Exploration of higher-order Thermo-Elastic Responses in 2-D Functionally Graded Panels in Turbine Blades through Crank-Nicolson Method

This study addresses the essential limitations of conventional functionally graded materials (FGMs) in justifying thermal distribution challenges employing the Crank-Nicolson heat conduction method. Conventional FGMs exhibit uniform composition on all outer surfaces, proving insufficient for machine elements with multidirectional temperature variations. To overcome this, the study introduces two-dimensional functionally graded materials (2D-FGM), characterized by material properties varying in two directions. The aim is to investigate and enhance the understanding of thermal stresses in panels, contributing to advancements in aerospace engineering for optimized structural performance and longevity. The research investigates FGMs in plate form with in-plane compositional variations for in-plane heat fluxes. The study focuses on challenges associated with thermal gradient problems in conventional FGMs and the potential of 2D-FGM as a solution. Numerical simulations reveal the effectiveness of 2D-FGM in reducing thermal stresses, with temperature variations in the range of \(\:300\:K\) to \(\:600\:K\). This study investigates thermo-mechanical behavior in functionally graded plates, revealing a reciprocal relationship between thermal conductivity and metallic content at \(\:n=0.5\). A thermal loading cycle (q _max = \(\:400\:kW/{m}^{2}\) to q _min \(\:=\:200\:kW/{m}^{2}\)) is employed, and Model Validation examines temperature variations (\(\:1000K\) to \(\:2000K\)). Transient temperature distribution is explored using Explicit and Crank-Nicolson methods. The research endeavors to offer valuable insights into advanced materials and their application in engineering, particularly in aerospace engineering, where precise thermal stress management is critical for the optimal structural performance of turbine blade panels.