Continuum Mechanics

Linear continuum mechanics beyond flow. Fourier’s heat equation smooths a temperature field mode by mode. The explicit, Crank-Nicolson, and spectral solvers show how stability and accuracy trade off. Sound in a pipe or a room rings at a discrete set of standing-wave frequencies, recovered here from a single pressure pulse. A pressurized thick-walled cylinder, solved with plane-strain finite elements, reproduces Lamé’s closed-form stresses.

Sound in pipes and rooms: standing modes from a single pulse

Sound in pipes and rooms: standing modes from a single pulse

Fourier’s heat equation: every mode decays on its own

Fourier's heat equation: every mode decays on its own

Lamé’s thick-walled cylinder: plane-strain finite elements

Lamé's thick-walled cylinder: plane-strain finite elements