Description of the inputs¶
Input by defining a model data base¶
The easiest way to define the data of a NL_2D_FEM object is
to fill the field of a Matlab structure called
the model data structure (mds).
An empty mds can be created as mds = create_empty_mds().
Otherwise, an existing mds can be simply copied and edited.
The NL_2D_FEM model model can be initialized automatically
with the method model = model.set_model_from_mds(mds).
Geometry input¶
There are two ways to define the geometry:
Provide a list of points and lines that will be discretized automatically.
Provide a mesh directly by giving the coordinates of the nodes and the connectivity table.
Global geometry input¶
The field geom of the mds governs the global geometry input.
There are three sub-fields to be defined:
mds.geom.geom_node: List of number and coordinates of the key points of the geometry. Each line is of the type (point number, x coordinate, y coordinate).mds.geom.geom_element: List of lines of the geometry. Each line is of the type (line number, point 1, point 2).mds.geom.discretisation: List of number of elements in each line (list of integers, with size the number of lines of the geometry).
If the geometry is inputted, the mesh is generated automatically.
User-defined mesh input¶
Alternatively, the geometry input can be left empty, if the mesh is provided directly.
The field mesh of the mds governs the mesh.
There are two sub-field to be defined:
mds.mesh.nodes: List of number and coordinates of the nodes of the mesh. Each line is of the type (node number, x coordinate, y coordinate).mds.mesh.connect: Connectivity table; list of elements of the mesh. Each line is of the type (element number, node 1, node 2).
Properties input¶
The field prop of the mds governs the cross-section profile and the material properties.
The three sub-fields to be defined are:
mds.prop.S: Area of the cross-section (constant for all elements).mds.prop.I: Second moment of area of the cross-section (constant for all elements).mds.prop.k: Shear coefficient of the cross-section (constant for all elements).mds.prop.rho: Material density (constant for all elements).mds.prop.E: Material Young’s modulus (constant for all elements).mds.prop.poisson: Material Poisson’s ratio (constant for all elements).mds.prop.alpha: Material damping coefficient (linear Rayleigh damping, constant for all elements).
The shear modulus \(G\) is computed automatically from the data.
Visualization input¶
The field visu of the mds governs the visualization input.
There is only a single field, representative of a cell of structures:
mds.visu.visu_node_list: List (cell array) of observed node(s) and dof.mds.visu.visu_node_list{n}is a structure with two fields:mds.visu.visu_node_list{n}.node: Node number.mds.visu.visu_node_list{n}.dof: List of dof number(s).
Boundary conditions input¶
The field boundary of the mds governs the (Dirichlet) boundary conditions.
There is only a single field, representative of a cell of structures:
mds.boundary.bc_node_list: List (cell array) of observed node(s) and dof.mds.boundary.bc_node_list{n}is a structure with two fields:mds.boundary.bc_node{n}.node: Node number(s).mds.boundary.bc_node{n}.dof: List of dof number(s).
Force definition¶
Static force definition¶
The field force.static of the mds governs the definition of static forces.
Static point forces¶
The first forces to consider are static point loads, which are defined as:
mds.force.static.static_ponctual_force_node_list: List (cell array) of forced node(s) and dof.mds.force.static.static_ponctual_force_node_list{n}is a structure with three fields:mds.force.static.static_ponctual_force_node_list{n}.node: Node number(s).mds.force.static.static_ponctual_force_node_list{n}.dof: List of dof number(s).mds.force.static.static_ponctual_force_node_list{n}.amplitude: List of force amplitudes (one amplitude for each dof in the previous field).
Static distributed forces¶
Next, we consider static distributed forces, which are defined as:
mds.force.static.static_distributed_force_direction: List of directions, chosen from among (1) x-axis, (2) y-axis or (3) moment.mds.force.static.static_distributed_force_amplitude: List of amplitudes (linear force density).
Periodic force definition¶
Periodic loadings can also be applied to the structure.
The field force.periodic of the mds governs the definition of periodic forces.
Periodic point forces¶
As before, consider first periodic point loads, defined as:
mds.force.periodic.periodic_ponctual_force_node_list: List (cell array) of forced node(s) and dof.mds.force.periodic.periodic_ponctual_force_node_list{n}is a structure with three fields:mds.force.periodic.periodic_ponctual_force_node_list{n}.node: Node number(s).mds.force.periodic.periodic_ponctual_force_node_list{n}.dof: List of dof number(s).mds.force.periodic.periodic_ponctual_force_node_list{n}.amplitude: List of force amplitudes (one amplitude for each dof in the previous field). Each element of the list is a complex number \(z\).mds.force.periodic.periodic_ponctual_force_node_list{n}.harmonic: List of harmonics (one harmonic for each dof in the previous field).
For each forced dof, the force is written as: \(f(t) = \mathrm{Re}(z) \cos(h t) + \mathrm{Re}(z) \sin(h t)\).
Periodic distributed forces¶
Next, consider the definition of periodic distributed forces, defined as:
mds.force.static.static_distributed_force_direction: List of directions, chosen from among (1) x-axis, (2) y-axis or (3) moment.mds.force.static.static_distributed_force_amplitude: List of amplitudes, complex numbers (linear force density).mds.force.static.static_distributed_force_harmonic: List of harmonics.