RF-CONCRETE Surfaces – Online Manual Version 5

Online manuals, introductory examples, tutorials, and other documentation.

RF-CONCRETE Surfaces – Online Manual Version 5

Switch to Fullscreen Mode Exit Fullscreen Mode

2.8.2.3 Methods for solving nonlinear equations

Methods for solving nonlinear equations

The application of the FE method for solving nonlinear differential equations results in algebraic equations that can be expressed in the following form:

K(d) · d = f 

where

Table 2.2

K

stiffness matrix of the model

d

vector of the unknown (usually of nodal parameters of the deformation)

f

vector of the right sides (usually of nodal forces)

The matrix K is the function of d and therefore cannot be evaluated without knowing the vector of the system roots d. Since this nonlinear system cannot be solved directly, iteration methods that are aimed at progressively increasing the precision of the solution are used.

RF-CONCRETE NL uses the iteration method according to Picard. This method is also known as the Direct Iteration Method or Secant Modulus Method.

Figure 2.129 Direct iteration method