PetitPas

PetitPas is a finite element solver for mechanical structural problems.

"PetitPas" means "small step" in French.

##Features

• 2D linear triangles
• 3D linear tetrahedrons
• elastic material (Hooke's law): 2D plane stress, 2D place strain and 3D
• JSON file as input and/or output via JsonCpp
• export output to vtk files (use Paraview for visualization)
• compute displacements, strains and stresses
• use of sparse matrices to reduce memory usage thanks to Eigen library
• code fully tested with unittest++
• Object-Oriented code

##Usage

Here is a minimal input JSON file that defines a 2D plane strain problem with 4 elements and 6 nodes:

{
	"nodes":
	[
		{"id":1,"coordinates":[0,0]},
		{"id":2,"coordinates":[3,0]},
		{"id":3,"coordinates":[6,0]},
		{"id":4,"coordinates":[0,3]},
		{"id":5,"coordinates":[3,3]},
		{"id":6,"coordinates":[0,6]}
	],
	"elements":
	[
		{"id":1,"node_ids":[1,2,4],"material":"material_1"},
		{"id":2,"node_ids":[2,5,4],"material":"material_1"},
		{"id":3,"node_ids":[2,3,5],"material":"material_1"},
		{"id":4,"node_ids":[4,5,6],"material":"material_1"}
	],
	"materials":
	[
		{"id":"material_1", "young_modulus":30e3, "poisson_ratio":0.2, "hypothesis":"2d_plane_strain"}
	],
	"boundary_conditions":
	[
		{"type":"force", "node_id":4, "degree_of_freedom":0, "value":90.0},
		{"type":"force", "node_id":4, "degree_of_freedom":1, "value":-112.5},
		{"type":"force", "node_id":5, "degree_of_freedom":1, "value":-112.5},
		{"type":"force", "node_id":6, "degree_of_freedom":0, "value":15.0},
		{"type":"force", "node_id":6, "degree_of_freedom":1, "value":-37.5},
		{"type":"zero_displacement", "node_id":1, "degree_of_freedom":0},
		{"type":"zero_displacement", "node_id":1, "degree_of_freedom":1},
		{"type":"zero_displacement", "node_id":2, "degree_of_freedom":0},
		{"type":"zero_displacement", "node_id":2, "degree_of_freedom":1},
		{"type":"zero_displacement", "node_id":3, "degree_of_freedom":0},
		{"type":"zero_displacement", "node_id":3, "degree_of_freedom":1}
	]

}

The command line to run the simulation:

PetitPas -i input.json -o output.json

Add the switch -of vtk to export the output to vtk format:

PetitPas -i input.json -o output.vtk -of vtk

Then you may open the generated file output.vtk in Paraview for post-processing.

##Compilation

Open petitpas.workspace in Code::Blocks IDE (version >= 13.12), select the Release target and build the software.

##Disclaimer

The output values of the software are not guaranteed, so don't build a nuclear power plant with PetitPas.

Thanks a lot to @flolagale for his advices about the Finite Element Method.