Abstract: Numerically-simulated physical behaviors of workpiece sheet metal during a metal forming process having a predefined load path is obtained based on received FEA mesh model and mesh adjustment criteria as follows: initializing current simulation time; determining current simulation period from current simulation time and next mesh adjustment time; using characteristic length to establish a 3-D mesh refinement zone that contains a space encompassing a corresponding section of the predefined load path for the current simulation period; updating the FEA mesh model by refining those finite elements located within the 3-D mesh refinement zone to a desired level and by coarsening certain finite elements outside of the zone according to mesh coarsening criterion; conducting corresponding portion of the time-marching simulation using the updated FEA mesh model for current simulation period until current simulation time reaches next mesh adjustment time; and repeating until current simulation time passes the total simu

Abstract: First model representing a fixed barrier and second model representing an automobile to be improved according to crashworthiness criteria are received in a computer system. Time-marching simulation of an impact event between the first and the second models 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, search domain is automatically repositioned without any user interaction, to align with a local coordinate system affixed to the second computerized model that moves and rotates in response to detected contacts. Numerically-calculated structural behaviors obtained in the 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: Numerical simulation method includes receiving a manufacturing process configuration specification for moving various types of arbitrarily-shaped objects from an egress area onto a lower surface with desired mass flow rate in a predefined time period; creating a FEA model representing the lower surface; creating respective bonded discrete element models (BDEMs) representing the various types of the objects, each BDEM containing discrete elements connected by connection bonds; generating a list of BDEMs each with randomly-chosen types and orientation, such that total mass of the list of BDEMs exceeds a target total mass; and obtaining numerically-simulated physical behaviors of the objects in a time-marching simulation. At each solution cycle of the simulation, placing respective objects into randomly-selected ‘open’ sub-regions by activating next relevant portion of the BDEMs based on the mass flow rate and time-step size; releasing activated BDEMs from the egress area onto the lower surface.

Abstract: Methods and systems for creating a computerized model representing a layered shell-like structure are disclosed. 2-D reference mesh model and a user-specified definition of a layered shell-like structure are received in a computer system. The 2-D reference mesh model contains a plurality of reference nodes connected by a plurality of 2-D reference elements for representing the layered shell-like structure's mid-plane in the 2-D reference mesh model's thickness direction and the user-specified definition includes the number of layers and each layer's characteristics. A set of new nodal locations along respective reference nodes' normal vectors are calculated according to a set of rules derived from the user-specified definition. New nodes for defining a computerized model that represents the layered shell-like structure are created by reproducing the reference nodes at each corresponding new nodal location.

Abstract: Systems and methods of designing geometry of a tool set in a numerical simulation of sheet metal forming operations including springback compensation are disclosed. Computerized die face model representing an initial geometry of a tool set is generated for forming a sheet metal work-piece to a part's desired geometry. Numerically-simulated deep drawing operation, optional trimming operation and a springback effect are conducted to obtained a trial geometry of the part. A deviation between the trial geometry and the desired geometry is obtained. When the deviation is outside of tolerance, computerized die face model is regenerated according to a modified geometry of the tool set that includes an estimated amount of springback compensation derived from the deviation due to springback together with a node adjustment scheme for ensuring model conformity along the boundary line. Final modified geometry of the tool set is iteratively obtained.

Abstract: Methods and systems for specifying metal necking failure criteria in FEA are disclosed. FEA model contains many finite elements representing a structure, a loading condition and a metal necking failure criteria are received in a computer system. The loading condition includes a loading direction. The metal necking failure criteria includes critical strain and fracture strain values, the neck's width, and a profile of strain values between the critical strain value and the fracture strain value within the neck's width. At each solution cycle in the time-marching simulation of the structure, each finite element is check to determine whether it experiences a metal necking failure, which occurs when each finite element's strain obtained in that solution cycle is greater than an average strain value defined in a formula according to the critical strain and fracture strain values, the neck's width and the profile of the metal necking failure criteria.

Abstract: Methods of characterizing or classifying graphical representation of numerical simulation results are disclosed. A training database is created in a computer system by including a plurality of graphical representations of respective results obtained from a plurality of numerical simulations. Each graphical representation is associated with a textual description of a pertinent feature related to the numerical simulations by user. A quality index with respect to the associated textual description is calculated for each graphical representation by application module using an autocorrelation technique of correlating all graphical representations with one another in the training database. A new graphical representation obtained from another numerical simulation can then be characterized with one of the textual descriptions and a corresponding confidence score by comparing the new graphical representation with all graphical representations in the training database.

Abstract: Definition of a design space and an objective space for conducting multi-objective design optimization of a product is received in a computer system having a design optimization application module installed thereon. Design space is defined by design variables while objective space is defined by design objectives. First set of designs in the design space is selected. Each of the first set is evaluated in the objective space for non-dominance. Design space is partitioned into first and second regions using a multi-dimensional space division scheme (e.g., SVM). The first region is part of the design space containing all of the non-dominated design alternatives while the second region contains remaining of the design space. Second set of designs is selected within the first region. Each of the second set and existing non-dominated design alternatives are evaluated for non-dominance. Multi-objective optimization repeats the partition and evaluation until an end condition is reached.

Abstract: Meshfree model containing a number of particles to represent a structure made of brittle material is defined. At each non-initial solution cycle of a numerical simulation using the meshfree model based on damage mechanics, the following operations are performed: (a) determining one or more damage zones in the structure from simulated structural responses obtained in immediate prior solution cycle; (b) dividing the particles into a first group representing the damage zones and a second group representing the remaining of the meshfree model; (c) applying a meshfree regularization scheme by modifying each particle's strain field of the first group with a morphing function that ensures a homogeneous jump condition along respective borders of the damage zones; and (e) obtaining simulated structural behaviors of the structure using a meshfree stabilization scheme that applies to all of the particle's strain field. Each damage zone represents a crack that can grow over time.

Abstract: Characteristics of a blast source and a FEA model representing a surrounding fluid domain are defined. One layer of new border nodes and elements are created outside of the fluid domain's original outer boundary formed by the original border elements. Each new border element/node is associated with one of the original border elements/nodes as corresponding master element/node. At each time step of a time-marching simulation of an underwater explosion, simulated fluid behaviors are computed for all but the new border elements. The computed fluid behaviors of each original border element are saved into a corresponding lookup table configured to store the computed fluid behaviors for a predefined number of time steps in a first-in-first-out manner. Simulated fluid behaviors of each new border element are determined by interpolating, with the calculated blast wave propagation time from the master element, the stored fluid behaviors in the corresponding master element's lookup table.

Abstract: Numerical simulation techniques of physical behaviors of a string drawn out of a yarn feeder in a weaving/braiding machine are disclosed. A FEA model, representing a string having a source end at yarn feeder and a braiding end towards braiding/weaving operations, contains at least one truss element with a leading element directly connected to the source end at which pull-out force of the yarn feeder is predefined. Maximum and minimum lengths of a truss element are predefined for facilitating local remeshing. Simulated physical behaviors of the string are obtained by performing a time-marching simulation using the FEA model with the FEA application module having local remeshing capability. Simulated physical behaviors include axial forces in each truss element of the FEA model and the string's deformed geometry. Local remeshing is used for updating the computerized model by creating new leading element that satisfies consistent realistic condition, when local remeshing becomes necessary.

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: An N×N matrix is generated from computerized model representing a physical domain, comprises coefficients of N simultaneous linear equations with N unknown physical quantities associated with N degrees-of-freedom of the physical domain, and is represented by an undirected graph having N vertices connected by a plurality of edges. A best suitable partition scheme for dividing the N vertices into a separator group and, first and second mutually independent groups as follows: distance vectors of source vertices selected from the N vertices are calculated; for each distinct pair of the source vertices, the difference of respective distance vectors is used for finding a coarse graph whose adjacency coarse matrix is pentadiagonal; a trial partition scheme is determined using the coarse graph initially; the separator group is then iteratively improved by trimming vertices contained therein and merging them into one of the mutually independent groups until the separator group becomes minimal.

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 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: A finite element analysis (FEA) model of a vehicle and a rigid wall definition are received. The FEA model comprises a number of nodes connected by finite elements that are organized in groups. The rigid wall comprises one or more segments each corresponding to a load cell installed thereon. A list of groups that are desired to have a detailed rigid wall force (RWF) summary is defined by user. A contribution weighting factor is calculated for each node in the FEA model. A time-marching simulation of the vehicle colliding with the rigid wall is conducted. At each solution cycle, a nodal force contribution is calculated for each node according to node type. The calculated nodal force contribution modified with the contribution weighting factor is accumulated in the detail RWF summary under respective groups and segments. A full detailed RWF summary is presented.

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 for creating a computerized model containing polydisperse spherical particles packed in an arbitrarily-shaped volume are disclosed. To create the computerized model, a plurality of polydisperse spherical particles having statistical properties according the characteristic profile (e.g., minimum and maximum sizes and size distribution) is generated. First portion of the particles is used for forming a border layer within the volume's boundary. Any hole in the border layer is sealed with one or more null-sized particles. Second portion of the particles is used for filling up an interior space in a layer-to-layer scheme from the border layer inwards. The layer-to-layer scheme includes searching a best suitable location from a list of size-ranked candidate locations using power diagrams. Each of the second portion of the particles is allowed to pass through holes in the current layer towards the border layer when possible.

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 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.