Abstract: Systems and methods of predicting sheet metal forming failure using numerical simulations (e.g., finite element analysis) are disclosed. A FEA model is defined for a particular sheet metal forming process. Blank sheet metal is modeled with a plurality of shell elements. Additionally, a deformation path-dependent forming limit diagram (FLD) is converted to a path-independent FLD. A time-marching simulation of the sheet metal forming process is conducted using the FEA model. At each solution cycle, equivalent strain at each integration point of shell element is checked against the corresponding forming limit strain value of the path-independent FLD. The ratio of the equivalent strain and the forming limit strain is defined as formability index. A time history of the formability index of each shell element is saved into a file and displayed to a monitor upon user's instructions. When a particular element's formability index reaches one or higher, a localized necking is predicted.

Abstract: In one aspect of the invention, each bolt is modeled using a beam element in a FEA model. To apply desired pretension to one or more bolts, at least one pretension-versus-time curve is specified. Each pretension-versus-time curve includes ramp portion, desired pretension portion and optional unloading portion. Duration of the pretension-versus-time curve generally covers first 0.5-1% of total simulation time of a car crashworthiness analysis. Ramp portion starts from zero to desired pretension in a substantially linear manner, and hence being configured for applying desired pretension to a bolt gradually with smaller increments. Desired pretension portion is configured for ensuring the desired pretension can actually be applied to the beam element during an initialization process—a series of quasi-static analyses. Since the method is independent of the deformation of the beam, the method completely avoids the need to iteratively determine an axial strain or displacement that gives the desired pretension.

Abstract: Methods and systems using a numerical model to describe polymeric material properties are disclosed. FEM model of a product is defined. FEM model includes one or more solid elements of polymeric material. In a time-marching simulation of the product under loads, stress state of the solid elements is calculated from deformation gradient tensors. Stress state incorporates the Mullins effect and strain hardening effect, also includes elastic stress, viscoelastic stress and back stress. A yield surface is defined to determine whether the elements are under plastic deformation. Plastic strain is obtained to update the deformation gradient tensor, which is then used to recalculate the stress state. Calculations continue until updated stress state is within a tolerance of the yield surface, at which time the results of polymeric material elements are obtained. The numerical model takes into account all characteristics of a polymeric material.

Abstract: Systems and methods of numerically simulating airflow within porous materials are disclosed. Engineering product (e.g., car seat) represented by a finite element analysis model containing in part porous material with permeability. In each solution cycle of a time-marching simulation, each of the elements of porous material is evaluated with airflow in conjunction with the traditional mechanical response. Each element's volume change results into different pore air pressure hence a pressure gradient, which in turn is used for airflow calculated in accordance with a fluid seepage law that depends upon permeability of the porous material. Therefore, a more realistic simulation of structural behavior of porous materials can be achieved. The volume change and pressure of each element of porous material is evaluated using ideal gas law. A general form of Darcy's law includes user control parameters is used for evaluating airflow based on the pressure gradient and permeability.

Abstract: System and method of simulating large deformation and rotation of a structure in a finite element analysis used for improving structural design is disclosed. A solid finite element is configured for simulating large deformations and/or rotations of a structure. The solid finite element comprises only corner nodes with each node having six degrees-of-freedom (DOF), three translational and three rotational. In other words, each node is configured to include translational deformation and rotation deformation, each of the translational and rotational deformation has three components corresponding to one of the six DOFs. The solid finite element has a plurality of external edges. Each external edge has two ends, each end is located at one of the adjacent corner nodes. Additionally, translational deformation at mid-edge point of each external edge is implicitly embedded in the translational and rotational deformations of two adjacent corner nodes.

Abstract: A method of identifying most influential design variables in a multi-objective engineering design optimization of a product is disclosed. According to one aspect of the present invention, a product is optimized with a set of design variables and a set of response functions as objectives and constraints. Representative product design alternatives (samples) are chosen from the design space and evaluated for responses. Metamodels are then used for fitting the sample responses to facilitate a global sensitivity analysis of all design variables versus the response functions. A graphical presentation tool is configured for allowing the user to conduct “what-if” scenarios by interactively applying respective weight factors to response functions to facilitate identification of most influential design variables. Engineering design optimization is then conducted in a reduced design space defined by the most influential design variables.

Abstract: Methods and systems for numerically predicting surface imperfections on stamped sheet metal parts are disclosed. FEM mesh includes a plurality of shell elements and a plurality of nodes that represents a stamped sheet metal part. At least one surface of the part needs to be examined for imperfection, which can be used for adjusting the die for forming the sheet metal part. Each surface is created by fitting all of nodes of a portion of the FEM mesh in a group-to-group scheme. A group is defined to include a center element and its neighbors. Neighbor elements share a side with the center element are always included in the group. Each group includes at least three neighbors in additional to the center element. Node-sharing elements are added into the group such that the criterion of at least three neighbors is met.

Abstract: Systems and methods of numerically simulating physical phenomena of firing an electromagnetic rail-gun using a coupled FEM-BEM procedure are disclosed. Electromagnetic rail-gun includes a pair of parallel rails and a projectile located therebetween. Rails and projectile are represented by a FEM model, while the ambient air surrounding the rail-gun is represented by a BEM mesh for simulating the electromagnetic fields. The BEM mesh is generated from the FEM model as a surface encasing the projectile and rails. A sliding contact interface between each of the rails and the projectile causes the BEM faces in contact to be removed and thus resulting into a hole/gap in the BEM mesh. The hole/gap is patched up with new triangular BEM faces without adding new nodes in accordance with a predefined set of rules, such that the resulting BEM mesh is suitable for carrying out the coupled FEM-BEM procedure.

Abstract: Systems and methods of obtaining a set of better converged and diversified Pareto optimal solutions in an engineering design optimization of a product (e.g., automobile, cellular phone, etc.) are disclosed. According to one aspect, a plurality of MOEA based engineering optimizations of a product is conducted independently. Each of the independently conducted optimizations differs from others with parameters such as initial generation and/or evolutionary algorithm. For example, populations (design alternatives) of initial generation can be created randomly from different seed of a random or pseudo-random number generator. In another, each optimization employs a particular revolutionary algorithm including, but not limited to, Nondominated Sorting Genetic Algorithm (NSGA-II), strength Pareto evolutionary algorithm (SPEA), etc. Furthermore, each independently conducted optimization's Pareto optimal solutions are combined to create a set of better converged and diversified solutions.

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: Methods and systems for conducting a time-marching simulation of a product using a finite element analysis model including at least one multiscale substructure are disclosed. According to one aspect, a FEA model of a product is defined for a time-marching simulation. The FEA model comprises an overall structure, and at least one multiscale substructure. Each substructure corresponds to some of the master representative segments defined in the overall structure. Time-marching simulation of the product is conducted with first and second sets of timescale due to significantly different characteristic dimension of the FEA model. The first set is configured for the overall structure or master group, while the second set for the substructures or slave group. The first set is run at a time step significantly larger than the second set. Synchronization of the responses is at the end of each solution cycle corresponds to the first set of timescale.

Abstract: The present invention discloses systems and methods of conducting multi-objective evolutionary algorithm (MOEA) based engineering design optimization of a product (e.g., automobile, cellular phone, etc.). Particularly, the present invention discloses an archive configured for monitoring the progress and characterizing the performance of the MOEA based optimization. Further, an optimization performance indicator is created using the archive's update history. The optimization performance indicator is used as a metric of the current state of the optimization. Finally, a stopping or termination criterion for the MOEA based optimization is determined using a measurement derived from the optimization performance indicators. For example, a confirmation of a “knee” formation has developed in the optimization performance indicators. The optimization performance indicators include, but are not limited to, consolidation ratio, improvement ratio, hypervolume.

Abstract: Systems and methods of limiting contact penetration in numerical simulation of non-linear structure response using implicit finite element analysis are described. According to one aspect, a finite element analysis (FEA) model of a structure is defined as a number of nodes and elements based on geometry and material properties of the structure. A time-marching analysis of the FEA model is then performed. The time-marching analysis results contain a number of solutions of non-linear structure response at respective time steps. Solution at each time step requires at least one iteration to compute. Non-linear structure response is determined in the following manner: 1) determining a search direction; 2) calculating a contact penetration parameter in the search direction; and 3) finding a minimum energy imbalance location along the search direction as a solution which is further restricted by the CPP such that contact penetration of the structure is substantially limited.

Abstract: Each spot weld in a structure is represented by a cluster of at least one solid element in a finite element analysis model of the structure. Each spot weld is used for tying together two parts. Each of the two parts are generally represented or modeled as a number of two-dimension shell elements. Since the tie-connection between the spot weld and the two parts can be located arbitrarily within the respective part, the shell elements representing the two parts do not have to be aligned in space. The only requirement is the two shell elements must be overlapped each other such that the spot weld can tie the two shell elements (i.e., one from each part) together. A spot weld failure criterion used for determining failure including shear and axial stresses acted on the spot weld, shell element size and spot weld location sensitivity scale factors and strain rate effect.

Abstract: Improved methods and systems for defining and creating simulated rigid bodies in finite element analysis are disclosed. One or more rigid finite elements in a finite element model are designated for forming one or more simulated rigid bodies (RBs). Each simulated RB comprises an arbitrary number of rigid finite elements connecting to one another in an arbitrary shape. Each simulated RB is created by locating all of the elements embedded in the 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 RBs defined in the model can be located efficiently. Once all RBs have been located, each unique RB is defined as a unique list of connected rigid finite elements.

Abstract: The present invention discloses systems and methods of conducting multi-objective evolutionary algorithm (MOEA) based engineering design optimization of a product (e.g., automobile, cellular phone, etc.). Particularly, the present invention discloses an archive configured for monitoring the progress and characterizing the performance of the MOEA based optimization. Further, an optimization performance indicator is created using the archive's update history. The optimization performance indicator is used as a metric of the current state of the optimization. Finally, a stopping or termination criterion for the MOEA based optimization is determined using a measurement derived from the optimization performance indicators. For example, a confirmation of a “knee” formation has developed in the optimization performance indicators. The optimization performance indicators include, but are not limited to, consolidation ratio, improvement ratio, hypervolume.

Abstract: Hybrid elements that enable coupling effects between SPH particles and FEM solid are disclosed. According to one aspect of the present invention, hybrid elements are configured to facilitate coupling effect of solid element based on finite element method (FEM) and one or more corresponding particles based on smoothed particle hydrodynamics (SPH). Hybrid elements are defined in a computer aided engineering (CAE) grid model as a buffer or interface between the SPH particles and FEM solids. For example, a portion of the grid model comprises SPH particles because the likelihood of enduring large deformation, while the rest of the model comprises FEM solid elements. Hybrid elements are placed between the solids and the particles. Each hybrid element comprises two layers: solid layer and particle layer.

Abstract: Systems and methods of numerically simulating airflow within porous materials are disclosed. According to one aspect of the present invention, engineering product represented by a finite element analysis model containing in part porous material with permeability. In each solution cycle of a time-marching simulation, each of the elements of porous material is evaluated with airflow in conjunction with the traditional mechanical response. Each element's volume change results into different air-pore pressure hence a pressure gradient, which in turn is used for airflow calculated in accordance with a fluid seepage law that depends upon permeability of the porous material. Therefore, a more realistic simulation of structural behavior of porous materials can be achieved. The volume change and pressure of each element of porous material is evaluated using ideal gas law. A general form of Darcy's law includes user control parameters is used for evaluating airflow based on the pressure gradient and permeability.

Abstract: Methods and systems for calculating electron or ion dynamics using spin-dependent quantum trajectories are disclosed. According to one exemplary embodiment of the present invention, electron or ion dynamics are obtained by solving a set of equations for electrons' motion using spin-dependent quantum trajectories calculated from electron current with one equation for each electron in the atomic structure of a material of interest. The set of equations is time-dependent Schrödinger or Dirac equations for the nonrelativistic and relativistic regime, respectively. The electron current contains a set of spin-dependent terms that guarantee Fermi-Dirac statistics are obeyed. Steady state solution of the set of equations for electrons' motion is a set of wave functions in a three-dimensional space and in time. The spin-dependent quantum trajectories for each of the electrons are updated at each solution cycle, and therefore, mean-field approximation is avoided.

Abstract: Methods and systems for simulating beam-to-surface contacts in finite element analysis (FEA) are disclosed. A FEA model contains at least one beam element and at least one surface mesh. Surface mesh comprises a plurality of two-dimensional finite elements having arbitrary mesh density. A minimum characteristic length (CL) of the surface mesh is calculated. One or more interior points are defined for those beam elements with length longer than CL. For every nodal point (i.e., end nodes and interior points if any), a parametric coordinate between 0 and 1 inclusive is established and kept constant throughout the FEA analysis. Distributed nodal masses are used for calculating a stiffness value for calculating nodal force to resist penetration.