ABSTRACT
The finite element analysis of an engineering problem is usually a complex process. Linear static cases mean the situations where all external loads to a finite element system are time-independent and material properties of each element do not change during an entire loading process. This chapter focuses on the design of methods for solving problems that are suited for computer implementation, i.e., the design of algorithms. It proposes an incremental and iterative algorithm for dynamic soil-machine interactions. The chapter introduces numerical methods for solving non-linear equations including higher-degree polynomial ones and transcendental ones. It examines two iterative methods for solving a set of simultaneous linear equations. The methods include Jacobi method and Gauss-Seidel method. One major disadvantage associated with iterative methods is that the solution method does not proceed to the answer in a fixed number of arithmetic operations. The chapter addresses the problems with large deformation.
