求解粘弹性问题的时域自适应比例边界方法

The numerical solutions for viscoelastic problems are of significant scientific interest in practical engineering and theoretical research. In order to compute the time-space coupling viscoelastic problems, the applied numerical methods should have good accuracy,convergence and effectivity in both time and space domain.In this program a new numerical model for viscoelastic problems is developed by combining an adaptive algorithm in time domain and scaled boundary method. In time domain the piecewise adaptive algorithm in time domain is employed to maintain computing accuracy under different step size by virtue of adaptive technique.In space domain the Scaled Boundary Method (SBM) is proposed no only providing an alternative accurate boundary based method for general viscoelastic problems but also very suitable for those involving stress singularity or unbounded domains.Particularly more efforts will be made for viscoelastic fracture problems including the simulation of the initiation and propagation of crack and unbounded domain viscoelastic problems.Besides,both the coupling model combining SBM with other space methods and the acceleration computing for structures with cyclic symmetry will be researched together in order to make proposed algorithm more conveniently and effectively. The research of this program will provide a new approach and numerical tool for the research in the areas of viscoelastic problems.It appeals that currently there is very few work directly relative to this program, thus it is a good opportunity to make innovative work as well.

粘弹性问题的数值求解具有重要的工程应用背景和理论探讨价值。为了能够更精确地求解具有时空耦合性质的粘弹性问题，所采用的数值方法需要同时在时域和空间上都具有良好的精度、收敛性和计算效率。在本项目中，拟将时域自适应算法和比例边界法相结合，发展一种新的求解粘弹性问题的数值模型。在时域上，采用分段时域自适应算法，借助自适应技术充分保证时域计算精度；在空间上，采用比例边界法，能够为一般的粘弹性问题提供一种具有较高精度的边界类方法，同时能够更加有效地求解带有应力奇异性或无限域的问题。特别关注粘弹性断裂问题和无限域粘弹性问题的计算，实现对粘弹性裂纹开裂和扩展的数值模拟。此外，还将研究比例边界法与其他空间方法的耦合模型和旋转周期对称结构的加速计算，以提高其适用性和计算效率。为粘弹性问题的研究提供一种新的途径和数值求解工具。目前粘弹性问题研究中似很少有类似本项目的直接相关报道，是开展创新性研究的良好契机。

粘弹性问题的数值求解具有重要的工程应用背景和理论探讨价值。为了能够更精确地求解具有时空耦合性质的粘弹性问题，所采用的数值方法需要同时在时域和空间上都具有良好的精度、收敛性和计算效率。在本项目中，将时域自适应算法和比例边界法相结合，发展了一种新的求解粘弹性问题的数值模型。在时域上，采用分段时域自适应算法，借助自适应技术充分保证时域计算精度；在空间上，采用比例边界法，能够为一般的粘弹性问题提供一种具有较高精度的边界类方法，同时能够更加有效地求解带有应力奇异性或无限域的问题。特别关注粘弹性断裂问题和无限域粘弹性问题的计算。此外，还研究了比例边界法的加速计算，以提高其适用性和计算效率。本项目研究为粘弹性问题的理论研究和工程应用提供一种新的途径和数值求解工具。