Recently in learning the basics of the finite element method, roughly summed up my understanding of the core idea of the finite element method. The field of finite element method applied very widely, plans to organize a series of notes, finite element elastic mechanics problem solving method, for example, gives the basic idea of the finite element method. Finally, summarize the finite element method, the basic idea for solving various problems of the weighted residual amount method.
Finite Element Method basic steps:
(1) The problem of a finite field discrete units, (for example, triangular patches, tetrahedral units, etc.) point (mesh nodes) in the discrete domain, called nodes .
(2) Select a function unit (sub-domain) of a physical value of the node (for example, displacement, etc.), the value of any point within the unit (sub-domain) uniquely represents the physical quantity. This function is called interpolation function .
(3) by known physical relationship, in the respective units (sub-domain), calculates a number of columns. For example, integral, calculate the elastic force size, and so on. The core idea is that any point in the cell may be represented by the value of the physical quantity at the junction. Thus, the final column which some calculations, have become a node of a function of the physical quantity units / calculation.
(4) From the results in the respective units (sub-domain), through some form of integration to calculate the whole problem domain. Thus, calculation for the entire problem domain / satisfies the equation becomes a function of the respective junction points of physical quantities. That is, a continuous problem into a discrete problem.
(5) the limited dimensions of the problem are obtained to solve.
summary
Also I felt that the foggy. Or in the elasticity problem for example, sum over Finite Element Method. Further, finite element method for solving other types of problems, and the method of weighting the residual amount, etc., also collectively comb example.
1-- Finite Element Method elastic problems (a): Frame Structure
2 - Finite Element elasticity Solving Problem (ii): elastic plane problems
3 - Finite Element elasticity problem solving (III): Elasticity space issues