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A non-local dissipative Lagrangian modelling for generalized thermoelasticity in solids

机译：固体广义热弹性的非局部耗散拉格朗日模型

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摘要

A generalized thermoelasticity theory emanating from the discretized Euler-Lagrange equation with dissipation in the non-local realm is formulated and proposed. The main idea of the present work is to interpolate the coupled thermal and deformation fields in solids via the discrete Lagrangian and Dissipation associated with the interaction of particles in a discrete system. The resulting governing equations for different fields are described with a full Lagrangian description such that the updating of the weight functions is eliminated in the numerical procedure. Numerical examples include (a) a one-dimensional bar with various thermal flux models, such as Fourier-type, Jeffrey-type, and Cattaneo-type thermal fluxes and (b) a two-dimensional plate with insulted cracks. In the one-dimensional case, the numerical results with a small particle influence domain show excellent agreement with the classical local model in each case while the non-locality leads to a stiffer thermal and deformation profiles of the system. In the two-dimensional case, the thermodynamic responses are easily predicted using the proposed Lagrangian-based approach. Moreover, a unified time integration is exploited to achieve the time marching of the coupled first/second order in time system. (C) 2019 Elsevier Inc. All rights reserved.
机译：提出并提出了由离散的Euler-Lagrange方程在非局部范围内耗散产生的广义热弹性理论。本工作的主要思想是通过离散系统中与粒子相互作用相关的离散拉格朗日和耗散来插值固体中的热场和形变场。用完整的拉格朗日描述描述了所得的不同领域的控制方程，从而在数值过程中消除了权重函数的更新。数值示例包括（a）具有各种热通量模型（例如傅立叶型，Jeffrey型和Cattaneo型热通量）的一维钢筋，以及（b）带有裂纹的二维板。在一维情况下，具有较小粒子影响域的数值结果在每种情况下均与经典局部模型显示出极佳的一致性，而非局部性导致系统的刚性和变形轮廓更加僵硬。在二维情况下，使用建议的基于拉格朗日方法可以轻松预测热力学响应。而且，利用统一的时间积分来实现时间系统中耦合的第一/第二阶的时间行进。 （C）2019 Elsevier Inc.保留所有权利。

著录项

  • 来源
    《Applied Mathematical Modelling》 |2019年第9期|247-265|共19页
  • 作者

    Xue Tao; Zhang Xiaobing; Tamma Kumar K.;

  • 作者单位

    Nanjing Univ Sci & Technol, Sch Energy & Power Engn, Nanjing 210094, Jiangsu, Peoples R China;

    Nanjing Univ Sci & Technol, Sch Energy & Power Engn, Nanjing 210094, Jiangsu, Peoples R China;

    Univ Minnesota Twin Cities, Dept Mech Engn, 111 Church St SE, Minneapolis, MN 55455 USA;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    Non-local theory; Meshfree method; Thermoelasticity;

    机译：非局部理论;无网格法;热弹性;

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