有限元误差分析.pdfVIP

Chapter 7 Error Analysis There are various sources of errors in finite element analysis. Error analysis has become indispensable in today’s engineering application of finite element software. In this chapter, we will discuss the mature basis of error analysis for linear static analysis using finite elements. § 1 Sources of error The error of finite element results may arise at any procedures of finite element analysis. A good and mature user of finite element method should be aware of the all possible error sources in the finite element analysis. Generally, possible major sources of error can be put into the following categories 1) Modeling error It refers to the difference between a physical system and its mathematical model. It should be kept at an acceptable degree. Otherwise, the mathematical model need be revised. Usually, simplifications are introduced into the mathematical model. In the model, for instance, probably small holes and other geometric irregularities in the structure are neglected; loads are simplified; boundary conditions are idealized as by treating a component with relatively large stiffness as rigid. Quite often a two-dimensional problem is studied, ignoring its three-dimensional characteristic; a static analysis is performed, ignoring the dynamic character. 2) Discretization error The mathematical model has infinite number of dof, but finite dof are used in finite element analysis. The finite element solution is affected by the number of elements in the model, the dof per node, the numerical integration rule, and etc. Actually, this kind of error has been discussed at the first section of last chapter. 3) Truncation error or rounding error It refers to loss of information due to truncation or roun