This paper discusses the stresses developed in a thin-walled pressure vessels. Pressure vessels (cylindrical or spherical) are designed to hold gases or liquids at a pressure substantially higher than the ambient pressure. Equations of static equilibrium along with the free body diagrams will be used to determine the normal stresses 1 σ in the circumferential or hoop direction and 2 σ in the longitudinal or axial direction. A case study of internal pressure developed in a soda can was determined by measuring the elastic strains of the surface of the soda can through strain gages attached to the can and connected to Strain indicator Vishay model 3800.

In this paper, we suggest a shortest trajectory planning algorithm for wheeled mobile robots with constraints; bounded curvature paths and moving forwerd only motion of robots; for example, aerial vehicles or moving forward car-like mobile robots. The main purpose of the paper is to find the optimal shortest path between a starting point and a goal point with constraints. Based on the Dubins' car and the shortest path synthesis [I], a geometrical approach is addressed to solve the problem. First we define patterns of existed shortest paths on the origin of the starting point and the goal point. Second, an arbitrary given configuration is compared with one of the patterns and the motion of the vehicle i s determined left turn or right turn. The proposed method is suitable for rapid decisions. Simulation results are provided to demonstrate the efficacy of the approach.

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