Design and Optimization Study of Shell Structures Made of Advanced Materials Under Different Types of Loadings

Abstract

The ongoing advancement in technology leads to increasingly intricate projects, which are more computationally expensive. Shell geometries present additional complexities, including varying curvature and thickness, which can render the formulation and implementation of shell elements more challenging than simpler beam and plate elements. Moreover, they often demand higher computational resources and more sophisticated numerical techniques to accurately capture their behavior, resulting in increased computational cost and complexity. Additionally, the development and validation of shell elements entail extensive experimental and numerical testing, potentially limiting the availability of accurate and reliable formulations compared to beam and plate elements. Lastly, the application of shell elements is typically more specialized and specific to certain industries or engineering disciplines, leading to a narrower research focus compared to the broader applicability of beam and plate elements across various fields. In recent years, the p-version of the finite element method has gained prominence due to its higher accuracy and faster convergence rates compared to traditional methods, requiring fewer degrees of freedom for accurate results. It provides better representation of complex geometries, increased flexibility in mesh adaptation, and reduced spurious oscillations in solutions, making it a valuable tool for engineering simulations. By leveraging the thick shell theory, the p-version of the finite element method is combined with the third-order shear deformation theory (TSDT) to develop a new type of p-version shell element. A computer code based on this element type has been developed, tested, and successfully validated. The code’s performance and robustness were assessed through the analysis of a wide range of shell structures exhibiting free vibration, bending, and thermal buckling behavior, isotropic and bidirectional functionally graded materials, and arbitrary geometrical shapes. The mathematical formulation, code structure, as well as results, are presented in the following sections.