Function expressions

Many input values — boundary-condition data, initial conditions, Neumann tractions and pressures, level-set surfaces, and mesh-smoothing size fields — are given as function strings rather than constants. Each string is a symbolic expression evaluated at each node.

Available symbols

Exactly four symbols are available in every function expression:

The spatial coordinates are always the reference configuration coordinates, not the deformed ones.

Syntax

Expressions are parsed and compiled with the Symbolics package, so any Julia numeric syntax that Symbolics understands is valid: arithmetic (+ - * / ^), elementary functions (sin, cos, exp, log, sqrt, abs, tanh, …), the constant pi, and ifelse(condition, a, b) for piecewise definitions. Multiple statements separated by semicolons are allowed, with the last expression supplying the value:

function: "a = 0.001; s = 0.02; a * exp(-z*z / s/s / 2)"

Constants are a single number written as a string:

function: "0.0"

A linear ramp in time:

function: "0.01 * t"

A smooth pressure pulse:

function: "-937.5e3 * 1500 * (0.5 - 0.5 * cos(pi * t / 1500.0))"

Time derivatives (Dirichlet and initial conditions)

For a Dirichlet boundary condition and for a displacement initial condition, the function gives the displacement. The corresponding velocity and acceleration are obtained automatically by symbolic differentiation in t — you do not supply them separately. A velocity initial condition sets the velocity directly from its function.

Because differentiation is symbolic, a displacement expression that depends on t produces the physically consistent velocity and acceleration; a time-independent displacement produces zero velocity and acceleration.