Stress distribution optimization in dished ends of cylindrical pressure vessels

The standard geometries of dished ends of cylindrical pressure vessels were developed at the beginning of the last century. Among them, there are ellipsoidal and torispherical geometries characterized by disadvantageous stress distribution, which is the primary determinant when designing shell structures. This paper focuses on shape optimization of dished ends with the depth equivalent to the standard ones, with the intent to minimize the maximum von Mises stress in a cylindrical pressure vessel. Referring to the Bezier curve (BC), a unique geometry of arbitrary order is developed to describe the parametric shape of the dished end. The optimization is implemented using two approaches. Initially, the fitness function is obtained analytically through the membrane theory (MT). A deterministic optimization algorithm is adopted to complete the procedure. Further, the optimization method is modified to obtain the fitness function using the finite element method (FEM). To process the solution, a genetic algorithm (GA) is employed. The obtained improvement of stress distribution is compelling while maintaining the manufacturability of the shell structure.

Automated summary

This paper focuses on the shape optimization of dished ends in cylindrical pressure vessels to minimize the maximum von Mises stress. A unique geometry is developed using the Bezier curve to describe the parametric shape of the dished end. The optimization is implemented using both membrane theory and finite element method, with deterministic optimization algorithm and genetic algorithm.