Continuum Mechanics

Continuum mechanics treats a solid body as a continuous distribution of material rather than a collection of discrete particles. This assumption allows displacement, strain, stress, and material properties to be represented as fields over the geometry.

In finite element analysis, the continuous body is approximated by a finite number of elements. Within each element, displacement is interpolated from nodal values using shape functions. The continuous field problem is therefore converted into a finite-dimensional algebraic problem.

The main continuum quantities used in structural analysis are:

• Displacement field, which describes how each material point moves.
• Strain field, which measures local deformation.
• Stress field, which measures internal force intensity.
• Body forces and surface tractions, which represent external loading.

The finite element method approximates the continuum equations while preserving key physical principles such as compatibility, equilibrium, and constitutive behavior.