STUDY ON THE PROBLEMS OF CONTACT IN THE NUMERICAL SIMULATION OF SHEET FORMING

This study is concerned with the problems of contact in the process of numerical simulation of sheet metal forming in rigid visco-plastic shell FEM. In respect of analysis of sheet deep drawing process,for the tool model described by triangular elements, a kind of contact judging algorithm about the correlation between the node of deformed mesh and the triangular element of a tool is presented. In SPF/DB Lagrangian multiplier method is adopted to solve the contact problem between deformed meshes, and a new reliable practical dynamic contact checking algorithm is presented. As computation examples, the simulation results of metal sheet deep drawing and SPF/DB are introduced in this paper.

Theoretical investigations on lattice Boltzmann method:an amended MBD and improved LBM

This paper presents theoretical investigations of lattice Boltzmann method(LBM)to develop a completed LBM theory.Based on H-theorem with Lagrangian multiplier method,an amended theoretical equilibrium distribution function(EDF)is derived,which modifies the current Maxwell–Boltzmann distribution(MBD)to include the total internal energy as its parameter.This modification allows the three conservation laws derived directly from lattice Boltzmann equation(LBE)without additional small-parameter expansions adopted in references.From this amended theoretical EDF,an improved LBM is developed,in which the total internal energy like the mass density and mean velocity is a new macroscopic variable to be updated for different times and cells during simulations.The developed method provides a means to consider external forces and energy generation sources as generalised forces in LBM simulations.The corresponding model and implementation process of the improved LBM are presented with its performance theoretically investigated.Analytically hand-workable examples are given to illustrate its applications and to confirm its validity.The paper will excite more researchers and scientists of this area to numerically practice the new theory and method dealing with complex physical problems,from which it is expected to further advance LBM benefiting science and engineering.

Left-Invariant Minimal Unit Vector Fields on the Solvable Lie Group

Bozek(1980)has introduced a class of solvable Lie groups Gn with arbitrary odd dimension to construct irreducible generalized symmetric Riemannian space such that the identity component of its full isometry group is solvable.In this article,the authors provide the set of all left-invariant minimal unit vector fields on the solvable Lie group Gn,and give the relationships between the minimal unit vector fields and the geodesic vector fields,the strongly normal unit vectors respectively.

Investigating and Mitigating Failure Modes in Physics-Informed Neural Networks(PINNs)

This paper explores the difficulties in solving partial differential equations(PDEs)using physics-informed neural networks(PINNs).PINNs use physics as a regularization term in the objective function.However,a drawback of this approach is the requirement for manual hyperparameter tuning,making it impractical in the absence of validation data or prior knowledge of the solution.Our investigations of the loss landscapes and backpropagated gradients in the presence of physics reveal that existing methods produce non-convex loss landscapes that are hard to navigate.Our findings demonstrate that high-order PDEs contaminate backpropagated gradients and hinder convergence.To address these challenges,we introduce a novel method that bypasses the calculation of high-order derivative operators and mitigates the contamination of backpropagated gradients.Consequently,we reduce the dimension of the search space and make learning PDEs with non-smooth solutions feasible.Our method also provides a mechanism to focus on complex regions of the domain.Besides,we present a dual unconstrained formulation based on Lagrange multiplier method to enforce equality constraints on the model’s prediction,with adaptive and independent learning rates inspired by adaptive subgradient methods.We apply our approach to solve various linear and non-linear PDEs.