Patent ID: 7392163
Filing Date: 2008-06-24
Classification: G06F

Abstract:
1. A method for controlling hourglass deformations of an under-integrated solid element in a finite element analysis for designing and analyzing a structural product, the method comprising: establishing a local initial element coordinate system of the under-integrated solid element from an initial undeformed geometry of the solid element; establishing a local current element coordinate system of the solid element from a current deformed geometry of the solid element; calculating a set of initial nodal coordinates of the solid element in the local initial element coordinate system; calculating a set of current nodal coordinates of the solid element in the local current element coordinate system; evaluating a set of hourglass shape vectors of the solid element from the initial nodal coordinates; calculating a set of hourglass deformation magnitudes of the solid element as set forth in Equation as follows: Equation: where: N=total number of the corner nodes in the solid element, J=one of the corner nodes, ĝ {circumflex over (x)} evaluating a set of generalized hourglass forces from the hourglass deformation magnitudes, the local initial nodal coordinates, and material constants of the solid element; calculating a set of counter nodal forces for controlling the hourglass deformations in the local current element coordinate system from the generalized hourglass forces and the hourglass shape vectors; and designing and analyzing a structural product by applying the set of counter nodal forces in directions opposing to the hourglass deformations such that the hourglass deformations are controlled in the finite element analysis.