Probabilistic Thermo-Viscoelastic Response of a Composite Plate Under Parabolic Temperature Distribution Using a Non-linear Finite Difference Approach

Abstract: This study undertakes a stochastic exploration into the thermo-viscoelastic behavior of a composite plate subjected to a parabolic temperature profile. Our methodology meticulously scrutinizes the temporal interaction between material attributes and thermal impacts, which is pivotal for sophisticated engineering implementations. The presented model integrates time-variant relaxation moduli and thermal expansion coefficients into a holistic framework designed to portray the plate's dynamic properties. A detailed development of the system’s potential energy, encompassing both elastic strain energy and thermal work, is delineated. Trigonometric basis functions are employed to estimate the stress and displacement distributions. This technique precisely captures the interdependent thermo-mechanical and viscoelastic reaction of the plate, emphasizing the influence of thermal expansion and time-dependent stresses. The unknown factors of the basis functions are derived through an optimization procedure, which facilitates a refined assessment of the system's behaviour. This probabilistic methodology is paramount in comprehending how changes in temperature, time, and material characteristics affect the plate’s structural soundness. Our investigation provides a comprehensive perspective into the dynamic response of composite plates when exposed to time-variant thermal and mechanical loads. The methodology incorporates a Non-linear Finite Difference Approach, which is crucial for understanding the time-dependent effects in the thermo-viscoelastic response. This detailed study allows us to consider uncertainties in material properties and environmental conditions, thereby contributing to more robust designs. The analysis of thermal effects, along with material attributes, is achieved using a robust numerical framework that effectively models the time-varying response of the composite plate.