]. [PERSON] et al. [9] introduced a model of NPT with natural rubber material instead of synthetic one for the tread. Moreover, a comparison study was conducted on various structures such as the honeycomb, plate spokes, triangular, and diamond shape to identify the structure that exhibits the least deformation. The diamond shape was found to perform better. [PERSON] et al.