Week - 2 - Explicit and Implicit Analysis

Aim-

To write a detailed report about Implicit and explicit methods & to solve the equation F(u) = u3+9u2+4u using both Explicit and Implicit Methods.

Explanation-

Implicit FEA

Implicit FEA is a method that solves equations using the Newton-Raphson method to solve nonlinear equations. It is a method that requires iterative computations, and the equations are solved in a step-by-step process. Implicit FEA is best suited for problems that involve slow and steady loading, such as static and quasi-static analysis. It is also used for problems that involve large deformations, material nonlinearity, and geometric nonlinearity.

Explicit FEA

Explicit FEA is a method that solves equations using a direct integration method, which means that the equations are solved without iterative computations. It is a time-stepping method that is best suited for problems that involve high-speed impacts, explosions, and crash simulations. It is also used for problems that involve short-duration loading. The advantages of explicit FEA include faster computation time and the ability to simulate complex dynamic events accurately.

Comparison

Implicit FEA is best suited for problems that involve slow and steady loading, while explicit FEA is best suited for problems that involve high-speed impacts and crash simulations. Implicit FEA is more accurate and stable, but it requires more computation time than explicit FEA. On the other hand, explicit FEA is faster but less accurate than implicit FEA. Explicit FEA is also more prone to numerical instability and requires smaller time steps to maintain stability.

- The calculations are performed in the excel sheet by referring to the PDF provided.

Conclusion-

Both implicit and explicit FEA have their advantages and disadvantages. The choice between them depends on the nature of the problem being analyzed. For problems with long-duration, slow or quasi-static loads, implicit FEA is generally preferred, while for problems with short-duration, high-speed or impact loads, explicit FEA is preferred.