Abstract In this paper, a new solution approach of using Free Element Method (FrEM) is proposed to solve thermal-mechanical problems consisting of composite materials and cracks. In this approach, the computational domain of the problem is discretized into multi-zones and in each zone a set of local nodes are generated. At the local nodes of each zone, the high order free elements are used to collocate the governing differential equations, and at the interface nodes of adjacent zones the balance (conservative) conditions are employed to set up the global system of equations according to the connectivity of each zone’s local nodes with respect to the defined global nodes. To improve the ability of the proposed zonal FrEM in solving large-scale problems, the physical variables within each zone are condensed to the boundary variables of the zone through an ingenious equation solving technique. To simulate the discontinuity of the fluxes/tractions at corners and cracks meeting by different zones or on the outer boundaries with jumped fluxes/tractions, a discontinuous zone technique is proposed at these places by defining multiple nodes at the same corner. A number of numerical examples including cracks and functionally graded materials (FGMs) are analyzed to verify the correctness and efficiency of the proposed method.

中文翻译：

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可变冷凝不连续区自由单元法及其在带裂纹功能梯度材料结构热应力分析中的应用

摘要 本文提出了一种利用自由单元法（FrEM）求解复合材料和裂纹热力学问题的新方法。在这种方法中，问题的计算域被离散化为多个区域，并在每个区域中生成一组本地节点。在每个区域的局部节点处，利用高阶自由单元来配置控制微分方程，在相邻区域的界面节点处，根据连通性，采用平衡（保守）条件建立全局方程组每个区域的本地节点相对于定义的全局节点。为了提高所提出的区域 FrEM 解决大规模问题的能力，通过巧妙的方程求解技术，将每个区域内的物理变量浓缩为区域的边界变量。为了模拟不同区域相遇的拐角处的通量/牵引力的不连续性，或者在具有跳跃通量/牵引力的外边界上，通过在同一拐角处定义多个节点，在这些地方提出了一种不连续区域技术。分析了包括裂纹和功能梯度材料（FGM）在内的许多数值例子，以验证所提出方法的正确性和有效性。通过在同一角落定义多个节点，在这些地方提出了一种不连续区域技术。分析了包括裂纹和功能梯度材料（FGM）在内的许多数值例子，以验证所提出方法的正确性和有效性。通过在同一角落定义多个节点，在这些地方提出了一种不连续区域技术。分析了包括裂纹和功能梯度材料（FGM）在内的许多数值例子，以验证所提出方法的正确性和有效性。