Abstract: Provided are a computer-based method and system of simulating a physical real-world system. Such a method begins by defining, in memory of a processor, a model comprising a plurality of design variables where the defined model represents a real-world physical system and where behavior of the model is given by an equation stored in the memory. The method/system uses the equation to iteratively optimize the defined model with respect to a given one of the plurality of design variables by simultaneously solving for equilibrium of the model and for the design response sensitivity of the given design variable, for the equilibrium, in a given optimization iteration. According to such an embodiment, iteratively optimizing the model results in an improved simulation of the real-world physical system.

Abstract: Embodiments provide methods and systems for optimizing a physical system. One such example embodiment begins by defining, in memory of a processor, a model comprising a plurality of design variables where the defined model represents a real-world physical system where behavior of the model is given by an equation that includes corresponding sensitivity equations for the plurality of design variables. The example method continues by iteratively optimizing the model with respect to a given design variable of the plurality, using the equation. In an example embodiment, the optimizing includes the processor accounting for a given external intervention event between equilibriums by adding a term for design response sensitivity of the given one of the plurality of design variables to the corresponding sensitivity equation of the given design variable. Such optimizing results in an improved optimization of the real-world physical model.

Abstract: Modal dynamic analysis for finite element models (FEMs) that include Lagrange multipliers may generate incorrect stress and reaction forces. Computer systems and computer-implemented methods are provided for modifying the modal analysis to correctly generate stress and reaction forces. The systems and methods perform the modal analysis by employing a FEM and modeling stress and reaction forces of the FEM using Lagrange multipliers. The systems and methods calculate a correction term that comprises corrected values of the Lagrange multipliers. The methods and systems modify (and improve) the modal analysis by using the correction term to correct the Lagrange multipliers of the FEM, which enables the modal analysis to generate correct stress and reaction forces.

Abstract: A computer-implemented method is provided for use in finite element analysis of a three-dimensional (3D) representation of a physical object. The computer-implemented method includes combining a plurality of retained degrees of freedom of the 3D representation to form a root substructure, reducing a structure of the 3D representation on to a reduced automated multilevel substructuring (AMLS) subspace, and computing a plurality of eigenmodes and condensed operators based on the reduced structure, and computing constraint modes using an AMLS transformation matrix. The computer-implemented method also includes generating at least one substructure of the 3D representation based on the plurality of eigenmodes, constraint modes, and condensed operators, and storing the at least one substructure in a memory area.

Abstract: Provided are a computer-based method and system of simulating a physical real-world system. Such a method begins by defining, in memory of a processor, a model comprising a plurality of design variables where the defined model represents a real-world physical system and where behavior of the model is given by an equation stored in the memory. The method/system uses the equation to iteratively optimize the defined model with respect to a given one of the plurality of design variables by simultaneously solving for equilibrium of the model and for the design response sensitivity of the given design variable, for the equilibrium, in a given optimization iteration. According to such an embodiment, iteratively optimizing the model results in an improved simulation of the real-world physical system.

Abstract: Embodiments provide methods and systems for optimizing a physical system. One such example embodiment begins by defining, in memory of a processor, a model comprising a plurality of design variables where the defined model represents a real-world physical system where behavior of the model is given by an equation that includes corresponding sensitivity equations for the plurality of design variables. The example method continues by iteratively optimizing the model with respect to a given design variable of the plurality, using the equation. In an example embodiment, the optimizing includes the processor accounting for a given external intervention event between equilibriums by adding a term for design response sensitivity of the given one of the plurality of design variables to the corresponding sensitivity equation of the given design variable. Such optimizing results in an improved optimization of the real-world physical model.

Abstract: Modal dynamic analysis for finite element models (FEMs) that include Lagrange multipliers may generate incorrect stress and reaction forces. Thus, embodiments of the present invention provide methods and systems for performing a modal analysis that corrects these errors. One such embodiment begins by providing a FEM, the FEM is employed in a modal analysis modeling stress and reaction forces of the FEM using Lagrange multipliers. Next, a correction term is calculated. Then, the method concludes by modifying (and thus improving) the modal analysis using the correction term to alter the Lagrange multipliers.

Abstract: A computer-implemented method for use in simulating dynamic behavior of complex engineering systems comprised of several subsystems includes computing a Jacobian matrix based on output derivatives, wherein the output derivatives are based on corresponding state variable derivatives related to corresponding first input variables for each of a plurality of subsystems. The method also includes modifying the first input variables and computing second input variables and residuals for each of the plurality of subsystems based on corresponding state variable derivatives.

Abstract: A computer-implemented method for use in simulating dynamic behavior of complex engineering systems comprised of several subsystems includes computing a Jacobian matrix based on output derivatives, wherein the output derivatives are based on corresponding state variable derivatives related to corresponding first input variables for each of a plurality of subsystems. The method also includes modifying the first input variables and computing second input variables and residuals for each of the plurality of subsystems based on corresponding state variable derivatives.

Abstract: A computer-implemented method is provided for use in finite element analysis of a three-dimensional (3D) representation of a physical object. The computer-implemented method includes combining a plurality of retained degrees of freedom of the 3D representation to form a root substructure, reducing a structure of the 3D representation on to a reduced automated multilevel substructuring (AMLS) subspace, and computing a plurality of eigenmodes and condensed operators based on the reduced structure, and computing constraint modes using an AMLS transformation matrix. The computer-implemented method also includes generating at least one substructure of the 3D representation based on the plurality of eigenmodes, constraint modes, and condensed operators, and storing the at least one substructure in a memory area.