Abstract: A method, apparatus, and system provide the ability to perform a drop test using a response surface. Inputs including a target safety factor (T-SF), a drop height, and a computer model, are acquired. An initial template is evaluated by computing a safety factor for a set of orientations, for each model point MP in the computer model across a set of times (t). A minimum safety factor is determined and a response surface for the model is generated. An actual safety factor SFm is generated by conducting a drop test simulation of the model based on a point having the minimum safety factor and a corresponding orientation. Consistency/validity of the actual safety factor is compared to the target safety factor and the model either passes or additional points may be added to the set of points and the process repeats based on an updated response surface.

Abstract: Methods, systems, and apparatus, including medium-encoded computer program products, for computer aided design of physical structures using generative design processes, where the three dimensional (3D) models of the physical structures are produced in accordance with a design criterion that limits a minimum thickness of the generatively designed 3D models, include: obtaining a design space for an object to be manufactured and one or more design criteria including a thickness constraint; iteratively modifying a generatively designed 3D shape of the modeled object in the design space in accordance with the one or more design criteria, including measuring a current thickness for the 3D shape using an overall relationship of a volume of the 3D shape with respect to a surface area of the 3D shape; and providing the generatively designed model for use in manufacturing the physical structure using one or more computer-controlled manufacturing systems.

Abstract: Methods, systems, and apparatus, including medium-encoded computer program products, for computer aided design of physical structures, where the 3D models of the physical structures are produced so as to facilitate 2.5-axis subtractive manufacturing, include: obtaining one or more design criteria and one or more boundary conditions, modifying a 3D shape of a modeled object in accordance with the one or more design criteria and the one or more boundary conditions, including employing geometry filtering or simulation results filtering in the iterative loop or inserting voids at locations selected using one or more shape skeleton lines, and providing the 3D shape of the modeled object for use in manufacturing the physical structure using one or more computer-controlled manufacturing systems that employ the 2.5-axis subtractive manufacturing process.

Abstract: Methods, systems, and apparatus, including medium-encoded computer program products, for computer aided design of physical structures include: obtaining a design space, design criteria, and boundary conditions for numerical simulation; defining an application of the boundary conditions to a voxelized mesh, including specifying a distribution of a load to nodes of voxels in the voxelized mesh that correspond to a surface of preserve geometry; and iteratively modifying a generatively designed three dimensional shape in the design space in accordance with the design criteria and a physical response of the modeled object determined by the numerical simulation performed using the application of the boundary conditions to the voxelized mesh, wherein the distribution of the total loading value during determination of the physical response ensures an equivalence between the total loading value and a sum of loading values distributed to the respective nodes of the voxels that correspond to the surface.

Abstract: Methods, systems, and apparatus, including medium-encoded computer program products, for computer aided design of physical structures using three-dimensional model synthesis processes. A method includes: obtaining a draft angle, an ejection direction, and a 3D shape for a casting or molding process; modifying data values in discrete elements (from which the 3D shape is determinable) to add material to the modelled object, including, for each of the discrete elements, changing a current value of the discrete element based on a comparison of the current value with an other value and a constant value, the other value being determined from one or more values found in one or more other discrete elements in the data structure located away from the discrete element along the ejection direction, and the constant value being determined for the draft angle; and providing the data structure with the modified data values for further processing.

Abstract: Methods, systems, and apparatus, including medium-encoded computer program products, for computer aided design of physical structures using generative design processes include: obtaining one or more design criteria, a model of an object for which a physical structure is to be manufactured, and a set of eigenmodes from a modal analysis of the model of the object; extracting a proper subset of non-zero eigenmodes from the set of eigenmodes, wherein the proper subset of non-zero eigenmodes include at least three lowest valued, non-zero eigenmodes; combining data of the proper subset of non-zero eigenmodes to form a strain energy field for the model of the object; iteratively modifying a generatively designed shape of the model of the object using the strain energy field to drive changes to the generatively designed shape of the model; and providing the generatively designed shape of the model of the object.

Abstract: Methods, systems, and apparatus, including medium-encoded computer program products, for computer aided design of physical structures include: obtaining a design space for a modeled object and boundary conditions including a location where load is applied; checking whether, the boundary conditions include a specified direction for the load; assigning a direction for the load at the location when no specified direction is included; iteratively modifying a three dimensional shape in the design space in accordance with a physical response of the modeled object determined by a numerical simulation employing a linear analysis, where the iterative modification comprises determining a respective maximum sustainable load for each of two or more versions of the modified three dimensional shape; presenting to a user the two or more versions of the modeled object having different shapes; and receiving a user selection of one of the two or more versions of the modeled object.

Abstract: One embodiment of the present invention sets forth a technique for modeling assemblies using generative design techniques. The technique includes determining a portion of an assembly to model as a superelement and computing a mathematical model representing the superelement. The technique further includes eliminating one or more interior degrees of freedom from the mathematical model and computing a reduced stiffness matrix corresponding to the superelement by solving one or more equations associated with the mathematical model using an iterative sparse matrix solver.

Abstract: Methods, systems, and apparatus, including medium-encoded computer program products, for computer aided design of physical structures using generative design processes, where the three dimensional (3D) models of the physical structures are produced in accordance with a design criterion that limits a minimum thickness of the generatively designed 3D models, include: obtaining a design space for an object to be manufactured and one or more design criteria including a thickness constraint; iteratively modifying a generatively designed 3D shape of the modeled object in the design space in accordance with the one or more design criteria, including measuring a current thickness for the 3D shape using an overall relationship of a volume of the 3D shape with respect to a surface area of the 3D shape; and providing the generatively designed model for use in manufacturing the physical structure using one or more computer-controlled manufacturing systems.

Abstract: Methods, systems, and apparatus, including medium-encoded computer program products, for computer aided design of physical structures using generative design processes, where the three dimensional (3D) models of the physical structures are produced in accordance with a design criterion that limits a minimum thickness of the generatively designed 3D models, include: obtaining a design space for an object to be manufactured and one or more design criteria including a thickness constraint; iteratively modifying a generatively designed 3D shape of the modeled object in the design space in accordance with the one or more design criteria, including measuring a current thickness for the 3D shape using an overall relationship of a volume of the 3D shape with respect to a surface area of the 3D shape; and providing the generatively designed model for use in manufacturing the physical structure using one or more computer-controlled manufacturing systems.

Abstract: Methods, systems, and apparatus, including medium-encoded computer program products, for computer aided design of physical structures using generative design processes, where the 3D models of the physical structures are produced so as to facilitate manufacturing of the physical structures using 2.5-axis subtractive manufacturing systems and techniques, include: obtaining a design space for an object to be manufactured, design criteria, and load case(s); iteratively modifying a generatively designed 3D shape of the modeled object, including generating 2D profile representations (corresponding to discrete layers) of an updated version of the 3D shape, extruding the 2D profile representations along the milling direction, and forming a next version of the 3D shape of the modeled object from a combination of the 3D representations produced by the extruding; and providing the generatively designed 3D shape of the modeled object for use in manufacturing the physical structure using a 2.

Abstract: A method, apparatus, and system provide the ability to perform a drop test using a response surface. Inputs including a target safety factor (T-SF), a drop height, and a computer model, are acquired. An initial template is evaluated by computing a safety factor for a set of orientations, for each model point MP in the computer model across a set of times (t). A minimum safety factor is determined and a response surface for the model is generated. An actual safety factor SFm is generated by conducting a drop test simulation of the model based on a point having the minimum safety factor and a corresponding orientation. Consistency/validity of the actual safety factor is compared to the target safety factor and the model either passes or additional points may be added to the set of points and the process repeats based on an updated response surface.

Abstract: Methods, systems, and apparatus, including medium-encoded computer program products, for computer aided design of physical structures using generative design processes include: obtaining one or more design criteria, a model of an object for which a physical structure is to be manufactured, and a set of eigenmodes from a modal analysis of the model of the object; extracting a proper subset of non-zero eigenmodes from the set of eigenmodes, wherein the proper subset of non-zero eigenmodes include at least three lowest valued, non-zero eigenmodes; combining data of the proper subset of non-zero eigenmodes to form a strain energy field for the model of the object; iteratively modifying a generatively designed shape of the model of the object using the strain energy field to drive changes to the generatively designed shape of the model; and providing the generatively designed shape of the model of the object.

Abstract: Methods, systems, and apparatus, including medium-encoded computer program products, for computer aided design of physical structures using generative design processes, where the 3D models of the physical structures are produced so as to facilitate manufacturing of the physical structures using 2.5-axis subtractive manufacturing systems and techniques, include: obtaining a design space for an object to be manufactured, design criteria, and load case(s); iteratively modifying a generatively designed 3D shape of the modeled object, including generating 2D profile representations (corresponding to discrete layers) of an updated version of the 3D shape, extruding the 2D profile representations along the milling direction, and forming a next version of the 3D shape of the modeled object from a combination of the 3D representations produced by the extruding; and providing the generatively designed 3D shape of the modeled object for use in manufacturing the physical structure using a 2.

Abstract: A method, apparatus, and system provide the ability to perform a drop test using a response surface. Inputs including a target safety factor (T-SF), a drop height, and a computer model, are acquired. An initial template is evaluated by computing a safety factor for a set of orientations, for each model point MP in the computer model across a set of times (t). A minimum safety factor is determined and a response surface for the model is generated. An actual safety factor SFm is generated by conducting a drop test simulation of the model based on a point having the minimum safety factor and a corresponding orientation. Consistency/validity of the actual safety factor is compared to the target safety factor and the model either passes or additional points may be added to the set of points and the process repeats based on an updated response surface.

Abstract: Methods, systems, and apparatus, including medium-encoded computer program products, for computer aided design of physical structures include: obtaining a design space, design criteria, and boundary conditions for numerical simulation; defining an application of the boundary conditions to a voxelized mesh, including specifying a distribution of a load to nodes of voxels in the voxelized mesh that correspond to a surface of preserve geometry; and iteratively modifying a generatively designed three dimensional shape in the design space in accordance with the design criteria and a physical response of the modeled object determined by the numerical simulation performed using the application of the boundary conditions to the voxelized mesh, wherein the distribution of the total loading value during determination of the physical response ensures an equivalence between the total loading value and a sum of loading values distributed to the respective nodes of the voxels that correspond to the surface.

Abstract: Methods, systems, and apparatus, including medium-encoded computer program products, for computer aided design of physical structures using generative design processes, where the 3D models of the physical structures are produced so as to facilitate manufacturing of the physical structures using 2.5-axis subtractive manufacturing systems and techniques, include: obtaining a design space for an object to be manufactured, design criteria, and load case(s); iteratively modifying a generatively designed 3D shape of the modeled object, including generating 2D profile representations (corresponding to discrete layers) of an updated version of the 3D shape, extruding the 2D profile representations along the milling direction, and forming a next version of the 3D shape of the modeled object from a combination of the 3D representations produced by the extruding; and providing the generatively designed 3D shape of the modeled object for use in manufacturing the physical structure using a 2.

Abstract: Methods, systems, and apparatus, including medium-encoded computer program products, for computer aided design of physical structures using generative design processes, where the three dimensional (3D) models of the physical structures are produced in accordance with a design criterion that limits a minimum thickness of the generatively designed 3D models, include: obtaining a design space for an object to be manufactured and one or more design criteria including a thickness constraint; iteratively modifying a generatively designed 3D shape of the modeled object in the design space in accordance with the one or more design criteria, including measuring a current thickness for the 3D shape using an overall relationship of a volume of the 3D shape with respect to a surface area of the 3D shape; and providing the generatively designed model for use in manufacturing the physical structure using one or more computer-controlled manufacturing systems.

Abstract: Methods, systems, and apparatus, including medium-encoded computer program products, for estimating the physical properties of 3D printed objects that include: obtaining a three dimensional (3D) model of a 3D object to be manufactured by a 3D extrusion printer; obtaining at least a portion of tool path data for the 3D extrusion printer to build the 3D object in accordance with the 3D model; creating unit cell geometry from the at least a portion of tool path data using at least one limitation on one or more unit cells of the unit cell geometry with respect to an aspect of the 3D extrusion printer's build of the 3D object; generating a numerical simulation of one or more microstructural properties of the 3D object to be built using the unit cell geometry; and estimating one or more macroscale properties, of the 3D object to be built, from the numerical simulation.

Abstract: A method, apparatus, and system provide the ability to perform a drop test using a response surface. Inputs including a target safety factor (T-SF), a drop height, and a computer model, are acquired. An initial template is evaluated by computing a safety factor for a set of orientations, for each model point MP in the computer model across a set of times (t). A minimum safety factor is determined and a response surface for the model is generated. An actual safety factor SFm is generated by conducting a drop test simulation of the model based on a point having the minimum safety factor and a corresponding orientation. Consistency/validity of the actual safety factor is compared to the target safety factor and the model either passes or additional points may be added to the set of points and the process repeats based on an updated response surface.