《余能理论》引领中国变分原理的研究

正今年是钱令希院士诞辰100周年,带着崇敬的心情我们缅怀先生的一生。作为一名杰出的科学家,除了在很多研究工作中取得优秀的成果,钱令希先生的战略眼光更值得我们学习。1950年钱令希先生在中国科学杂志发表《余能理论》1]。论文中钱令希先生引用了Westergaard 1941年关于余能原理的论文,特别引用了Westergaard的观点,认为余能方法没有受到与其价

The paper "Principle of complementary energy" guides the research of variational principles in China

Research progress of the hybrid modeling methods of peridynamics(PD)and the finite element method(FEM)is reviewed.All the basic principles and features of the existing hybrid modeling methods and the research work of our group on this topic are introduced.There are four types of existing hybrid modeling methods,including the displacement constraint method,force coupling method,morphing function method and submodeling method.Except submodeling method,the other ones belong to the concurrent multiscale analysis method,whose basic modeling idea is that the computational structure can be divided into peridynamic subregion,finite element subregions,and junction regions (or overlapping regions,or interface elements,or transition zones).The submodeling method can be regarded as an explicit and explicit analysis method.It is first solved by the FEM globally,then solved by PD locally.The computational accuracy of the junction and the ghost force need to be eliminated during the hybrid modeling.Through a comprehensive analysis,our group proposes a new approach to coupling the discretized PD and FEM based on the implicit scheme to take advantage of both methods.There is no longer an overlapping regions between PD subregions and FE subregions,therefore a truss element is introduced to bridge FE subregions and PD subregions.The FE nodes at the interface interact not only with other FE nodes of their connected elements,but also with PD points within the sphere of certain radius.As it has been proved to be effective and efficient in analyzing crack propagation problems,the proposed hybrid model is effective for failure analysis of engineering structures.