Direct stiffness method

About: Direct stiffness method is a research topic. Over the lifetime, 2584 publications have been published within this topic receiving 53131 citations.

Numerical aspects of the eXtended Finite Element Method

Abstract: The eXtended Finite Element Method (XFEM) is a very efficient way to reduce mesh dependencies when analysing crack growth. Displacements and stresses around the crack tip are calculated using additional shape functions which span the analytical displacement field around a crack tip. In this paper the following numerical aspects of the XFEM are discussed: • The integration of the stiffness matrix has to be done accurately. Therefore singular functions have to be integrated and an error estimator must be available. We will compare the estimated error and the necessary number of integration points when using different routines. • In case a crack truncates a very small part of a finite element the global stiffness matrix may become singular. One possibility to overcome this problem is to delete some of the enhanced degrees of freedom in the finite element analysis. Another way is to remove zero eigenvalues in the global stiffness matrix algebraically by a stabilization term. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Stiffness modeling of a family of 6-DoF parallel mechanisms with three limbs based on screw theory

Abstract: The stiffness modeling of a family of six degrees of freedom (DoF) parallel mechanisms with configurations of 3-RUPU is presented The mobility of the mechanisms is firstly analyzed, and then the stiffness analysis and modeling of the family of mechanisms is developed by a novel screw-theory based method The method employs screw theory as a tool for force analysis and deformation analysis Based on the developed stiffness model, two global flexibility indices, which refer to the maximum and minimum singular values of compliance matrix, are introduced to evaluate the compliance of parallel mechanisms Finally, a case study is presented to demonstrate the effectiveness of the method in analyzing and evaluating the stiffness behavior of the presented parallel mechanisms

Penalty Based Algorithms for Frictional Contact Problems

Abstract: The finite element method is a numerical method that can be successfully used to generate solutions for problems belonging to a vast array of engineering fields: stationary, transitory, linear or nonlinear problems. For the linear case, computing the solution to the given problem is a straightforward process, the displacements are obtained in a single step and all the other quantities are evaluated afterwards. When faced with a nonlinear problems, in this case with a contact nonlinearity, one needs to account for the fact that the stiffness matrix of the systems varies with the loading, the force vs. stiffness relation being unknown prior to the beginning of the analysis. Modern software using the finite element method to solve contact problems usually approaches such problems via two basic theories that, although different in their approaches, lead to the desired solutions. One of the theories is known as the penalty function method, and the other as the Lagrange multipliers method. The hereby paper briefly presents the two methods emphasizing the penalty based ones. The paper also underscores the influence of input parameters for the case of the two methods on the results when using the software ANSYS 12.