## Topics in Computational Mechanics: Part 3

Recall the continuum approach to mechanics. We view the body, the structure of our interest, as a continuous region $\Omega$ in the vector space of $\mathbb{R}^{3}$. Then, we can completely describe the structure’s state by finding the set of fields $\{\sigma,\,\varepsilon,\,\vec{u}\}$ that satisfies the force and moment equilibriums, the stress-strain relation (constitutive equation), and the strain-displacement relation (kinematics).

The problem is, finding the fields exactly is impossible for all but simple structures. Today, we will look at how to make the problem simpler so that we can analyze real-life structures.