Applying the double side method of weighted residual to the solution of shell deformation problem

The double side approximate method uses mathematical programming and the Method of Weighted Residual to solve differential equations. The method is a semi-exact solution, in which a collocation method and mathematical programming are used to create the bilateral inequality. In this way, the differential equation problem becomes a mathematical programming problem. By using the Genetic Algorithms (GAs) optimization method, it is possible to obtain the minimum and maximum solutions which satisfy the inequality. The advantage of this method is that it requires less computer memory than finite element methods. This paper considers the application of this method to the solution of nonlinear differential equation problems. The efficiency, accuracy, and simplicity of this approach are illustrated, indicating that the proposed method can be easily extended to solve a wide range of physical engineering problems.