Abstract: A computer-implemented method for designing a sheet part comprising beads. The method comprises providing a CAD model representing the part. The CAD model includes a feature tree. The feature tree has one or more CAD parameters each having an initial value. The method further comprises providing a bead optimization program specified by one or more use and/or manufacturing performance indicators. The one or more indicators comprise one or more objective function(s) and/or one or more constraints. The method further comprises modifying the initial values of the one or more CAD parameters by solving the optimization program using a gradient-based bead optimization method. The optimization method has as free variables the one or more CAD parameters. The optimization method uses sensitivities. Each sensitivity is an approximation of a respective derivative of a respective performance indicator with respect to a respective CAD parameter.

Abstract: A computer-implemented method for designing a manufacturing product. The method includes obtaining a CAD model representing the manufacturing product. The CAD model includes a feature tree. The feature tree has one or more CAD parameters each having an initial value. The method also includes obtaining an optimization program. The optimization program is specified by one or more use and/or manufacturing performance indicators. The one or more indicators having one or more objective functions and/or one or more constraints. The method further includes modifying the initial values of the one or more CAD parameters by solving the optimization program using a gradient-based optimization method. The optimization method has as free variable the one or more CAD parameters and uses sensitivities. Each sensitivity is an approximation of a respective derivative of a respective performance indicator with respect to a respective CAD parameter.

Abstract: A computer-implemented method for designing a mechanical product formed in one or more materials including obtaining inputs including a finite element model representing the mechanical product and having an initial value of design variables, one or more load cases, a corresponding load history for each load case, boundary conditions, fatigue properties of the one or more materials, and a fatigue calculation scheme. The method further includes computing a distribution of fatigue damage over the finite element model based on the inputs, computing a distribution of sets of fatigue damage sensitivities over the finite element model based on the computed distribution of fatigue damage, each fatigue damage sensitivity of each set approximating a derivative of the fatigue damage relative to a respective design variable, and updating the value of the design variables based on the fatigue damage sensitivities.

Abstract: The disclosure notably relates to a computer-implemented method for designing a modeled object. The method includes obtaining a finite element mesh, data associated to the finite element mesh and a non-uniform distribution of one or more local quantity constraints. The data associated to the finite element mesh include forces, boundary conditions, parameters, and a global quantity constraint. The method also comprises performing a topology optimization based on the finite element mesh, the data associated to the finite element mesh, and the non-uniform distribution. The method improves the design of a modeled object representing a mechanical part by topology optimization.

Abstract: A computer-implemented method for designing a 3D modeled object representing a transmission mechanism with a target 3D motion behavior. The method including obtaining a 3D finite element mesh and data associated to the mesh, performing a topology optimization based on the mesh and on the associated data, therefore obtaining a density field representing distribution of material quantity of the 3D modeled object. The method further includes computing a signed field based on the density field and the associated data, identifying one or more patterns of convergence and divergence in the signed field, each pattern forming a region of the signed field, and for each identified pattern, identifying a joint representative of the identified pattern and replacing a part of the density field corresponding to the respective region formed by the identified pattern by a material distribution representing the identified joint.

Abstract: The disclosure notably relates to a computer-implemented method for designing a part by topology optimization. The method comprises defining a working volume for the optimization of the part and at least one boundary condition applied to the part, computing a vector field over the working volume, each vector of the field representing an optimal direction and a quantity of material corresponding to satisfy the at least one boundary condition, computing a set of flow lines by propagating from starting points in the vector field. For each flow line of the set, an element for the primary structure of the part is computed and a secondary structure of the part linking the set of primary as well as the secondary structure elements together is computed.

Abstract: A discrete geometrical pattern library guides a method for design optimization of a finite element model in a computer aided design (CAD) environment. Boundary conditions are applied to the finite element model, design variables for the bounded finite element model are initialized, and an objective function for the finite element model is evaluated. A gradient of the objective function is evaluated with respect to the design variables, an appearance constraint function is evaluated for the finite element model, and a gradient of the appearance constraint function is evaluated with respect to the design variables. The design variables are updated using a mathematical programming, and a convergence in the design optimization is detected, producing a converged design optimization of the finite element model is produced.

Abstract: A computer-implemented method for designing a 3D modeled object. The 3D modeled object represents a mechanical part formed in a material having an anisotropic behavior with respect to a physical property. The method includes obtaining a 3D finite element mesh and data associated to the 3D finite element mesh. The data associated to the 3D finite element mesh includes a plurality of forces and boundary conditions. The plurality of forces forms multiple load cases. The method further comprises optimizing an orientation field distributed on the 3D finite element mesh with respect to an objective function. The objective function rewards orientation continuity with respect to the physical property. The optimizing is based on the 3D finite element mesh and on the data associated to the 3D finite element mesh. This constitutes an improved method for designing a 3D modeled object.

Abstract: A computer-implemented method of automatically determining an optimized design for manufacturing a real-world object includes: defining, in memory of a computer-based processor, a finite element model representing a real-world object, the finite element comprising a plurality of elements; evaluating, with the computer-based processor, a distribution of a design variable throughout a vicinity of the finite element model, using singular value decomposition (SVD), to produce a singular value for the design variable in each respective element in the vicinity of the finite element model; defining optimization constraints for the vicinity of the finite element model based on the singular values produced from the SVD; and optimizing the finite element model with respect to the design variable by locally enforcing a geometry of the real-world object in the vicinity based on the defined optimization constraints.

Abstract: One goal in automated product designing of additive manufacturing is to obtain designs having overhangs without support structures if the criterion for overhangs is rigorously geometrical. In an embodiment of the present invention, designers can request automated optimization and design, using simulation and sensitivity-based optimization, of structures having overhangs in the print direction that do not need any support structures. In an embodiment, a method includes, at a processor, calculating model design responses and model sensitivities of a computer-aided engineering (CAE) model in a CAE system based on design variables of the CAE model for various design responses being either applied in objective or constraints. The method further includes optimizing values of the design variables. The method further includes calculating physical design variables by employing a penalty function. Additionally, the calculations can also be in conjunction with employing material interpolation schemes.

Abstract: An example embodiment designs a real-world object by defining a first model of the object being produced using an additive manufacturing (AM) process, where behavior of the object being produced is given by a first equation which includes a first plurality of corresponding sensitivity equations for a first plurality of design variables. Similarly, such an embodiment defines a second model of the object after being produced, wherein behavior of the object after being produced is given by a second equation which includes a second plurality of corresponding sensitivity equations for a second plurality of design variables. In turn, the second model is iteratively optimized with respect to a given one of the second plurality of design variables using both the first plurality of corresponding sensitivity equations and the second plurality of corresponding sensitivity equations.

Abstract: Embodiments automatically determine optimized designs for manufacturing real-world objects. An embodiment begins with defining a finite element model comprised of a plurality of elements that represents a real-world object. Next, equilibriums and design responses of the object in response boundary conditions are determined, which includes calculating a local volume constraint for a given element of the finite element model. Then, design response sensitivities of the object in response to the boundary conditions are determined, which includes differentiating the calculated local volume constraint to determine sensitivity of a sizing design variable.

Abstract: Embodiments automatically determine optimized designs for manufacturing real-world objects. An embodiment begins with defining a finite element model comprised of a plurality of elements that represents a real-world object. Next, equilibriums and design responses of the object in response boundary conditions are determined, which includes calculating a local volume constraint for a given element of the finite element model. Then, design response sensitivities of the object in response to the boundary conditions are determined, which includes differentiating the calculated local volume constraint to determine sensitivity of a sizing design variable.

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: The disclosure notably relates to a computer-implemented method for designing a modeled object. The method includes obtaining a finite element mesh, data associated to the finite element mesh and a non-uniform distribution of one or more local quantity constraints. The data associated to the finite element mesh include forces, boundary conditions, parameters, and a global quantity constraint. The method also comprises performing a topology optimization based on the finite element mesh, the data associated to the finite element mesh, and the non-uniform distribution. The method improves the design of a modeled object representing a mechanical part by topology optimization.

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: The disclosure notably relates to a computer-implemented method for designing a part by topology optimization. The method comprises defining a working volume for the optimization of the part and at least one boundary condition applied to the part, computing a vector field over the working volume, each vector of the field representing an optimal direction and a quantity of material corresponding to satisfy the at least one boundary condition, computing a set of flow lines by propagating from starting points in the vector field. For each flow line of the set, an element for the primary structure of the part is computed and a secondary structure of the part linking the set of primary as well as the secondary structure elements together is computed.

Abstract: An example embodiment designs a real-world object by defining a first model of the object being produced using an additive manufacturing (AM) process, where behavior of the object being produced is given by a first equation which includes a first plurality of corresponding sensitivity equations for a first plurality of design variables. Similarly, such an embodiment defines a second model of the object after being produced, wherein behavior of the object after being produced is given by a second equation which includes a second plurality of corresponding sensitivity equations for a second plurality of design variables. In turn, the second model is iteratively optimized with respect to a given one of the second plurality of design variables using both the first plurality of corresponding sensitivity equations and the second plurality of corresponding sensitivity equations.

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.