Recent advances in artificial intelligence have established physics-informed neural networks (PINNs) as a transformative paradigm for solving complex mechanics problems. This paper presents a unified PINN framework that comprehensively addresses three fundamental problems in functionally graded materials (FGMs) cylinder analysis: forward prediction, inverse identification, and stress optimization. The proposed methodology embeds physical laws including constitutive relations and equilibrium equations into a deep learning architecture, yielding a meshless solution with rigorous mechanical consistency. For forward problems, the framework accurately predicts displacement and stress fields under arbitrary material gradations. The inverse solution enables simultaneous identification of gradient parameters and Young's modulus with high precision. For optimization challenges, the architecture introduces coupled displacement-material networks with exact boundary condition enforcement and a multi-objective loss function that achieves stress minimization while maintaining mechanical equilibrium. Numerical results demonstrate three key capabilities: (1) PINN achieves excellent agreement with reference solutions in forward analysis of FGMs cylinders arbitrarily varying material properties, (2) the inverse problem yields accurate identification of both the gradient parameter and the varying Young’s modulus, even under measurement noise, and (3) the optimization problem outperforms conventional power-law distributions by reducing peak von Mises stress while preserving exact mechanical consistency. The integrated framework combines the computational efficiency of parametric methods with the design freedom of free-form optimization, offering an end-to-end solution from problem formulation to sensitivity analysis. This research establishes PINNs as a versatile tool for FGMs design, providing both theoretical foundations and practical methodologies for engineering applications ranging from mechanical analysis to optimal material design.
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