CAJ | 학술논문

针对修正一阶区间摄动有限元法存在的一阶Taylor展开误差较大和求解摄动逆矩阵时计算效率不高的缺陷，提出区间矩阵分解摄动有限元法(Decomposed interval matrix perturbation finite element method, DIMPFEM)。该方法将系统动态刚度矩阵分解为若干系统子矩阵之和，每个系统子矩阵的摄动矩阵用摄动因子和常量矩阵的乘积表示，避免了摄动矩阵的 Taylor展开误差；采用Epsilon算法求解摄动逆矩阵的修正Neumann级数，有效提高了计算效率。将DIMPFEM应用于具有区间参数的二维管道和二维商务车声腔模型的声压响应分析，分析结果表明，与修正一阶区间摄动有限元法比较，DIMPFEM获得了更高的计算精度和计算效率。
침대수정일계구간섭동유한원법존재적일계Taylor전개오차교대화구해섭동역구진시계산효솔불고적결함，제출구간구진분해섭동유한원법(Decomposed interval matrix perturbation finite element method, DIMPFEM)。해방법장계통동태강도구진분해위약간계통자구진지화，매개계통자구진적섭동구진용섭동인자화상량구진적승적표시，피면료섭동구진적 Taylor전개오차；채용Epsilon산법구해섭동역구진적수정Neumann급수，유효제고료계산효솔。장DIMPFEM응용우구유구간삼수적이유관도화이유상무차성강모형적성압향응분석，분석결과표명，여수정일계구간섭동유한원법비교，DIMPFEM획득료경고적계산정도화계산효솔。
To further improve the computational accuracy and efficiency of the modified interval perturbation finite element method (MIPFEM), a decomposed interval matrix perturbation finite element method (DIMPFEM) is proposed. In the proposed method, the dynamic stiffness matrix of an acoustic system is decomposed into the sum of several sub-matrices whose perturbation matrix can be expressed as the products of perturbation factors and determine matrices, thus the errors arising from the first-order Taylor expansion can be avoided. To achieve a higher computational efficiency, the inverse perturbation matrix, approximated by the modified Neumann series expansion is calculated by the epsilon-algorithm. Numerical examples on a 2D acoustic tube and a 2D acoustic cavity of a multi-purpose vehicle (MPV) with interval parameters verify that the computational accuracy and efficiency of DIMPFEM are higher than those of MIPFEM.