An introduction to finite element analysis using MATLAB and Abaqus
Usually, engineers and physicists describe a physical phenomenon by means of a system of ordinary or partial differential equations that are true in a certain range and provide appropriate initial and boundary conditions. In fact, a differential equation with required boundary and initial conditions is a complete mathematical model of a phenomenon. In order to find the distribution of the desired variables whose relationship is expressed in the differential form by the governing equation, the aforementioned equation must be solved so that the numerical values of each related quantity can be obtained at desired points. But due to the fact that only very simple forms of these equations can be solved in very simple geometric regions with analytical methods, there is a big problem in solving most of the governing equations by analytical methods. In order to deal with such problems and also to use the most powerful tool available in the current century, i.e. the computer, it is necessary to cast the problem in a completely algebraic format so that solving them only requires algebraic operations. To achieve such a goal, different types of discretization methods of a continuous problem defined by differential equations can be used. In these methods, the unknown function or functions, which can be represented by an infinite set of numbers, are replaced by a finite number of unknown parameters, which naturally includes some kind of approximation in the general case.
The three main methods for numerically solving a differential equation are as follows:
Finite element method
Method of change
Weighted residual method
And the first method is the finite element method, which is the basic pillar of the abaqus software, and a famous abaqus book called Introduction to Finite Element Analysis Using MATLAB® and Abaqus has a close reference to this issue. We introduce and at the end of the article we have put the download link of this Abacus book.