An Adaptive Meshless Method for Analyzing Large Mechanical Deformation and Contacts

Design for manufacturing of equipment (that handles deformable objects) and disposable medical devices (such as medical needles, optic fibers, and catheters for inserting into the human body) involves solving mechanical contact problems. Unlike rigid component manufacturing, which has been relatively well established, the handling of deformable bodies remains a challenging research. This paper offers an adaptive meshless method (MLM) for solving mechanical contact problems, which automatically insert additional nodes into large error regions identified in terms of mechanical stresses. This adaptive MLM employs a sliding line algorithm with penalty method to handle contact constraints. The method does not rely on small displacement assumptions; thus, it can solve nonlinear contact problems with large deformation. We validate the method by comparing results against those computed by using a commercial FEM software and analytical solution for two different situations, namely, large deformation and contact. Four practical applications are illustrated: large deflection of a compliant finger, mechanical contact, snap-fit assembly, and surgical needle insertion.