Finite_Element_Method_FULL_FULL_FULL.ppt

singularities: the FE method is based on polynomial shape functions to interpolate all fields of interest. When boundary value problems involve singularities (such as the mechanical fields around a crack tip or a sharp notch, or the thermal fields around a point heat source), then the polynomial interpolation inherently cannot lead to a good approximate solution. As a consequence, results are usually mesh-dependent: the smaller the elements (e.g., at the crack tip), the higher the calculated stress values within those elements adjacent to the crack tip. It is for this reason that classical FEM is problematic when dealing with fracture problems (or, generally, any problem involving singularities), and results must be interpreted with utmost care. An h-convergence study usually reveals the diverging solution quickly.singularities: the FE method is based on polynomial shape functions to interpolate all fields of interest. When boundary value problems involve singularities (such as the mechanical fields around a crack tip or a sharp notch, or the thermal fields around a point heat source), then the polynomial interpolation inherently cannot lead to a good approximate solution. As a consequence, results are usually mesh-dependent: the smaller the elements (e.g., at the crack tip), the higher the calculated stress values within those elements adjacent to the crack tip. It is for this reason that classical FEM is problematic when dealing with fracture problems (or, generally, any problem involving singularities), and results must be interpreted with utmost care. An h-convergence study usually reveals the diverging solution quickly.singularities: the FE method is based on polynomial shape functions to interpolate all fields of interest. When boundary value problems involve singularities (such as the mechanical fields around a crack tip or a sharp notch, or the thermal fields around a point heat source), then the polynomial interpolation inherently cannot lead to a good approximate solution. As a consequence, results are usually mesh-dependent: the smaller the elements (e.g., at the crack tip), the higher the calculated stress values within those elements adjacent to the crack tip. It is for this reason that classical FEM is problematic when dealing with fracture problems (or, generally, any problem involving singularities), and results must be interpreted with utmost care. An h-convergence study usually reveals the diverging solution quickly.singularities: the FE method is based on polynomial shape functions to interpolate all fields of interest. When boundary value problems involve singularities (such as the mechanical fields around a crack tip or a sharp notch, or the thermal fields around a point heat source), then the polynomial interpolation inherently cannot lead to a good approximate solution. As a consequence, results are usually mesh-dependent: the smaller the elements (e.g., at the crack tip), the higher the calculated stress values within thos