Development of an adaptive explicit algorithm for static simulation using the vector form intrinsic finite element method

The vector form intrinsic finite element (VFIFE) method is a solution technique for nonlinear structural problems, which describes a continuous body using a set of particles instead of a mathematical function. Thus, a dynamic particle equation can be established by Newton's law of motion, and a viscous or kinetic damping can be introduced to obtain the steady state of the structure. This paper focuses mainly on the development of a stability condition regarding the explicit central difference method used in VFIFE to guarantee the system's convergence. The process is established and evaluated in combination with a dynamic relaxation method with kinetic damping and discrete control theory. Four numerical examples of structure nonlinear problems are used to verify the accuracy, stability and efficiency of the method.