计算力学学报2024，Vol.41Issue(4)：689-695,7.DOI:10.7511/jslx20221222001
含V型缺口分数阶黏弹性复合材料反平面界面断裂的辛方法
A symplectic method for the anti-plane fracture analysis of an interface V-notch in fractional viscoelastic media
摘要
Abstract
This paper presents a symplectic method for the anti-plane fracture analysis of an interface V-notch in fractional viscoelastic composite media.The fractional Kelvin Zener model is used to describe the viscoelastic characteristics of materials.With the help of Laplace transform,the fundamental equations of an anti-plane viscoelastic fracture problem in time domain are transformed into frequency domain.By introducing the dual generalized stress variables,the Hamiltonian system is established.Then the eigenvalues and eigensolutions of the Hamiltonian dual equation are obtained by the method of separation of variables,and the unknown coefficients of the symplectic series are determined by the symplectic adjoint orthogonal relationship and the outer boundary conditions.In this way,the analytical expression of the anti-plane stress/strain intensity factor of the viscoelastic media with a V-notch is derived obtained.Finally,the intensity factor in time domain is found by inverse Laplace transform.In numerical examples,the accuracy of the presented method is verified,and the effects of fractional order parameters,notch angle and external load on the stress/strain intensity factor are revealed.关键词
辛方法/分数阶黏弹性/界面断裂/反平面/应力强度因子Key words
symplectic method/fractional viscoelastic media/interfacial fracture/anti-plane/stress intensity factor分类
数理科学引用本文复制引用
徐成辉,孙义国,冷森,邓子辰..含V型缺口分数阶黏弹性复合材料反平面界面断裂的辛方法[J].计算力学学报,2024,41(4):689-695,7.基金项目
陕西省自然科学基础研究计划(2022JM-016) （2022JM-016）
国家自然科学基金(12072266,11702221) （12072266,11702221）
西北工业大学教育教学改革研究项目(双碳专项)(ST2023JGY02)资助. （双碳专项）
