Design by numerical method

This chapter describes the numerical calculations in the methods commonly used in modern scientific computing, such as numerical integration and numerical differentiation and direct and iterative solutions to linear and non-linear equations. These include numerical solutions of matrix eigenvalue problems and numerical solutions of ordinary differential equations, such as for stress and strain, differential equations of machine component design such as spring elements, bars configurations, the frame system, the truss system, and beams, plates, and shells. The chapter is equipped with rich exercises and numerical test questions, along with some answers to the exercises using ANSYS software. The chapter focuses on the practicability of the content, the elaboration of basic ideas, and the application of numerical calculation methods. It features clear descriptions, a strong system, and many examples of numerical calculations. It can be used as teaching material in courses on numerical calculation methods for engineering majors in colleges and universities, and can also be used as a reference for scientific and technical personnel engaged in scientific and engineering calculations.