The novel computational scheme known as quasicontinuum (QC) has been widely utilized over the past decade for exploring extreme/multi-scale phenomena in the spatial domain, such as, mechanical behaviors of nanostructures or defect behaviors in crystalline materials. This work reports on the recent extension of the QC method to simulate mechanical behaviors or deformations of curved crystalline bodies such as carbon nanotubes (CNTs). In addition to QC implementation utilizing high-order triangular elements, this study presents a new QC approach based on what is known as “variable-node elements”. This proves to be extremely efficient when combined with a fully automatic adaptive refinement. Several numerical examples demonstrate the accuracy and effectiveness of the new method.

Welding is one of the most prevailing manufacturing processes. A critical concern is its quality in terms of residual stresses and deformations as well as the welding strength. In spite of such a key interest, the analysis of welding deformations has not been so successful as in structural analysis. This is partly because welding involves much more complex phenomena than purely mechanical processes, and such complexities are manifested by the kinetics process regarding the phase evolution and by the thermo-mechanical processes as well.

Two- and Three-dimensional variable-node elements have been developed using moving least square (MLS) approximation and point interpolation. For two-dimensional quadrilateral elements, the variable-node finite elements were proposed to allow an arbitrary number of nodes on element edge for four-node linear elements and nine-node quadratic elements. Moreover, based on an eight-node hexahedral element in three-dimensional domains, the variable-node element was developed to allow additional nodes on the element face as well as element edge. These elements satisfy the basic properties of finite elements, such as partition of unity, linear or quadratic completeness, Kronecker delta condition. Therefore, the variable-node elements are directly used in the framework of the conventional FEM, without any process such as projection, interpolation, and imposition of constraints on the interface between the different meshes. In addition, when the domain is constructed with the variable-node elements, the system matrix remains symmetric, and then the symmetric solver is applicable to efficiently obtain the solution. That is, the use of this element makes it possible to connect the different-level meshes in a seamless way, satisfying nodal connectivity and compatibility across the interface.

Fluid-solid interaction (FSI) is one of the most challenging problems in computational mechanics field. Also the demands of simulations for fluid-solid interaction problem are continuously increasing in the various industries. It is very difficult mission to obtain the numerical solution of FSI problems because of non-matching meshes along the fluid-solid interface. In this study, non-matching meshes on the fluid-solid interface are effectively connected by using variable-node element. The description of the presented scheme is posted on Fig.1. And, two numerical examples are posted to verify the performance of the present scheme.