Numerical Modelling of Geodynamic Processes

NUMERICAL MODELLING OF GEODYNAMIC PROCESSES The standard discrete system and origins of the finite element method. Element, node, nodal connection, Stiffness matrix, generalized load. Local and global reference system. Stiffness matrix and load vector for each grid element. Assembly of stiffness matrix and load vector. Displacement approach. Shape function. Shape function for a linear triangular element. Numerical approximation of deformation. Numerical approximation of stress. Linear elasticity. Stiffness matrix for the elastic flexural problem under plane stress conditions. Comparison between the exact solution and the numerical solutions at nodes or internal points for the elastic flexural problem, for different distributed load (constant and linearly varying with distance). Numerical integration: Gauss quadrature. Transformation from local to global coordinates. Jacob matrix. Generalization of the finite element concepts. Integral or "weak" statement equivalent to the differential equations. Galerkin weighted residual approach. Application of Galerkin approach to the 2D heat conduction equation.