Mixed Finite Element Formulation Using the Absolute Nodal Coordinate Formulation
The absolute nodal coordinate formulation is a numerical approach that is specifically designed for solving problems which include large rotations and deformations.In the absolute nodal coordinate formulation, the mass matrix of the element is constant and, therefore, an inertial force vector that depend quadradically on velocities vanishes from the equation of motion.In the formulation, orientation of a node is described using slopes vectors which are obtained by differentiation of position vectors with respect to the spatial coordinates.In contrary to mass matrix, the stiffness matrix of a finite element based on the absolute nodal coordinate formulation is nonlinear.It is also noteworthy that external forces and moments which act on the element are more complex to calculate when compared to conventional finite elements.A large number of finite elements based on the absolute nodal coordinate formulation can be found from a literature.Introduced elements are applied to a wide variety of application including belts, drapes and cables.The absolute nodal coordinate formulation is also applied to modeling of tendons in a dynamic knee model.In the case of biomaterials, the finite elements that allow modeling of the special material characteristics must be utilized. Because those materials often contain a number of interdependent parameters, it can be assumed that the applied finite element has to be able to handle more than one set of unknown variables.Those element types are called the group of mixed element formulation.This group of finite elements is large and includes numerous element formulations.Variables used in the mixed formulation are usually measurable quantities, such as stresses, strains, displacements, pressures, temperatures, physical effects, etc. Although the type of mixed finite element used depends on the object being modeled, the field of mixed formulation can be seen as potential source when researching the modeling of biomechanical phenomena.The objective of this paper is to show that it is possible to introduce a simple mixed element formulation in the absolute nodal coordinate formulation.The chosen mixed finite element includes two unknown variables those are displacements and stresses.
Altarriba, Elias Dmitrochenko, Oleg Mikkola, Aki
Department of Machine DesignLappeenranta University of TechnologyLappeenranta,Skinnarilankatu 34,538 Department of Machine Design Lappeenranta University of Technology Lappeenranta,Skinnarilankatu 34,5
国际会议
上海
英文
1-12
2012-08-26（万方平台首次上网日期，不代表论文的发表时间）