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52 reference sheets connect assumptions, equations, code and checks. Search by topic, then open a route for its derivation and evidence.

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52 of 52 sheets.

Physical formulations

What mechanical model is represented?

Shared foundations4 sheets

Equilibrium, approximation, measures, units and error definitions.

Solid elements6 sheets

Interpolation, mapped gradients, integration and element matrices.

Shell elements2 sheets

Membrane, bending, transverse shear and local condensation.

Beams and discrete entities2 sheets

Section kinematics, local frames, springs and concentrated inertia.

Material and section laws6 sheets

Elasticity, plasticity, StVK, laminate resultants and failure indicators.

Contact and friction5 sheets

Gap, complementarity, enforcement, tangential state and search.

Kinematic constraints1 sheets

Affine admissible coordinates and projected equilibrium.

Linear MPC / RBE2-style constraintsPhysical formulation · BOUNDED · homogeneous translational mixed routeLinear constraints connect selected DOFs through a visible reduced-system transformation.

Element scope notes1 sheets

Research-only and unsupported families, outside the ordinary public routes.

Pyramid5 and WEDGE15Scope note · PYRAMID5 RESEARCH_ONLY · WEDGE15 UNSUPPORTEDVisible boundaries prevent a mesh containing these families from being mistaken for an ordinary supported route.

Analysis methods

Which response or equilibrium problem is solved?

Static equilibrium1 sheets

The linear static route assembles element stiffness and load contributions, applies prescribed constraints, then solves for displacements and reactions. The analysis detail page separates the general route from the named element combinations whose maturity has been recorded.

Linear staticAnalysis method · QUALIFIED_BOUNDED · recorded combinations onlySmall-strain equilibrium is assembled from element stiffnesses and consistent load vectors.

Modal analysis1 sheets

The undamped modal route solves a constrained generalized eigenproblem for natural frequencies and mode shapes. It checks eigenpair residuals and mass normalization; a mode calculation does not provide forced-response amplitudes.

Sparse generalized eigenproblemAnalysis method · ROUTE-DEPENDENT · registry controls each familyThe default sparse path uses eigsh/ARPACK; dense conversion is explicit and bounded by an active-DOF cap.

Transient response1 sheets

Newmark average-acceleration advances displacement, velocity and acceleration through time. When the matrices and step size are constant, the effective matrix can be reused; stability, time-step sensitivity and model scope still need separate checks.

Newmark average-acceleration methodAnalysis method · ROUTE-DEPENDENT · linear dynamics; mixed route experimentalThe default β=1/4, γ=1/2 scheme uses a constant effective matrix when M, C, K, and Δt are fixed.

Harmonic response1 sheets

At each prescribed frequency, the route solves a complex dynamic-stiffness system and reports response amplitude and phase. A frequency sweep is a set of steady-state solves; it is not a transient simulation or a general damping identification method.

Linear harmonic responseAnalysis method · ROUTE-DEPENDENT · frequency sweep is model-specificA complex displacement amplitude is solved independently at each declared excitation frequency.

Linearized stability1 sheets

A proportional preload defines an initial-stress tangent pencil from which the first candidate instability factor is estimated. This is a linearized stability calculation about the chosen base state; it does not solve post-buckling or establish a general collapse load.

Preload and tangent pencilAnalysis method · ROUTE-DEPENDENT · bounded first-factor casesA converged preload is followed by an initial-stress decomposition and sparse generalized eigenvalue solve.

Composed nonlinear routes2 sheets

These routes combine a declared kinematic description, material law, element family and nonlinear solution lifecycle. Trial state, convergence and rollback rules matter alongside the constitutive equations. Evidence is limited to the named combinations; it does not qualify nonlinear mechanics as a whole.

Gyroscopic modal and Campbell3 sheets

The experimental rotating route forms a complex quadratic eigenvalue problem for a straight BEAM2 shaft with centered rigid axisymmetric disks at prescribed constant signed speeds. Campbell tracking preserves ambiguous mode associations; forced response, unbalance prediction and validated critical speeds remain outside the stated scope.

Algorithms and implementation

How does the numerical calculation proceed?

Nonlinear solution and state3 sheets

Newton corrections, trial history, continuation and acceptance.

Matrix and spectral solvers3 sheets

Factorization, Krylov preconditions and sparse or dense extraction.

Execution and result provenance2 sheets

Bounded MPI execution and the identities retained in exported fields.

V&V

Verification methods

How checks are designed. Read executed cases and decisions on the V&V pages.

Verification methods and benchmark design7 sheets

Understand what an oracle, correlation or workload record measures. Observed results and acceptance decisions remain on the V&V pages.

Inspect the recorded proof.

Contracts, frozen models, results and limitations belong to each recorded case.

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