Newton-Raphson method for Implicit Analysis

Few months back I blogged about difference between explicit dynamic and implicit analysis. Concisely summarizing, an implicit analysis is the one which is independent of time and explicit is the one which is of a short duration and time dependent. In this post, I would be going into details regarding an Implicit Finite Element Analysis. Newton-Raphson (NR) method is the commonly used method for most of the implicit FE solvers. In simple numerical terms, the N-R method is used for finding successively better approximations. Figure 1 shows the general iterative process for an implicit analysis. Click here to read more about N-R method. 

Implicit and Explicit Finite Element Analysis

Implicit and Explicit are two types of approaches that can be used to solve the finite element problem. The implicit approach is useful in problems in which time dependency of the solution is not an important factor [e.g. static, structural etc.] whereas Explicit Dynamics approach is most helpful in solving high deformation time dependent problems such as Crash, Blast, Impact etc.