WeakForm module.

Weak Formulation (fedoo.weakform)

In fedoo, the differential equations related to the problem to solve are written using weak formulations. The weak formations are defined in the WeakForm objects.

• The WeakForm object include the differential operators (with virtual fields) and can be automatically updated at each time step for non linear weak formulations.

• When created, a WeakForm object doesn’t in general know the domain of integration. The domain of integration is defined using a Mesh, and is only introduced when creating the corresponding Assembly.

The weakform library of Fedoo includes a few classical weak formulations. Each weak formulation is a class deriving from the WeakForm class. The developpement of new weak formulation is easy by copying and modifying an existing class.

The WeakForm library contains the following classes:

StressEquilibrium(constitutivelaw[, name, ...])	Weak formulation of the mechanical equilibrium equation for solids.
ImplicitDynamic(constitutivelaw, density, ...)	Weak formulation.
StressEquilibriumRI(constitutivelaw[, ...])	Stress equilibrium weak formulation with reduced integration.
SteadyHeatEquation(thermal_constitutivelaw)	Weak formulation of the steady heat equation (without time evolution).
HeatEquation(thermal_constitutivelaw[, ...])	Weak formulation of the heat equation.
BeamEquilibrium(material[, A, Jx, Iyy, Izz, ...])	Weak formulation of the mechanical equilibrium equation for beam models.
SpringEquilibrium(K[, name, nlgeom, space])	Weak formulation of the mechanical equilibrium equation for spring models.
PlateEquilibrium(PlateConstitutiveLaw[, ...])	Weak formulation of the mechanical equilibrium equation for plate models.
PlateEquilibriumFI(PlateConstitutiveLaw[, ...])	Weak formulation of the mechanical equilibrium equation for plate models.
PlateEquilibriumSI(PlateConstitutiveLaw[, ...])	Weak formulation of the mechanical equilibrium equation for plate models.
Inertia(Density[, name, space])	Weak formulation related to the inertia effect into dynamical simulation.
InterfaceForce(constitutivelaw[, name, ...])	Weak formulation of the interface equilibrium equation.
DistributedLoad(distributed_force[, name, ...])	Weak formulation for a distributed load.
ExternalPressure(pressure[, name, nlgeom, space])	Weak formulation for a pressure over a surface.
HourglassStiffness([stiffness_coef, name, ...])	Hourglass stiffness weak formulation for reduced integration elements.
StressEquilibriumFbar(constitutivelaw[, ...])	Weak formulation of the mechanical equilibrium equation for solids.