Fundamentals of the Finite Element Method

Abstract

This chapter summarizes the principles, governing equations, and basic algorithms related to the finite element method (FEM), which has been the most general and powerful computation tool in the engineering design and analysis since the later 1960s. The “standard” and “hierarchical” shape functions using orthogonal polynomial series are elucidated in details, based on which the algorithms with regard to the fields of permeability, temperature, and deformation are elaborated. The solution techniques particularly important for hydraulic structures related to the issues of rock EDZ, phreatic surface, concrete hydration heating, reservoir water temperature, dynamic response, are addressed. This chapter is closed with the discussion on the safety criteria of hydraulic structures.