  The Inertia Relief (IR) technique is widely used by industry and produces
equilibrated loads allowing to analyze unconstrained systems without resorting
to the more expensive full dynamic analysis. The main goal of this work is to
develop a computational framework for the solution of unconstrained parametric
structural problems with IR and the Proper Generalized Decomposition (PGD)
method. First, the IR method is formulated in a parametric setting for both
material and geometric parameters. A reduced order model using the encapsulated
PGD suite is then developed to solve the parametric IR problem, circumventing
the so-called curse of dimensionality. With just one offline computation, the
proposed PGD-IR scheme provides a computational vademecum that contains all the
possible solutions for a pre-defined range of the parameters. The proposed
approach is nonintrusive and it is therefore possible to be integrated with
commercial FE packages. The applicability and potential of the developed
technique is shown using a three dimensional test case and a more complex
industrial test case. The first example is used to highlight the numerical
properties of the scheme, whereas the second example demonstrates the potential
in a more complex setting and it shows the possibility to integrate the
proposed framework within a commercial FE package. In addition, the last
example shows the possibility to use the generalized solution in a
multi-objective optimization setting.
