This paper aims at introducing a new nodal-integration-based finite element method for the numerical calculation of residual stresses induced by welding processes. The main advantage of the proposed method is to be based on first-order tetrahedral meshes, thus greatly facilitating the meshing of complex geometries using currently available meshing tools. In addition, the formulation of the problem avoids any locking phenomena arising from the plastic incompressibility associated with von Mises plasticity and currently encountered with standard 4-node tetrahedral elements. The numerical results generated by the nodal approach are compared to those obtained with more classical simulations using finite elements based on mixed displacement–pressure formulations: 8-node Q1P0 hexahedra (linear displacement, constant pressure) and 4-node P1P1 tetrahedra (linear displacement, linear pressure). The comparisons evidence the efficiency of the nodal approach for the simulation of complex thermal–elastic–plastic problems.

中文翻译：

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基于节点积分的有限元新方法用于焊接过程数值模拟

本文旨在介绍一种基于节点积分的新型有限元方法，用于数值计算焊接过程中产生的残余应力。所提出的方法的主要优点是基于一阶四面体网格，从而大大简化了使用当前可用的网格划分工具对复杂几何形状进行网格划分的过程。此外，该问题的提出避免了由与冯·米塞斯（von Mises）塑性相关的塑性不可压缩性引起的任何锁紧现象，并且这种现象目前在标准4节点四面体单元中遇到。将节点方法产生的数值结果与使用基于混合位移-压力公式的有限元进行的经典模拟得到的结果进行比较：8节点Q1P0六面体（线性位移，恒定压力）和4节点P1P1四面体（线性位移，线性压力）。这些比较证明了节点法在模拟复杂的热弹塑性问题方面的效率。