Download Akantu User's Guide - Computational Solid Mechanics Laboratory

Chapter 4
Solid Mechanics Model
The solid mechanics model is a specific implementation of the Model interface dedicated to handle
the equations of motion or equations of equilibrium. The model is created for a given mesh. It will
create its own FEEngine object to compute the interpolation, gradient, integration and assembly
operations. A SolidMechanicsModel object can simply be created like this:
SolidMechanicsModel model(mesh);
where mesh is the mesh for which the equations are to be solved. A second parameter called
spatial_dimension can be added after mesh if the spatial dimension of the problem is different
than that of the mesh.
This model contains at least the the following six Arrays :
blocked_dofs contains a Boolean value for each degree of freedom specifying whether that degree is blocked or not. A Dirichlet boundary condition can be prescribed by setting the
blocked_dofs value of a degree of freedom to true . A Neumann boundary condition can
be applied by setting the blocked_dofs value of a degree of freedom to false . The displacement, velocity and acceleration are computed for all degrees of freedom for which the
blocked_dofs value is set to false . For the remaining degrees of freedom, the imposed
values (zero by default after initialization) are kept.
displacement contains the displacements of all degrees of freedom. It can be either a computed
displacement for free degrees of freedom or an imposed displacement in case of blocked
ones (u in the following).
velocity contains the velocities of all degrees of freedom. As displacement, it contains computed
or imposed velocities depending on the nature of the degrees of freedom (u̇ in the following).
acceleration contains the accelerations of all degrees of freedom. As displacement, it contains
computed or imposed accelerations depending on the nature of the degrees of freedom (ü
in the following).
force contains the external forces applied on the nodes ( f ext in the following).
residual contains the difference between external and internal forces. On blocked degrees of
freedom, residual contains the support reactions. (r in the following). It should be mentioned
that at equilibrium residual should be zero on free degrees of freedom.
Some examples to help to understand how to use this model will be presented in the next
sections.
15