Biomedical Engineering Reference
In-Depth Information
Table 5.1
RPIM or EFGM linear elastostatic flow chart
Step
Action
1.
Discretize the problem domain with an adequate nodal distribution
2.
Construct an adequate background integration mesh using a Gauss-Legendre quadrature
scheme
3.
Establish the influence-domain of each interest point
4.
Loop over the integration points set, in order to numerically integrate the terms of the
Galerkin weak form expression
4.1
Using the previously defined influence-domains, determine the nodes that directly
influence each integration point
4.2
Construct the RPI or MLS shape functions, and the respective partial derivatives, for
each integration point
4.3
Evaluate the stiffness, the mass and the body load at each integration point
4.4
Assemble the contribution of each integration point in order to construct the complete
system of equations
5.
Determine the external force vector on the natural boundaries
6.
Impose the displacement constrains directly on the stiffness matrix for the RPIM or enforce
the displacement constrains using the Lagrange-Multipliers for the EFGM
7.
Solve the algebraic system of equation and obtain the nodal displacement field
8.
Evaluate the strain field and the stress field at each integration point
Table 5.2
NNRPIM linear elastostatic flow chart
Step
Action
1.
Discretize the problem domain with an adequate nodal distribution
2.
Determine the natural neighbours of each field node and construct the Voronoï diagram of
the nodal distribution discretizing the problem domain
3.
Determine the integration points using the Voronoï cells
4.
Establish the influence-cells (first or second degree)
5.
Loop over the integration points set, in order to numerically integrate the terms of the
Galerkin weak form expression
5.1
Using the previously defined influence-cells, determine the nodes that directly
influence each integration point
5.2
Construct the RPI shape functions, and the respective partial derivatives, for each
integration point
5.3
Evaluate the stiffness, the mass and the body load at each integration point
5.4
Assemble the contribution of each integration point in order to construct the complete
system of equations
6.
Determine the external force vector on the natural boundaries
7.
Enforce the displacement constrains directly on the stiffness matrix
8.
Solve the algebraic system of equation and obtain the nodal displacement field
9.
Evaluate the strain field and the stress field at each integration point
