Dynamic contact of a beam–rod system with Signorini typed contact conditions and thermal effects

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Real World Applications Pub Date : 2025-06-27 DOI:10.1016/j.nonrwa.2025.104440

Sangmin Chun , Jeongho Ahn

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引用次数: 0

Abstract

This paper provides mathematical and numerical analyses for a beam–rod system with thermal effects. Its motion is described by a partial differential equation system with Signorini typed contact conditions. These conditions that cause a nonlinear model are interpreted as complementarity conditions (CCs) with a convolution. In particular, the convolution plays a role in incorporating a thermal effect of the surface of a rigid obstacle, which inspires us to investigate possibilities of proving conservation of energy under some assumptions. We employ the one-step-

θ

schemes to show that numerical trajectories for a variational formulation and the CCs are convergent. Additionally, an alternative approach supports the convergence results which are proved through the time discretizations. Finite element methods are combined with time discretization techniques to propose the fully discrete numerical schemes. Numerical stability is validated and simulations with selected data are presented as well.

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具有sigorini型接触条件和热效应的梁杆系统的动态接触

本文对具有热效应的梁杆系统进行了数学和数值分析。它的运动用带有sigorini型接触条件的偏微分方程组来描述。这些导致非线性模型的条件被解释为具有卷积的互补条件（cc）。特别是，卷积在包含刚性障碍物表面的热效应方面发挥了作用，这激励我们研究在某些假设下证明能量守恒的可能性。我们采用一步-θ格式来证明变分公式的数值轨迹和cc是收敛的。此外，另一种方法支持通过时间离散化证明的收敛结果。将有限元方法与时间离散技术相结合，提出了完全离散的数值格式。验证了该方法的数值稳定性，并对所选数据进行了仿真。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Nonlinear Analysis-Real World Applications 数学-应用数学

CiteScore

3.80

自引率

5.00%

发文量

176

审稿时长

59 days

期刊介绍： Nonlinear Analysis: Real World Applications welcomes all research articles of the highest quality with special emphasis on applying techniques of nonlinear analysis to model and to treat nonlinear phenomena with which nature confronts us. Coverage of applications includes any branch of science and technology such as solid and fluid mechanics, material science, mathematical biology and chemistry, control theory, and inverse problems. The aim of Nonlinear Analysis: Real World Applications is to publish articles which are predominantly devoted to employing methods and techniques from analysis, including partial differential equations, functional analysis, dynamical systems and evolution equations, calculus of variations, and bifurcations theory.