workflow

High-level workflow helpers

Small workflow helpers for course-ready examples.

build_bar_1d_local_problem()

Build the complete 1D bar/Poisson local element problem symbolically. Derives the weak form from the strong form d/dx(EA·du/dx) + q = 0, applies integration by parts, enforces homogeneous Dirichlet at x=0 and Neumann traction P at x=L, substitutes P1 shape functions, and extracts the 2×2 element stiffness matrix and 2×1 load vector. Returns a dict with keys: x, L, E, A, q, P (symbols); u, v (fields); weak_bilinear, weak_linear (forms); Ke (2×2 Matrix), fe (2×1 Matrix).

build_poisson_triangle_p1_local_problem()

Build a teaching-first local P1 triangle problem for scalar Poisson/diffusion.

build_bar_1d_mass_matrix()

Build the consistent mass matrix for a 1D bar element. Derives M_e from the L2 inner product ∫ ρA·u·v dx on a two-node linear element. Used in time-dependent problems: M·a_ddot + K·a = F. Returns a dict with keys: x, L, rho, A (symbols); Me (2×2 Matrix).

build_elasticity_triangle_p1_2d(formulation)

Build local element matrices for 2D linear elasticity on a P1 triangle. Demonstrates the full pipeline: constitutive matrix D, gradient pullback, B-matrix construction, and K_e = t A B^T D B. Parameters ———- formulation : str Either “plane_stress” or “plane_strain”. Returns a dict with: E_sym, nu (material); D (3×3 constitutive); B (3×6 strain-displacement); Ke (6×6 element stiffness); geometry; etc.

build_elasticity_tetra_p1_3d()

Build local element matrices for 3D linear elasticity on a P1 tetrahedron. Derives the full pipeline: 6×6 constitutive matrix D, gradient pullback via 3×3 Jacobian, B-matrix (6×12), and K_e = V B^T D B (12×12). Returns a dict with: E, nu (material); D (6×6); B (6×12); Ke (12×12); vertex symbols; etc.