Description

About the Course

The course aims to cover the important aspect of implicit and explicit analysis in finite element method using commercial finite element software

Description of the Course

Finite element method is the foundation of simulation software to calculate the state of a given system or continuum. Finite element method is used to simulate naturally or artificially occurring phenomena in a system or continuum for engineers to assess their designs of critical variables involved in the phenomenon before prototyping or implementation stages. Most of the engineering problems are expressed through mathematical partial differential equations (PDE’s). While today’s digital computers can’t single-handedly solve these partial differential equations, they are equipped to solve matrix equations. These matrix equations can be linear or nonlinear.

Implicit and explicit methods are the approaches used in finite element method for obtaining numerical approximations to the solutions of time-dependent ordinary and partial differential equations, as is required in computer simulations of physical processes. Implicit methods find a solution by solving an equation involving both the current state of the system and the later one, while. explicit methods calculate the state of a system at a later time from the state of the system at the current time. Both methodologies give numerical approximations to solutions of time-dependent and partial differential equations.

We refer to problems as quasi-static or time-independent when loads are gradually applied. Since the loading time is too small the acceleration effects are negligible the implicit analysis can be adopted. In contrast when the problem is nonlinear or time-dependent the effects of acceleration are pronounced and cannot be neglected during which explicit analysis should be preferred.