Effects of adaptive discretization on numerical computation using meshless method with live-object handling applications

Numerical methods that are more reliable, general and stable have become increasingly popular in industry. As the most widely applied engineering computational method, the Finite Element Method (FEM) has difficulty solving certain problems where its mesh has to be modified during the computation. In this research, we focus on a new computational method called the Meshless Method (MLM). This method is built upon the same theoretical framework as FEM but needs no mesh. Consequently, the computation becomes more stable and the adaptive computational scheme becomes easier to develop.; The major issue associated with MLM is its lower computational efficiency compared with FEM. Adaptive computations can help reduce the number of nodes used in computation and improve the efficiency. For this reason, this research investigates practical issues related to the MLM and develops an adaptive algorithm to automatically insert additional nodes and improve computational accuracy. The study has been in the context of the two engineering problems: magnetic field computation and large deformation contact. First, we investigate the effect of two discretization methods (strong-form and weak-form) in MLM for solving linear magnetic field problems. Special techniques for handling the discontinuity boundary condition at material interfaces are proposed in both discretization methods to improve the computational accuracy. Next, we develop an adaptive computational scheme in MLM that is comprised of an error estimation algorithm, a nodal insertion scheme and a numerical integration scheme. As a more general approach, this method can automatically locate the large error region around the material interface and insert nodes accordingly to reduce the error. We further extend the adaptive method to solve nonlinear large deformation contact problems. Contact problems are time-consuming to solve since they are highly nonlinear problems and often need a lot of iterations to converge. With the ability to adaptively insert nodes during the computation, the developed method is capable of using fewer nodes for initial computation and thus, effectively improves the computational efficiency.; Engineering applications of the developed methods have been demonstrated by two practical engineering problems encountered in the development of the live object transfer project at Georgia Tech. In the first problem, the MLM has been utilized to simulate the dynamic response of a non-contact mechanical-magnetic actuator for optimizing the design of the actuator. In the second problem, the contact between the flexible finger and the live poultry product has been analyzed by using MLM. These applications show the developed method can be applied to a broad spectrum of engineering applications where an adaptive mesh is needed.