We review the treatment of trimmed geometries in the context of design, data exchange, and
computational simulation. Such models are omnipresent in current engineering modeling …

The aim of this manuscript is to give a practical overview of meshless methods (for solid
mechanics) based on global weak forms through a simple and well-structured MATLAB …

In this paper, we introduce a new approach based on distance fields to exactly impose
boundary conditions in physics-informed deep neural networks. The challenges in satisfying …

Abstract Partial Differential Equations (PDEs) are fundamental to model different
phenomena in science and engineering mathematically. Solving them is a crucial step …

Predicting history-dependent materials' responses is crucial, as path-dependent behavior
appears while characterizing or geometrically designing many materials (eg, metallic and …

A higher order nonlocal operator method for the solution of boundary value problems is
developed. The proposed higher order nonlocal operator brings several advantages as …

Deep learning (DL) and the collocation method are merged and used to solve partial
differential equations (PDEs) describing structures' deformation. We have considered …

A meshfree method for thin shells with finite strains and arbitrary evolving cracks is
described. The C1 displacement continuity requirement is met by the approximation, so no …

We present a one‐parameter family of approximation schemes, which we refer to as local
maximum‐entropy approximation schemes, that bridges continuously two important limits …

Physics‐informed neural networks have gained growing interest. Specifically, they are used
to solve partial differential equations governing several physical phenomena. However …