Mathematical Principles for the Discrete Equation——Discrete Analysis on Engineering Structures

Based on new generalized variational principles, the piecewise structure of the unknown functions and their mutual complement, we derived new mathematical principles to establish the discrete equations of the finite element type, the boundary element type, the sub domain type and the weighted residual type. These mathematical principles are of the generality, the facility and the variety to solve the engineering problems, and of the unity fundamentals to establish the discrete equation for the large general programme system.