Abstract: Dynamically-positioned search domain in a time-marching numerical simulation of automobile crashworthiness is disclosed. A first computerized model representing a first object and a second computerized model (e.g., FEA model) representing a second object are received in a computer system. A time-marching numerical simulation of an impact event between the first and the second objects is conducted. Based on user-specified parameters, a search domain representing three-dimensional space of interest for detecting contacts between first and second objects is established. At each solution cycle of the time-marching simulation, search domain is repositioned as the second model deforms. Structural behaviors obtained in time-marching numerical simulation include effects from detected contacts within the search domain. Any finite element having broken free from the FEA model and being located outside of the search domain is excluded from further detection of contacts and deleted from the calculation in the simulation.

Abstract: FEA model representing a product made of at least in-part frequency-dependent material and subjected to external harmonic excitations in a range of external excitation frequencies is received in a computer system. The range of frequencies is partitioned into N frequency bands based on predefined criteria. In each frequency band, a representative frequency is selected for calculating the material properties and an eigensolution frequency range is determined for establishing upper and lower limits of subsequent eigensolution. N eigensolutions (one for each frequency band) are performed to extract natural vibration frequencies and associated mode shapes of the product. Depending upon which one of the N frequency bands each of the external harmonic excitations is located, a corresponding set of extracted natural vibration frequencies and mode shapes is selected and used in a modified mode-superposition technique to obtain steady-state dynamic (SSD) responses of the product.

Abstract: Systems and methods to create a numerical model for rubber-like material including Mullins effect based on test data obtained in a bi-axial tension test of a specimen of a rubber-like material of interest are disclosed. Based on inflating-pressure versus displacement-at-the-pole data, first set of constants of the Mooney-Rivlin constitutive equation used as strain-energy density function are determined in the loading phase. Second set of numerical constants in an unloading-phase damage function are determined. The unloading-phase damage function is used for modifying the strain-energy density function in the unloading phase and contains a hyperbolic tangent function with dimensionless operands that include a peak strain energy value occurred immediately before the unloading phase. Third set of constants in a subsequent reloading-phase damage function are determined. The subsequent reloading-phase damage function is used for modifying the strain-energy density function in the reloading phase.

Abstract: Methods and systems for conducting design sensitivity analysis of a product are disclosed. FEA model representing a product is received in a computer system having a FEA software installed thereon. The FEA software is configured for using both explicit and implicit solution schemes and allowing the FEA model to be switched back and forth between said explicit and said implicit solution schemes. Numerically simulated structural behaviors are then obtained by conducting a time-marching simulation using the FEA model in the computer system with the explicit solution scheme. Then, DSA is conducted by performing one or more snapshot structural analyses at respective predetermined solution cycles using the same FEA model with the implicit solution scheme. Each snapshot structural analysis is based on the simulated structural behaviors obtained at that solution cycle. The DSA includes one or more partial derivatives of a structural response of interest versus a selected design variable.

Abstract: Techniques for reporting realistic kinetic energy of a multi-part FEA model are disclosed. FEA model representing a product is received. The product contains more than one parts, each part comprises multiple finite elements. Nodal lumped masses are defined therein to ensure a realistic mass distribution. Kinetic energy of the nodal lumped masses shared by multiple parts is acutely computed for the shared parts. Each of the nodal lumped masses is allocated and accumulated into respective portions as an added mass contribution in accordance with a set of predefined rules for various sharing situations of the finite elements that share the nodal lumped mass. Numerically-simulated structural responses are obtained by conducting a time marching simulation using the FEA model. Finally, kinetic energy of each finite element is reported; calculated using the obtained structural responses, the element mass, and the corresponding added mass contribution from the nodal lumped masses.

Abstract: Methods and systems for conducting numerical simulation of structural behaviors in solid mechanics using smoothed particle Galerkin formulation are disclosed. A meshfree model representing a physical domain defined by a plurality of particles is received in a computer system. Each particle is configured for material properties of portion of the physical domain it represents. A smoothed displacement field of the physical domain subject to defined boundary condition is obtained by conducting a time-marching simulation using the meshfree model based on smoothed particle Galerkin formulation. The smoothed displacement field is derived from a set of smoothed meshfree shape functions that satisfies linear polynomial reproduction condition. The set of smoothed meshfree shape functions is constructed by convex meshfree approximation scheme and configured to avoid calculation second order derivatives.

Abstract: A bond model in DEM is disclosed. The model includes receiving initial location, volume, mass density, bulk shear moduli of discrete particles representing physical domain made of heterogeneous material; assigning an influence range to each discrete particle; establishing a plurality of bonds for connecting the discrete particles, each of the bonds is divided into first and second sub-bonds with the first sub-bond connecting to a first discrete particle and the second sub-bond connecting to a second discrete particle, the said first and second discrete particles are located within the influence range. Each discrete particle is connected to one or more sub-bonds; dividing the volume of each discrete particle into one or more sub-bonds so that one or more sub-bonds are assigned with properties that include length and cross-section area; and obtaining numerically simulated physical phenomena within the physical domain by conducting a time-marching simulation of the bonds with assigned properties.

Abstract: Techniques of joining imperfectly-matching NURBS patches to form a computerized model suitable for FEA are disclosed. Definitions of first and second patches are received for joining together along a physical boundary defined in first and second curves that are imperfectly-matching. Both curves' knot-vectors are normalized such that the parametric length equals the physical length, respectively. The curve having less number of control points is designated as master curve, the other as slave curve. If the curves are partially overlapped the first and second curves are adjusted such that first and second projection points correspond to starting and end locations of the common curve, respectively A set of linear constraint equations for numerically connecting the patches along the physical boundary by computing dependencies of the slave curve's control points to the master curve's control points. The patches together with the constraint equations enable a computerized model created therefrom suitable for FEA.

Abstract: Systems and methods of conducting a time-marching simulation of manufacturing a sheet metal part that requires progressive lancing operation (PLO) are disclosed. The time-marching simulation is conducted with a connection-separation scheme for nodes along the lancing route to ensure a smooth timely separation of a lancing cut. The scheme includes creating a set of surrogate lancing route nodes by duplicating nodal coordinates of the existed nodes located along the lancing route. Nodal constraints to initially link together the existed nodes and the corresponding surrogate nodes are then created. The nodal constraint is removed in accordance with a separation time schedule established using start and end locations of the lancing route and corresponding start and end time for making the lancing cut. The nodal constraints can also be removed based on the zones of the lancing route defined by a user.

Abstract: Methods used in gravity loading phase of a deep drawing manufacturing simulation including effects of sheet metal blank in contact with guide pins are disclosed. Computerized models of sheet metal blank and guide pins are created. A subset of the nodes in the first computerized model is defined as parent nodes. First and second characteristic lengths are then determined. One or more child nodes are created between each pair of the parent nodes using a formula based on the ratio between the first and second characteristic lengths. Deformed configuration of the sheet metal blank is obtained under its own weight subject to the lateral constraints by conducting computer simulation of gravity loading phase, lateral constraints are created and added to at the child node's parents, when a contact between a child node and a particular finite element representing portion of outer surface of one of the guide pins is detected.

Abstract: Systems and methods of numerical simulation of FSI using the space-time CE/SE method with a moving space-time fluid mesh coupled to a method of numerically simulating structural mechanics are disclosed. A FSI interface is determined based on fluid domain and structure definitions received in a computer system. Fluid forces acting on the FSI interface are initialized. Simulated structural behaviors are obtained using FEA in response to the received fluid forces at the FSI interface. Structural behaviors include nodal positions on the structure's exterior boundary, which are used for updating the FSI interface of the space-time fluid mesh Inner nodes of the fluid mesh are adjusted accordingly using a user-selected mesh adjustment strategy. Simulated fluid behaviors are obtained by updating fluid solutions using the CE/SE solver with the adjusted fluid mesh. The fluid forces are again applied to the FEA model for obtaining simulated structural behaviors for the next solution cycle.

Abstract: Methods and systems for creating a contact surface definition involving lower order and quadratic finite elements (QFE) in a FEA model used for numerically simulating an impact event are disclosed. FEA model is organized by one or more groups of finite elements. Each group represents one of the product's parts and is identified by a part ID. Further, the FEA model is configured with one or more contact surface definitions for detecting contacts amongst the parts due to the impact event. For each determined group that is determined to contain QFE, a new group is created. The new group is associated with a unique part ID. Contact segments for the new group are then generated in accordance with a set of predefined rules for subdividing one or more geometric shapes associated with the QFE. Contact surface definitions are updated by replacing each determined group with the new group.

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 conducting design optimization of a product using multiple metamodels are described. First and the second metamodels are configured with common kernel function. Kernel width parameter is the output or result of the first metamodel while the second metamodel requires a set of substantially similar kernel width parameters defined a priori. Further, the second metamodel is configured with an anisotropic kernel. First and second metamodels are trained in two stages. In the first stage, kernel width parameters are obtained by fitting known responses (obtained in numerical simulations) into the first metamodel with one or more prediction trends. Additional kernel width parameter set is derived by algebraically combining the obtained kernel width parameters.

Abstract: Methods and systems for numerically simulating structural behaviors of a product using explicit FEA with a combined technique of subcycling and mass scaling are disclosed. A FEA model representing a product and a minimum time step size (?tmin) for a time-marching simulation of the product are specified. N element groups is established with the first element group associated with ?tmin as required minimum time step size, while other element groups with integer multiples of ?tmin according to formula ?ti=2i-1?tmin, n=1, 2, . . . , N. Finite elements are periodically resorted into N element groups based on their new respective ?tcr. To ensure all finite elements in the FEA model are processed at the user specified minimum time step size, proper amount of mass scaling is applied to those finite elements that are or have become too small to maintain a stable solution in the first element group.

Abstract: Methods and systems for numerically simulating structural behaviors of a product using explicit FEA with a mass scaling enhanced subcycling technique are disclosed. A FEA model of the product defined by a plurality of nodes and finite elements is received. A critical time step size is calculated for each finite element and then assigned to associated nodes. Elements are partitioned into N element groups with first group requiring minimum time step size ?t1 and other element groups requiring respective time step sizes (?tN=2N?1?t1). In order not to resort or repartition the finite elements and still obtain a stable solution, respective proper amounts of mass scaling are applied to those elements that have become too small to maintain a stable solution in their respective element groups. A time-marching simulation using explicit FEA with the mass scaling enhanced subcycling technique is then conducted with such a FEA model.

Abstract: Systems and methods for numerically creating corresponding 2-D mesh models for a plurality of airbag fabric panels from a 3-D computerized model of a fully-inflated airbag are disclosed. 3-D computerized model comprises a plurality of nodes and a plurality of shell finite elements. Each shell element is categorized as to which one of a plurality of fabric panels that form the airbag it belongs. Each fabric panel occupies a continuous surface area of the airbag. Shell finite elements of a particular fabric panel are unfolded to a 2-D mesh one fabric panel at a time. The total surface area of a particular fabric panel is compared with the total area of the corresponding 2-D model. Adjust the 2-D mesh model until the areas are within a predetermined tolerance. The final “total-area-matched” 2-D mesh model is further orientated to a fabric material coordinate system of warp and weft for determining manufacturability.

Abstract: Methods and systems for creating numerically-simulated rigid bodies in finite element analysis are disclosed. At least one rigid finite element in a finite element model is designated for forming one or more numerically-simulated rigid bodies (RBs). Each numerically-simulated RB comprises an arbitrary number of rigid finite elements connecting to one another in an arbitrary shape. Each numerically-simulated RB is created by locating all of the elements embedded in the FEA model through shared node or nodes. A procedure of using element definition as a guide to set up an array of node flags, each node flag for one node such that all numerically-simulated RBs defined in the model can be located efficiently. Once all numerically-simulated RBs have been located, each unique numerically-simulated RB is defined as a unique linked-list of connected rigid finite elements.

Abstract: Systems and methods for numerically simulating muscle's movements along bones and around joints are disclosed. A computerized model containing a plurality of truss elements along with one or more rollers is used. The truss elements are configured for modeling a muscle strand while each roller is configured for a joint. Each truss element includes two end nodes and is configured or associated with a muscle bio-mechanical property model. Each roller is fixed at the location of a corresponding joint. To simulate the muscle strand movements around the joint, each pair of truss elements straddling a roller is adjusted dynamically in a time-marching simulation (e.g., computer simulation of an impact event of an automobile and one or more occupants). Adjustments are performed at each solution cycle of the time-marching simulation. Adjustments include two types—“slipping” and “swapping”.

Abstract: Systems and methods of computer aided engineering analysis using hybrid approach of finite element method (FEM) and adaptive smoothed particle hydrodynamics (SPH) are described. According to one aspect, a computer-aided engineering analysis is performed to simulate an impact event between structures. A FEM grid model is created to represent the structures using a plurality of solid elements which represents geometry and material properties. Once a contact between two structures resulted into a material or structural failure according to predefined material constitutive equation, solid elements representing the failed portion of the structure are removed. Each failed solid element is then replaced by a plurality of particles to be analyzed using the SPH analysis. The particles replacing the failed element inherit all of the states and properties of the failed element, such as location, mass, velocity, acceleration, etc.