基于波谱单元法的结构动力响应分析

Dynamic analysis of structures by using spectral element method

通过修改波谱单元法中单元刚度矩阵的波数,在既有波谱单元算法基础上引进了结构外部粘滞阻尼和内部粘弹性阻尼.采用拉普拉斯变换替代快速傅里叶变换,克服了基于快速傅里叶变换的波谱单元法主要用于分析无限长和半无限长结构的局限性.数值计算结果表明:考虑了外部粘滞阻尼和内部粘弹性阻尼后,采用波谱单元法仍能十分简便地计算结构的动力响应,并大大减少单元数量,提高计算效率.对于文中算例,相比于有限元法,波谱单元法在精度大幅提高的情况下,计算时间至少节约了50%.

An extended spectral element method （SEM） for structural dynamic analysis is proposed. Both external viscous damping and internal viscoelastic damping of structures were considered in this method. The damping of structure was introduced by modifying the wave number in the spectral element stiffness matrix. Because of the periodicity of fast Fourier transform （FFT）,the FFT-based SEM mainly concentrated on infinite or semi-infinite elements. Laplace transform instead of FFT is presented to avoid the periodicity in SEM. In order to verify the effectiveness of SEM,the numerical results obtained from SEM were compared with those obtained from the finite element method （FEM）. The results show that by modifying the wave number properly,both internal viscoelastic damping and external viscous damping can be considered without any difficulty. The SEM has been proved to be an efficient method to analyze the dynamic responses of structures while the numbers of elements can be greatly decreased. The SEM can obtain up to 50% reduction in computations versus traditional FEM for numerical simulation.