  Physics-Informed Neural Networks (PINNs) have gained considerable interest in
diverse engineering domains thanks to their capacity to integrate physical laws
into deep learning models. Recently, geometry-aware PINN-based approaches that
employ the strong form of underlying physical system equations have been
developed with the aim of integrating geometric information into PINNs. Despite
ongoing research, the assessment of PINNs in problems with various geometries
remains an active area of investigation. In this work, we introduce a novel
physics-informed framework named the Geometry-Aware Deep Energy Method (GADEM)
for solving structural mechanics problems on different geometries. As the weak
form of the physical system equation (or the energy-based approach) has
demonstrated clear advantages compared to the strong form for solving solid
mechanics problems, GADEM employs the weak form and aims to infer the solution
on multiple shapes of geometries. Integrating a geometry-aware framework into
an energy-based method results in an effective physics-informed deep learning
model in terms of accuracy and computational cost. Different ways to represent
the geometric information and to encode the geometric latent vectors are
investigated in this work. We introduce a loss function of GADEM which is
minimized based on the potential energy of all considered geometries. An
adaptive learning method is also employed for the sampling of collocation
points to enhance the performance of GADEM. We present some applications of
GADEM to solve solid mechanics problems, including a loading simulation of a
toy tire involving contact mechanics and large deformation hyperelasticity. The
numerical results of this work demonstrate the remarkable capability of GADEM
to infer the solution on various and new shapes of geometries using only one
trained model.
