CAJ | 학술논문

建立了求解多裂纹扩展的扩展有限元法。引入裂纹交叉汇合加强函数以分析多裂纹交叉汇合过程；在裂纹附近区域使用广义形函数，并引入线增函数消除混合单元，可有效地提高裂纹附近的精度；用砂浆法（线段-线段接触法）结合增广型Lagrange乘子法处理裂纹段的接触条件，可以精确地模拟裂纹面约束，并方便地求解控制方程。算例分析了两方面内容：（1）计算交叉裂纹体的应力强度因子，结果表明提出的方法精度高；（2）模拟多裂纹扩展及交叉汇合过程，模拟的裂纹扩展路径与试验结果吻合得较好，表明了方法的可靠性。
건립료구해다렬문확전적확전유한원법。인입렬문교차회합가강함수이분석다렬문교차회합과정；재렬문부근구역사용엄의형함수，병인입선증함수소제혼합단원，가유효지제고렬문부근적정도；용사장법（선단-선단접촉법）결합증엄형Lagrange승자법처리렬문단적접촉조건，가이정학지모의렬문면약속，병방편지구해공제방정。산례분석료량방면내용：（1）계산교차렬문체적응력강도인자，결과표명제출적방법정도고；（2）모의다렬문확전급교차회합과정，모의적렬문확전로경여시험결과문합득교호，표명료방법적가고성。
The extended finite element method of multiple crack growth is presented. The crack junction is analyzed using the junction enrichment function;the generalized nodal shape functions are used in a cluster of nodes around the cracks, a ramp function is used to avoid the blending element problem. These techniques can effectively improve the accuracy of stresses in the vicinity of crack. The mortar method (segment-to-segment contact approach) in combination with the augmented Larange method is adopted to establish the contact conditions between crack faces. Thus the contact is modeled precisely;and it is convenient to solve the control equations. Several numerical examples are analyzed as follows: (1) computing the stress intensity factors of the cross crack, the proposed method can obtain higher accuracy;(2) simulating the growth and coalescence of multiple cracks, the numerical results are good in agreement with the experiments;it shows the reliability of the present method.