基于比例边界有限元的温度断裂研究

Thermal fracture analysis based on the Polygon Scaled boundary finite element method

温度荷载是导致结构开裂、影响结构稳定性的一个重要因素。本文基于比例边界有限元方法提出了温度断裂分析的模型。利用比例边界有限元法求解结构温度场,结构分析中的温度荷载表示为径向坐标的函数并等效为若干项幂级数之和,基于线性叠加原理求解结构响应。该模型的特点包括:只需离散求解域的边界从而降低了求解问题的维数;在求解裂缝尖端的温度场、位移场和应力场时均可获得半解析解,应力强度因子求解精度高。通过多个板承受温度荷载的温度场分析与结构分析可以看出利用较少的网格即可获得较高的精度,模拟所得的应力强度因子随着裂缝长度的增长而增长,并且本模型计算的应力强度因子与现有文献结果一致,证明了本模型的有效性。

Thermal load can lead to cracking of structure and thus seriously influence the stability of the structure. A numerical model for the thermal fracture analysis is presented based on the Scaled Boundary Finite Element Method（SBFEM）. The temperature distribution is solved via the SBFEM,then the corresponding thermal load is divided into several items in the form of power functions,and the structural response is further obtained based on the principle of linear superposition. In the presented model,only the boundary of the structure is discretized,the temperature,displacement and stress fields can be obtained semi-analytically,thus the stress intensity factors are solved with high precision. Through multiple plate under temperature load,temperature field analysis and structure analysis can be seen that using fewer grid can obtain higher precision.Simulation results of stress intensity factor as the growth of the crack length increases,and the stress intensity factor consistent with the existing literature,which demonstrates the effectiveness of the model.