The h-, p-, and r-refinements of Finite Element Analysis of Flexible Slider Crank Mechanism

Abstract

Three common refinement methods of achieving more accurate finite element solutions are to increase the number of elements, to employ higher-degree interpolation functions, and to implement an adaptive mesh by moving the nodes but maintaining the same number of elements as well as the degree of interpolation functions. This paper presents a finite element analysis by applying these refinements to a flexible slider crank mechanism. The formulation is based on the Euler—Lagrange equation, for which the Lagrangian includes the components related to the kinetic energy, the strain energy, and the work done by axial loads in a link that undergoes elastic transverse deflection. A beam element is modeled based on a translating and rotating motion. An error analysis is demonstrated by defining several error indicators, which are based on energy of an entire mechanism, transverse displacement, and bending strain of midpoints on crank and coupler. This paper also demonstrates the effect of the stiffness of the crank.