Nonlinear pressure vessel stress analysis using the optimum programming approach

Abstract

T optimum programming technique was first developed by Bliss. Typical uses of the technique are found in Refs. 2 and 3. In the optimum programming technique, systems behavior is defined through a set of nonlinear ordinary differential equations of the first order. The independent variable may be either time or a characteristic dimensional quantity. In the system of equations, there may be one or more parameters that are controllable and are thus subject to adjustment. In other cases, the parameters are of unknown magnitudes because of ignorance. The guidance and control problem of a missile belongs to the former category, whereas the shell stress problem belongs to the latter category. The purpose of optimum programming is to find a best set of values of the parameters or control variables, so as to optimize the terminal value of a given function, fco be called the optimized function. At the same time, the control variables should be adjusted in such a manner that certain boundary conditions are satisfied. In the optimum programming technique, a set of nominal or most reasonable values of the control variables is first assumed. Based on the nominal values of the control variables, the systems equations are solved numerically. A set of adjoint functions is established which measures the influence of the change of a control variable at a specific station to the corresponding changes of the optimized function and the unsettled boundary conditions at the terminal point. It is possible to adjust the control variables in small steps so as to reduce the optimized function gradually to its optimum value and to make the state variables satisfy certain boundary conditions at the terminal point.