Mathematical and numerical analysis of composite circular membranes subjected to isothermal bulging pressure

Under thermo-mechanical loading via isothermal bulging pressure (IBP), composite circular membranes (CCMs) exhibit highly temperature-dependent mechanical behavior, characterized by distinct variations in Young’s modulus, yield strength, and residual stress. Subjecting the membranes to varied pressure and temperature profiles induces controlled deformation, enabling the characterization of composite material properties particularly for components deployed in microelectromechanical systems (MEMS) operating under extreme conditions. This study investigates the thermo-mechanical response of CCMs fabricated from basalt fiber-reinforced polymer (BFRP) subjected to thermal and mechanical stress utilizing the IBP methodology, focusing on diverse engineering and bioengineering sensor applications. In the experimental protocol, the membrane is initially pre-stressed and rigidly clamped between two fixtures. The application of a differential pressure subsequently induces out-of-plane bending. To characterize these thermo-mechanical phenomena, an analytical framework based on the IBP approach is developed to describe membrane behavior across both elastic and plastic regimes. Concurrently, a finite element model (FEM) is implemented to evaluate the analytical results and assess the specific influence of initial pre-stressing on the pressure tests. To comprehensively map the mechanical response under load, parametric variations in membrane thickness and constituent material configurations are systematically evaluated. Furthermore, the temperature dependence of the material properties is analyzed to isolate its effect on the overall thermo-mechanical response. The relative error ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>E</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>r</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> ) for the maximum deflection ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>w</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">max</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> ) between the analytical and numerical results remains below 0.3%. The analytical computations and numerical simulations are executed using MATLAB, the MATLAB PDE Toolbox, and ANSYS. Finally, the findings demonstrate strong agreement with established empirical data from the literature, thereby validating the reliability, accuracy, and robust applicability of the proposed identification technique.