基于近场动力学微分算子的含裂纹正交各向异性板热传导分析方法

Heat Conduction Analysis of Cracked Orthotropic Plates by Using Peridynamic Differential Operator

采用近场动力学微分算子(Peridynamic Differential Operator,PDDO)理论建立正交各向异性板热传导的非局部模型.通过构造近场动力学函数,将边界条件和热传导方程由局部微分形式转化为非局部积分形式,引入Lagrange乘子,采用变分分析对含裂纹正交各向异性板温度及裂纹尖端的热通量分布进行求解.通过对比算例,验证了该模型具有较好的收敛性和有效性.分析了正交各向因子、材料铺设角、裂纹倾角及间距对裂纹尖端热通量的影响.结果表明,基于PDDO建立的含裂纹正交各向异性板稳态热传导模型,考虑了稳态热传导问题中的非局部性,能有效提高计算精度,预测含裂纹板中裂纹尖端出现的奇异性.

The steady-state heat conduction in cracked orthotropic plates with the Neumann and Dirichlet boundary conditions are studied by employing the peridynamic differential operator(PDDO).A nonlocal model for analyzing heat conduction problems in orthotropic plates is first developed by using the PDDO.The nonlocal interactions between each material point and other points within certain neighboring domain are described,and the boundary conditions as well as the steady-state heat conduction equations are transformed from the local differential form in conventional continuum mechanics to the nonlocal integral form by introducing the peridynamic functions.The peridynamic functions for the derivatives are determined directly by making them orthogonal to each term in the Taylor series expansion(TSE).The Lagrange multipliers and variational analysis are introduced as numerical implementation schemes to solve the temperature field and heat flux distributions near the crack tip in orthotropic plates.The steady-state heat conduction in an orthotropic plate with different orthotropic factors and material ply angles is then analyzed,and the convergence and effectiveness of the proposed model are verified through benchmark tests.Moreover,the effects of different crack angles and spacing on heat flux at the crack tips in orthotropic plates are analyzed.The results show that the distribution of temperature and heat flux in an orthotropic plate vary with the properties of orthotropic materials,and the variations of crack angle and spacing significantly influence the heat flux at crack tip.It is shown that the proposed steady-state heat conduction model for orthotropic plate based on the PDDO can effectively improve the calculation accuracy and predict the singularity of crack tip.The PDDO-based nonlocal analysis approach provides a potential alternative for solving heat conduction problems in discontinuous and anisotropic media.