Multilayer Inhomogeneous Modeling for Enhanced Stress Prediction in Rotational Functionally Graded Spherical Shells

In recent years, functionally graded materials (FGMs) have sparked significant interest because they can gradually shift their properties across their structure. Unlike traditional composite materials, which are uniformly distributed throughout the overall structure, FGMs have a smooth transition in composition. This allows engineers to create materials that can be fine-tuned for specific areas, which is especially useful in industries like aerospace, automotive, and civil engineering, where materials face intense thermal and mechanical stress. Despite these advantages, however, it’s still challenging to accurately predict how FGMs will behave under these tough conditions. One of the biggest issues is the inhomogeneous nature of FGMs, particularly in components like spherical shells with rotation effect. Traditional models tend to simplify these changes assumptions, making it difficult to capture the full complexity of FGMs. As a result, engineers may struggle to predict and manage stress concentrations, especially in rotating components. To tackle these challenges, Dr. Jun Xie, PhD candidate Hui Li, Professor Fengjun Li, and Professor Pengpeng Shi from Ningxia University developed a new approach, which they shared in a recent paper published in Composite Structures. Their novel model, known as a multilayer heterostructure inhomogeneous model, focuses on functionally graded spherical shells that operate under rotation effect. Each radial layer in this model is given its own set of properties that vary continuously through the thickness of the material. By using this multilayer approach, the team aimed to more precisely capture the gradual changes in material properties, using mathematical functions to approximate each layer’s characteristics. Further analytical solutions to the problem are derived. This study factors in changes in elasticity, density, and other attributes across the layers—details that are often oversimplified or left out in traditional FGMs solution models.

To test how well their model could predict stress distribution, the researchers ran a series of numerical simulations on spherical shells. The rotating FGMs spherical shell is divided into multiple sublayers, and they attempted to approximate elastic modulus and density of rotating spherical shells by with various power functions to the next. For each single sublayer, the analytical solutions include two undetermined constants, which can be obtained from the boundary and continuity conditions. This approach helped them to get an analytical solution to the FGMs spherical shell for arbitrarily varying material properties. They found that as they increased the number of layers in the model—especially with more than 15 layers—the accuracy of the stress distributions improved noticeably. The model managed to overcome the typical oscillations in circumferential stress that are often seen in traditional multilayer heterostructure homogeneous models for FGMs structures, offering a much more stable and realistic view of how stress is distributed. The authors also looked at how different boundary conditions influenced their model’s accuracy. They discovered that the model’s flexibility allowed them to replicate a range of real-world constraints, like fixed or free boundaries, with much greater precision. In addition, FGMs structures optimize performance by adjusting the composition of materials in the structure, which can be achieved by adjusting the volume fraction index parameter. This ability to adjust and customize at such a detailed level showed the model’s potential for real-world engineering applications, where materials often need to perform consistently under various gradual changes in material properties.

In conclusion, the new study of Ningxia University researchers really breaks new ground in the way we understand and design FGMs structures, especially for applications where these structures are under rotation effect. Engineers have long grappled with the challenge of predicting how FGMs behave since these materials don’t have fixed properties throughout—they change gradually in a particular direction. Traditional models tend to oversimplify things, which leaves a lot of guesswork. This new model, however, takes a new layered approach, capturing the nuances of FGMs with much greater accuracy. We believe one of the most useful aspects of this study is how it brings practicality into focus. The model isn’t just theoretical—it offers engineers a clear way to make fine-tune material composition adjustments to things like material composition and understand the distribution of stress in FGM structures. This ability to adjust details with precision means engineers can strike the perfect balance between strength and flexibility in the final design. The model also tackles a common flaw in older FGMs multilayer heterostructure homogeneous models: circumferential stress oscillations, which create weak points that can lead to cracks or failures. By smoothing out these stress concentrations, this new approach not only boosts the reliability of the material but also extends its life, which is a huge win in high-stakes fields where durability is key. What’s also impressive about this model is its flexibility. Engineers can design FGMs that are precisely suited to the needs of each specific application. And, since this approach allows for more accurate material use, it can help reduce waste and cut costs, which makes high-performance designs both more efficient and accessible. In short, this model doesn’t just make FGMs stronger and safer—it makes advanced, sustainable engineering solutions more within reach.