Dynamic analysis of magnetoelectroelastic materials with cracks under Impact loading

在本项目中，将研究裂纹磁电弹性材料和结构在机械、电气和磁冲击载荷下的动态特性。为此，将发展一种准确、高效、高性能的时域边界元方法。基于磁电弹性表示公式，首先推导出强奇异和超奇异随时间变化的边界积分方程和相应的动力学基本解。对于边界积分方程的数值解，将采用一种新的时间步进格式。对于时间离散化将采用卷积正交法或配点法，而对于空间离散化将采用配点法或伽辽金法。所开发的时域边界元应能够并适用于具有任意边界和裂纹形态的电磁弹性材料和结构在机械、电气和磁冲击载荷作用下的数值模拟。在这个项目中，二维（2D）静态动态裂纹问题在无限和有限磁电弹性域将处理。特别是机械、电气和磁冲击载荷的瞬态动态效应，磁-电-弹耦合的效应，并详细系统地分析了不同电磁裂纹面边界条件对裂纹材料和结构中动态裂纹尖端表征参数（近场）以及弹性波（远场）的传播和散射的影响。在此续期建议中，在第一个资助期进行的研究工作应继续进行和推进，而项目的剩余研究工作应进行和完成。因此，这个更新建议对于实现项目的主要目标和成功完成项目是必要的。

In this project, the dynamic properties of cracked magnetoelectroelastic materials and structures under mechanical, electrical and magnetic impact loading will be investigated. For this purpose, an accurate, efficient and high-performance time-domain boundary element method (BEM) will be developed. Based on the magnetoelectroelastic representation formulae, strongly singular and hypersingular time-dependent boundary integral equations and the corresponding dynamic fundamental solutions required will be first derived. For the numerical solution of the boundary integral equations, a novel time-stepping scheme will be implemented. For the temporal discretization the convolution quadrature or the collocation method will be adopted, while for the spatial discretization either the collocation method or the Galerkin-method will be used. The developed time-domain BEM should be able and suitable for the numerical simulation of magnetoelectroelasti materials and structures with arbitrary boundaries and crack configurations under mechanical, electrical and magnetic impact loading. In this project, two-dimensional (2D) stationary dynamic crack problems in both infinite and finite magnetoelectroelastic domains will be dealt with. In particular, the transient dynamic effects of the mechanical, electrical and magnetic impact loading, the effects of the magnetoelectroelastic coupling, and the influences of the different electromagnetic crack-face boundary conditions on the dynamic crack-tip characterizing parameters (near-field) as well as the propagation and scattering of the elastic waves (far-field) in cracked magnetoelectroelasticE materials and structures will be analyzed in details and systematically. In this renewal proposal, the research works conducted in the first funding period should be continued and advanced, and the remaining research works of the project should be conducted and completed. This renewal proposal is therefore necessary to achieve the main objectives of the project and to successfully conclude the project.