Meshfree co‐rotational formulation for two‐dimensional continua

In this paper, a meshfree co‐rotational formulation for two‐dimensional continua is proposed. In a co‐rotational formulation, the motion of a body is separated into rigid motion and strain‐producing deformation. Traditionally, this has been done in the setting of finite elements for beams and shell‐type elements. In the present work every node in a meshfree discretized domain has its own co‐rotating coordinate system. Three key ingredients are established in order to apply the co‐rotational formulation: (i) the relationship between global and local variables, (ii) the angle of rotation of a typical co‐rotating coordinate system, and (iii) a variationally consistent tangent stiffness matrix. An algorithm for the co‐rotational formulation based on load control is provided. Maximum‐entropy basis functions are used to discretize the domain and stabilized nodal integration is implemented to construct the global system of equations. Numerical examples are presented to demonstrate the validity of the meshfree co‐rotational formulation. Copyright © 2009 John Wiley & Sons, Ltd.