The main aim of this article is to develop a new boundary element method (BEM) algorithm to model and simulate the nonlinear thermal stresses problems in micropolar functionally graded anisotropic (FGA) composites with temperature-dependent properties. Some inside points are chosen to treat the nonlinear terms and domain integrals. An integral formulation which is based on the use of Kirchhoff transformation is firstly used to simplify the transient heat conduction governing equation. Then, the residual nonlinear terms are carried out within the current formulation. The domain integrals can be effectively treated by applying the Cartesian transformation method (CTM). In the proposed BEM technique, the nonlinear temperature is computed on the boundary and some inside domain integral. Then, nonlinear displacement can be calculated at each time step. With the calculated temperature and displacement distributions, we can obtain the values of nonlinear thermal stresses. The efficiency of our proposed methodology has been improved by using the communication-avoiding versions of the Arnoldi (CA-Arnoldi) preconditioner for solving the resulting linear systems arising from the BEM to reduce the iterations number and computation time. The numerical outcomes establish the influence of temperature-dependent properties on the nonlinear temperature distribution, and investigate the effect of the functionally graded parameter on the nonlinear displacements and thermal stresses, through the micropolar FGA composites with temperature-dependent properties. These numerical outcomes also confirm the validity, precision and effectiveness of the proposed modeling and simulation methodology.

中文翻译：

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具有温度相关特性的微极性FGA复合材料非线性热应力建模和仿真的新边界元算法

本文的主要目的是开发一种新的边界元方法（BEM）算法，以建模和模拟具有温度相关特性的微极性功能梯度各向异性（FGA）复合材料中的非线性热应力问题。选择一些内部点来处理非线性项和域积分。首先使用基于基尔霍夫变换的积分公式来简化瞬态热传导控制方程。然后，在当前公式中执行残余非线性项。通过应用笛卡尔变换方法（CTM）可以有效地处理域积分。在提出的BEM技术中，在边界和一些内部域积分上计算非线性温度。然后，可以在每个时间步长计算非线性位移。利用计算出的温度和位移分布，我们可以获得非线性热应力的值。通过使用避免通信的Arnoldi（CA-Arnoldi）预调节器来解决由BEM产生的线性系统，以减少迭代次数和减少计算时间，我们提出的方法的效率得到了提高。数值结果建立了温度依赖性特性对非线性温度分布的影响，并通过具有温度依赖性特性的微极性FGA复合材料研究了功能梯度参数对非线性位移和热应力的影响。这些数值结果也证实了所提出的建模和仿真方法的有效性，准确性和有效性。