Module continuum 

Isoparametric machinery shared by the continuum elements: shape functions and their reference derivatives (shape), Gauss rules (quadrature), the Jacobian and physical derivatives (jacobian), and scale-aware geometry validation (validate). Everything here is dimension-agnostic bookkeeping; what is specific to an element (the B matrix shape, the constitutive reduction) stays in the element.

Re-exports

pub use jacobian::physical_derivatives;

pub use jacobian::Jacobian;

pub use quadrature::EDGE_GAUSS_2;

pub use quadrature::QUAD4_GAUSS_2X2;

pub use quadrature::TRI3_GAUSS_1;

pub use quadrature::TRI3_GAUSS_3;

pub use shape::quad4_dshape;

pub use shape::quad4_shape;

pub use shape::tri3_dshape;

pub use shape::tri3_shape;

pub use shape::QUAD4_CORNERS;

pub use validate::validate_quad;

pub use validate::validate_triangle;

Modules

jacobian

The 2D isoparametric Jacobian: J = [dx/dxi dy/dxi; dx/deta dy/deta] (row a is the derivative with respect to natural coordinate a), its determinant and inverse, and physical shape-function derivatives.

quadrature

Gauss rules as (xi, eta, weight) triples ((t, weight) for the edge rule). Triangle weights sum to the reference area 1/2, quadrilateral weights to 4, edge weights to 2.

shape

Shape functions and reference derivatives of the 3-node triangle (natural coordinates xi, eta on the unit triangle) and the 4-node quadrilateral (xi, eta in [-1, 1]). Node order is counter-clockwise; quad node k sits at the reference corner QUAD4_CORNERS[k].

validate

Geometry validation with a scale-aware tolerance: every threshold is relative to the element’s characteristic length squared (its longest node-to-node distance squared), never an absolute number, so a unit element and a 1e6-scaled copy are judged identically.