求解粘弹性问题的时域自适应等几何比例边界有限元法

A TEMPORALLY PIECEWISE ADAPTIVE ISOGEOMETRIC SBFEM FOR VISCOELASTIC PROBLEMS

提出一种基于分段时域自适应算法和等几何分析的求解粘弹性问题的数值方法。利用时域分段展开,建立了递推格式的比例边界元求解方程,环向比例边界采用等几何技术离散,在继承常规比例边界有限元半解析、便于处理应力奇异性/无限域问题等优点的同时,可更准确地描述几何边界,由此进一步提高了计算精度;在时域,通过分段时域自适应计算,保证不同时间步长下的计算精度。通过数值算例,从计算精度、收敛性等方面,对所提方法的有效性进行了验证。

A new numerical algorithm is presented to solve viscoelastic problems by combining a temporally piecewise adaptive technique with the isogeometric analysis.By expanding variables at a discretized time interval,a series of recursive scaled boundary finite element method equations in spatial domain is established with non-uniform rational B-spline discretization in the circumferential direction.The proposed algorithm not only takes advantages of conventional scaled boundary finite element method in dealing with singularity and unbounded domains,but also provides a more accurate geometric description of the boundary,resulting in more accurate special solutions.A piecewise adaptive process is utilized to fully maintain a steady accuracy in the time domain for different sizes of time step.Numerical examples are presented to demonstrate the effectiveness of the proposed model in term of computational accuracy and convergence.