Meshfree methods in solid mechanics pdf#

a mesh, but are rather based on interaction of each node with all its neighbors. Once the model is properly trained, solutions can be obtained almost instantly at any point in the domain, given its spatial coordinates. Meshfree methods 20 points and their Voronoi cells In the field of numerical analysis, meshfree methods are those that do not require connection between nodes of the simulation domain, i.e. The deep learning model is trained to learn the model's parameters yielding accurate approximate solutions. Data generation usually is the main bottleneck in most data-driven models. Two important ones are summarized as follows.

Meshfree methods in solid mechanics pdf#

We show that the DCM can capture the response qualitatively and quantitatively, without the need for any data generation using other numerical methods such as the FEM. Meshfree methods have several attributes that make them attractive for simulation in mechanics. Request PDF Meshfree Discretization Methods for Solid Mechanics Meshfree methods are used for the spatial discretization of partial differential equations, but in contrast to finite element. The presented DCM is meshfree and avoids any spatial discretization, which is usually needed for the finite element method (FEM). We propose a general and simple numerical method analogous to the mathematical theory of manifolds, in which the point-set surface is described. The performance of this deep collocation method (DCM) depends on the architecture of the neural network and the corresponding hyperparameters. We have considered different types of materials: linear elasticity, hyperelasticity (neo-Hookean) with large deformation, and von Mises plasticity with isotropic and kinematic hardening. Deep learning and the collocation method are merged and used to solve partial differential equations describing structures' deformation.