Abstract: Methods of numerically simulating structural behaviors of airbag made of coated fabric material are disclosed. A special purpose finite element is configured to include a membrane element and a pair of dynamically configured slave elements, which provides additional bending resistance of the coated fabric material. At each solution cycle of a time-marching simulation, nodal locations of the slave elements are updated from corresponding averaged nodal normal vector, fabric thickness and coating thickness of the coated fabric material. The averaged nodal normal vector of a particular node is an average of element normal vector of those membrane elements connected to that particular node. Respective nodal locations are offset at a distance at either side of the corresponding node of the membrane element along the averaged normal vector. Using updated nodal locations, strains and stresses of the slave elements are obtained and then converted to internal nodal forces for additional bending resistance.

Abstract: Methods of numerically simulating structural behaviors of airbag made of coated fabric material are disclosed. A special purpose finite element is configured to include a membrane element and a pair of dynamically configured slave elements, which provides additional bending resistance of the coated fabric material. At each solution cycle of a time-marching simulation, nodal locations of the slave elements are updated from corresponding averaged nodal normal vector, fabric thickness and coating thickness of the coated fabric material. The averaged nodal normal vector of a particular node is an average of element normal vector of those membrane elements connected to that particular node. Respective nodal locations are offset at a distance at either side of the corresponding node of the membrane element along the averaged normal vector. Using updated nodal locations, strains and stresses of the slave elements are obtained and then converted to internal nodal forces for additional bending resistance.

Abstract: Methods and systems for applying mass scaling in finite element analysis is described. Elements with a critical time step smaller than a user desired time step are identified. Out of these elements, elements located in a particular region requiring realistic simulated dynamic responses are processed with selective mass scaling and the rest are processed with regular mass scaling. Selective mass scaling requires more computation but can better preserve dynamic structural characteristics. The aforementioned method is referred to as a mixed mode mass scaling. Mixed mode mass scaling allows engineering simulation to be conducted within a reasonable turnaround time, because only a portion of the FEA model is subjected to more computation intensive selective mass scaling. Selective mass scaling technique includes reducing effects caused in three translational and three rotational rigid body modes of shell element.

Abstract: Improved 8-node hexahedral elements configured for reducing shear locking in finite element method are disclosed. According to one aspect, aspect-ratio based scale factors are introduced to modify partial derivatives of the isoparametric shape function of the hexahedral element with respect to isoparametric dimensions, respectively. The modified derivatives are used for calculating the Jacobian matrix thereby the rate-of-strain. The scale factor is configured such that no changes for a perfect cubic solid element (i.e., element having aspect ratio of 1 (one) in all three spatial dimensions), while significant changes for element having poor aspect ratio. In other words, elements with poor aspect ratio are mapped to a perfect cubic element using the aspect-ratio based scale factors. According to anther aspect, off-diagonal components in the local Jacobian matrix are directly modified by cancelling terms related to spurious shear deformation modes.

Abstract: Improved 8-node hexahedral elements configured for reducing shear locking in finite element method are disclosed. According to one aspect, aspect-ratio based scale factors are introduced to modify partial derivatives of the isoparametric shape function of the hexahedral element with respect to isoparametric dimensions, respectively. The modified derivatives are used for calculating the Jacobian matrix thereby the rate-of-strain. The scale factor is configured such that no changes for a perfect cubic solid element (i.e., element having aspect ratio of 1 (one) in all three spatial dimensions), while significant changes for element having poor aspect ratio. In other words, elements with poor aspect ratio are mapped to a perfect cubic element using the aspect-ratio based scale factors. According to anther aspect, off-diagonal components in the local Jacobian matrix are directly modified by cancelling terms related to spurious shear deformation modes.