The paper focuses on the nonlinear vibration of functionally graded graphene nanoplatelet reinforced composite doubly curved shallow shells resting on elastic foundations. The graphene nanoplatelet reinforced composites are assumed to be distributed uniformly and functionally graded through the thickness. The material properties are assumed to be temperature-dependent and are estimated through the Halpin–Tsai micromechanical model, while the Poisson’s ratio, density mass, and thermal expansion are implemented by the rule of mixtures. The mathematical formulation is developed based on the classical shell theory and Von Karman-Donnell geometrical nonlinearity assumption. The dynamical responses of a simply supported functionally graded-graphene nanoplatelet reinforced composite doubly curved shallow shells are obtained by employing the Airy’s stress function and the Galerkin’s method. The responses of nonlinear vibration as time history, frequency-amplitude curve, phase plane graphs, and Poincare maps are carried out in this paper. In addition, the effects of the environment, graphene nanoplatelets weight fraction, graphene nanoplatelets distribution patterns, and thickness-to-length ratio are scrutinized. The obtained results are also compared and validated with those of other studies.

In this study, we utilized digital twin technology in combination with genetic algorithms to optimize human–robot cooperation in a miniature light bulb assembly production line. First, the digital twin was used to find the robot’s motion trajectory; a digital replica of the assembly system and human was created by combining sensors that track the position and activity characteristics of the human in the workspace, which helped to prevent human–robot conflicts. Then, a multi-adaptive genetic algorithm was applied to calculate optimal ergonomics and create a worker’s movement schedule. To ensure continuous operation and no shortage of materials, the worker must observe and move to the input conveyor and material pallets to supply materials to the system. It aimed to provide more input materials for the assembly line while allowing the worker’s task to take place in parallel with the robotic assembly operation. The algorithm was designed to reduce the number of moves required to obtain materials and to ensure that the robot always had enough materials to assemble along the defined trajectory, thus, saving labor and optimizing the manufacturing process. The combination of a digital twin and multi-adaptive genetic algorithm optimized the robot’s movement path and the number of movements performed by the human operator in parallel.

The A* algorithm is a cornerstone in mobile robot navigation. However, the traditional A* suffers from key limitations such as poor path smoothness, lack of adaptability to dynamic environments, and high computational costs in large-scale maps. This review presents a comprehensive analysis of 20 recent studies (2020–2025) on improved A* variants and their hybrid integrations with complementary algorithms. The improvements are categorized into two core strategies: (i) geometric and structural optimization, heuristic weighting and adaptive search schemes in A* algorithm, and (ii) hybrid models combining A* with local planners such as Dynamic Window Approach (DWA), Artificial Potential Field (APF), and Particle Swarm Optimization (PSO). For each group, the mathematical formulations of evaluation functions, smoothing techniques, and constraint handling mechanisms are detailed. Notably, hybrid frameworks demonstrate improved robustness in dynamic or partially known environments by leveraging A* for global optimality and local planners for real-time adaptability. Case studies with simulated grid maps and benchmark scenarios show that even marginal improvements in path length can coincide with substantial gains in safety and directional stability. This review not only synthesizes the state of the art in A*-based planning but also outlines design principles for building intelligent, adaptive, and computationally efficient navigation systems.