Systems and methods for compliance mapping of a local feature for additive manufacturing applications

Abstract

A computer system for implementing finite element analysis is provided. The computer system is programmed to: divide a model of an additive manufacturing (AM) article of manufacture into a submodel of a region of interest and a remaining section; mesh the remaining section with a coarse mesh; calculate a compliance matrix for each layer of the remaining section based upon the coarse mesh; mesh the submodel with a fine mesh, wherein the fine mesh covers a subset of the geometry relative to the coarse mesh; divide the submodel into layers based upon the fine mesh; analyze each layer of the submodel based upon the fine mesh; determine an effect of the remaining section on the submodel based upon the plurality of compliance matrices; and generate an updated submodel based upon the analysis and the effect of the remaining section on the submodel.

Description

SYSTEMS AND METHODS FOR COMPLIANCEMAPPING OF A LOCAL FEATURE FOR ADDITIVEMANUFACTURING APPLICATIONSBACKGROUND

[0001] The present application relates generally to systems and methods for submodeling, and more particularly, to systems and methods for generating a compliance matrix of a submodel of a model for additive manufacturing applications using finite element analysis.

[0002] Additive manufacturing encompasses various manufacturing and prototyping techniques such as freeform fabrication, 3D printing, rapid prototyping / tooling, and the like in which stock material (such as a feed wire or powder) is applied across underlying substrates layer-by-layer to fabricate a freestanding object. The article of manufacture can be fabricated from a computer aided design (CAD) model stored in memory that is provided to the additive manufacturing system. The processes use an energy' beam to sinter or melt a powder material or a nozzle applies liquid material to create a solid three- dimensional object in which particles of the material are bonded together.

[0003] The layering cycle can include rapid heating and rapid solidification with simultaneous melting of the top powder layer and re-melting of underlying previously solidified layers, in which the article experiences steep temperature gradients and high cooling rates. Residual stresses caused by the thermal cycle can result in distortion or deformation of the article, which may cause the article to solidify out of specification tolerances.

[0004] Finite element analysis (FEA) systems and methods are commonly used to model physical properties and attributes of the article prior to fabrication. Computing devices and FEA software implement virtual modeling simulations to determine physical attributes such as residual stress, deformation, displacement of the article, and the like. Simulation of a coarse-mesh model of the article may result in a low-resolution FEA simulation of the physical attributes, and simulation of a fine-mesh model of the articlegenerally results in a high -resolution FEA simulation. However, FEA simulations of fine- mesh models require significant computational power and time.

[0005] Accordingly, it is desirable to reduce computational time for high- resolution, fine-mesh finite element analysis.BRIEF DESCRIPTION

[0006] In one aspect, a computer system for implementing finite element analysis is provided. The computer system including at least one processor in communication with at least one memory device. The at least processor is programmed to divide a model of an additive manufacturing (AM) article of manufacture into a submodel of a region of interest and a remaining section. The at least one processor is also programmed to mesh the remaining section with a coarse mesh. The at least processor is further programmed to calculate a compliance matrix for each layer of the remaining section based upon the coarse mesh. In addition, the at least processor is programmed to mesh the submodel with a fine mesh, wherein the fine mesh covers a subset of the geometry relative to the coarse mesh. Moreover, the at least processor is programmed to divide the submodel into layers based upon the fine mesh. Furthermore, the at least processor is programmed to analyze each layer of the submodel based upon the fine mesh. In addition, the at least processor is also programmed to determine an effect of the remaining section on the submodel based upon the plurality of compliance matrices. In addition, the at least processor is further programmed to generate an updated submodel based upon the analysis and the effect of the remaining section on the submodel. The computer system may include additional or alternative functionality, including that discussed elsewhere herein.

[0007] In another aspect, a computer implemented method for finite element analysis is provided. The method implemented on a computer system including at least one processor in communication with at least one memory device. The method includes dividing a model of an additive manufacturing (AM) article of manufacture into a submodel of a region of interest and a remaining section. The method also includes meshing the remaining section with a coarse mesh. The method further includes calculating a compliance matrix for each layer of the remaining section based upon the coarse mesh. In addition, the method includes meshing the submodel with a fine mesh, wherein the fine mesh covers asubset of the geometry relative to the coarse mesh. Moreover, the method includes dividing the submodel into layers based upon the fine mesh. Furthermore, the method includes analyzing each layer of the submodel based upon the fine mesh. In addition, the method also includes determining an effect of the remaining section on the submodel based upon the plurality of compliance matrices. In addition, the method further includes generating an updated submodel based upon the analysis and the effect of the remaining section on the submodel.BRIEF DESCRIPTION OF THE DRAWINGS

[0008] The Figures described below depict various aspects of the systems and methods disclosed therein. It should be understood that each Figure depicts an embodiment of a particular aspect of the disclosed systems and methods, and that each of the Figures is intended to accord with a possible embodiment thereof. Further, wherever possible, the following description refers to the reference numerals included in the following Figures, in which features depicted in multiple Figures are designated with consistent reference numerals.

[0009] There are shown in the drawings arrangements which are presently discussed, it being understood, however, that the present embodiments are not limited to the precise arrangements and are instrumentalities shown, wherein:

[0010] Figure 1 depicts an exemplary' configuration of a finite element analysis (FEA) computer device, in accordance with one embodiment of the present disclosure.

[0011] Figure 2 illustrates a region of interest on an article where stress may cause cracks in the manufactured article.

[0012] Figure 3 A illustrates a perspective view of an exemplary finite element model of the article show n in Figure 2 simulated by the FEA computer device 100 shown in Figure 1.

[0013] Figure 3B illustrates a perspective view of the model segmented into a matrix of coarse elements.

[0014] Figure 3C illustrates a perspective view of the model and the region of interest segmented into a matrix of coarse elements.

[0015] FIG. 3D illustrates a submodel of the region of interest of the model shown in FIG. 3A.

[0016] Figure 4A illustrates a model of the region of interest and the remaining section.

[0017] Figure 4B illustrates the model with just the remaining section (also known as the global domain) after the region of interest (also known as the subdomain) has been removed.

[0018] Figure 4C illustrates the removed region of interest.

[0019] Figure 5 illustrates the comparison of an example subdomain which is meshed at 0.2 mm and a global domain which is meshed at 0.8 mm

[0020] Figure 6 illustrates a process for finite element analysis (FEA) in accordance with at least one embodiment.

[0021] Unless otherwise indicated, the drawings provided herein are meant to illustrate features of embodiments of the disclosure. These features are believed to be applicable in a wide variety of systems comprising one or more embodiments of the disclosure. As such, the drawings are not meant to include all conventional features known by those of ordinary skill in the art to be required for the practice of the embodiments disclosed herein.DETAILED DESCRIPTION

[0022] Large parts built through additive manufacturing often crack. The elimination of these cracks involves redesign. However, experimental work is long and can take days and / or weeks. The system and method described herein allows automation of part design so that they can be printed without cracking.

[0023] The present application relates generally to systems and methods for submodeling, and more particularly, to systems and methods for generating a compliance matrix of a submodel of a model for additive manufacturing applications using finite element analysis. In the exemplary embodiment, a finite element analysis (FEA) computer device is programmed to generate the compliance matrix of submodels of a model for additive manufacturing applications using finite element analysis.

[0024] Shape optimization for residual stress minimization within a small subdomain of a large additive manufacturing part (DLML) automatically provides a geometrical improvement of local features with reduced residual stress and likelihood of cracking while retaining design requirements. Through an automated iterative optimization process, candidate geometries for a lower residual stress are generated (by variation of cad parameter or parametrized morphing of initial geometries). They are then evaluated by a quick, accurate residual stress computation.

[0025] A quick and accurate residual stress computation is key to the shape optimization. An inherent strain method is applied to the subdomain alone, but effect of the surrounding part needs to be considered. In many situations, direct force / displacement mapping is possible but inaccurate. Reduced order model such as Compliance + load through substructuring (z.e., superelement. Schur complement method, etc.) is preferred. In that situation, layer wise substructuring (z.e., superelement, Schur complement method, etc.) of all but that subdomain is calculated beforehand and then, for all iterations, is applied layerwise.

[0026] In many situations, shape optimization for additive manufacturing residual stress minimization requires a multitude of Finite Element simulations providing residual stress for each tested configuration. Some current methods, such as using finite element simulations with the inherent strain method require significant processing time and resources. Furthermore, the computing resource cost to provide the number of simulations necessary to reach optimization convergence is extremely high. In addition, small details may be missed.

[0027] Accordingly, the systems and methods herein describe creating a fine mesh to isolate and analyze the regions where the stress needs to be minimized. This fine mesh handles where the stress needs to be finely resolved. The fine mesh also may contain features that will only be capture by a small mesh size. In the exemplary embodiment, the fine mesh covers a subset of the geometry relative to the coarse mesh. In some additional embodiments, the fine mesh may be significantly smaller that the coarse mesh. In some of these embodiments, for example, consider a shape optimization application where someone wants to try to optimize a subset of the geometry’. It could be very natural to have the 'Tine mesh’7and “coarse mesh” to have the same voxel / element size. This would still allow for quick and efficient test changes to the geometry within the region of interest. In some embodiments, there are cases where someone prefers to use a larger voxel / element size within the region of interest.

[0028] The systems and methods described herein improve on the finite element method for solving residual stress in a bounded subdomain to provide a faster resolution at a fine resolution. In the exemplary embodiment, the FEA computer device receives a design of an additive manufacturing (AM) part, also called a domain. The FEA computer device divides the AM part into two sections. The first section is the subdomain of interest, where residual stress needs to be reduced in the AM part. Typically, the part cracks at a given location, so the subdomain includes the location of that crack, plus the region around that crack that is allowed to be modified. The second section is the rest of the part. The two sections are divided in any manner that makes sense to put the location of the residual stress in the first section and as much of the rest of the AM part in the second section.

[0029] Before the optimization starts, the FEA computer device meshes the AM part minus the subdomain of interest, aka the second section. The FEA computer device meshes the AM part so that it can be split into layers. In the exemplary embodiment, the mesh is a voxel mesh with a coarse mesh size.

[0030] For each layer, the FEA computer device calculates the compliance of the part, while retaining only the node laying at the "subdomain of interest / rest of the part boundary " as degrees of freedom. In other words, the linear system provided by the finite element method (including the thermal load, Dirichlet boundary condition) is not completely solved, but partially inverted. This provides a linear system of equations of size the numberof degrees of freedom at the "subdomain of interest / rest of the part boundary." This is referred to as a compliance matrix. This is referred as substructuring. Consequently, at the end of this step, the system ends up with as many compliance matrices as there are layers in that coarse "rest of the part" mesh, each being the size of the number of degrees of freedom at the "subdomain of interest / rest of the part boundary." The FEA computer device skips the layers below the domain of interest as they do not contribute to the stress in the "domain of interest."

[0031] In the exemplary embodiment, the FEA computer device begins proper shape optimization. The FEA computer device draws a configuration of the subdomain of interest (the first section) is draw n so it can be tested. The FEA computer device meshes the "domain of interest," so that it can be split into layers. The meshing on the domain of interest is performed at a much finer scale than was performed on the second section. The FEA computer device determines the resolution of the mesh based on the domain of interest.

[0032] The FEA computer device applies the layer-wise inherent strain method is applied to just the finely meshed "region of interest." The FEA computer device takes into account the effect (stiffness and load) of the rest of the part onto that "region of interest" by applying the stiffness matrices calculated above. The FEA computer device derives a mapping at each step between the degrees of freedom of the "rest of the part" at the ■‘rest of the part ' / "subdomain of interest” interface and the degrees of freedom of the "domain of interest" at the same interface. In some embodiments, this can be done by establishing a constraint equation on these degrees of freedom. Moreover, this mapping is made more consistent if the submodel is shifted up (or down) to make the top layer of the cunent "domain of interest" vertical position match the top layer of the "rest of the part" vertical position. Moreover, since the height of the domain of interest does not necessarily matches the height of the void left in the "rest of the part" after the subdomain was subtracted, additional layers of mesh below the "subdomain of interest" and may be used to complete the "subdomain of interest" as needed so that there are always nodes at the lower boundary.

[0033] At least one of the technical problems addressed by this system may include: (i) improving speed and accuracy of optimizing additive manufacturing; (ii) elimination of cracks in parts for additive manufacturing; (iii) improving strength andstability of additive manufacturing parts; (iv) improving strength and stability during the additive manufacturing process; (v) reducing computer resources needed in optimizing additive manufacturing; and / or (iv) facilitating automation of part design so that they can be printed without cracking.

[0034] The methods and systems described herein may be implemented using computer programming or engineering techniques including computer software, firmware, hardware, or any combination or subset thereof, wherein the technical effects may be achieved by performing at least one of the following steps: a) divide a model of an additive manufacturing (AM) article of manufacture into a submodel of a region of interest and a remaining section; b) mesh the remaining section with a coarse mesh; c) calculate a compliance matrix for each layer of the remaining section based upon the coarse mesh; d) mesh the submodel with a fine mesh, wherein the fine mesh covers a subset of the geometry relative to the coarse mesh; e) divide the submodel into layers based upon the fine mesh; 1) analyze each layer of the submodel based upon the fine mesh; g) determine an effect of the remaining section on the submodel based upon the plurality of compliance matrices; h) generate an updated submodel based upon the analysis and the effect of the remaining section on the submodel; i) select the region of interest where residual stress needs to be reduced; j) select the region of interest based on one or more reports of cracks in the article of manufacture; k) wherein the region of interest further includes an additional region around where the cracks were reported; 1) divide the remaining section into layers based upon the coarse mesh; m) wherein the coarse mesh is a voxel mesh; n) retain one or more nodes laying at one or more boundaries between the submodel and the remaining section as degrees of freedom; o) wherein the compliance matrix is a linear system of equation size by the number of degrees of freedom at the boundary of the submodel and the remaining section; p) determine a mapping at each step between the degrees of freedom of the remaining section at the remaining section submodel interface and the degrees of freedom of the submodel at the same interface; q) determine the mapping by establishing one or more constraint equations on the degrees of freedom; r) skip one or more layers of the remaining section below the submodel; s) perform shape optimization on the submodel; t) generate a configuration of the submodel to be tested; u) apply a layer-wise inherent strain method to the finely meshed submodel; v) wherein the effect includes at least one of stiffness or load; w) shift the submodel up or down to make atop layer of the submodel vertical position matcha top layer of the remaining section vertical position; and / or x) apply the updated subdomain to the remaining section to generate a build file for an additive manufacturing machine.

[0035] Advantages will become more apparent to those skilled in the art from the following description of the preferred embodiments which have been shown and described by way of illustration. As will be realized, the present embodiments may be capable of other and different embodiments, and their details are capable of modification in various respects. Accordingly, the drawings and description are to be regarded as illustrative in nature and not as restrictive.

[0036] Figure 1 depicts an exemplar ' configuration of a finite element analysis (FEA) computer device 100. in accordance with one embodiment of the present disclosure. FEA computer device 100 may be operated by a user 102.

[0037] FEA computer device 100 may include a processor 104 for executing instructions. In some embodiments, executable instructions may be stored in a memory area 106. Processor 104 may include one or more processing units (e.g., in a multicore configuration). Memory area 106 may be any device allowing information such as executable instructions and / or transaction data to be stored and retrieved. Memory' area 106 may include one or more computer readable media.

[0038] FEA computer device 100 may also include at least one media output component 108 for presenting information to user 102. Media output component 108 may be any component capable of conveying information to user 102. In some embodiments, media output component 108 may include an output adapter (not shown) such as a video adapter and / or an audio adapter. An output adapter may be operatively coupled to processor 104 and operatively couplable to an output device such as a display device (e.g., a cathode ray tube (CRT), liquid crystal display (LCD), light emitting diode (LED) display, or ‘‘electronic ink” display) or an audio output device (e.g., a speaker or headphones).

[0039] In some embodiments, media output component 108 may be configured to present a graphical user interface (e.g., a web browser and / or a client application) to user 102. A graphical user interface may include, for example, an interface for viewing stress information. In some embodiments, computing device 100 may includean input device 1 10 for receiving input from user 102. User 102 may use the input device 110 to, without limitation, provide information either through speech or typing.

[0040] Input device 110 may include, for example, a keyboard, a pointing device, a mouse, a stylus, a touch sensitive panel (e g., a touch pad or a touch screen), a gyroscope, an accelerometer, a position detector, a biometric input device, and / or an audio input device. A single component such as a touch screen may function as both an output device of media output component 108 and input device 110.

[0041] FEA computer device 100 may also include a communication interface 112, communicatively coupled to a remote device such as a client device (not shown). Communication interface 112 may include, for example, a wired or wireless network adapter and / or a wireless data transceiver for use with a mobile telecommunications network.

[0042] Stored in memory area 106 are. for example, computer readable instructions for providing a user interface to user 102 via media output component 108 and, optionally, receiving and processing input from input device 110. A user interface may include, among other possibilities, a web browser and / or a client application. Web browsers enable users, such as user 102, to display and interact with media and other information typically embedded on a web page or a website. For example, instructions may be stored by a cloud service, and the output of the execution of the instructions sent to the media output component 108.

[0043] In the exemplary embodiment, the processor 104 receives input parameters such as a three-dimensional virtual model, a mesh resolution, and a selection of a target region for submodeling. The processor 104 is further configured to execute the methods described herein as instructions to be executed by the processor 104. The processor 104 is also programmed to retrieve finite element analysis (FEA) applications (such as a Multiphysics modeling module 116) from memory 106 and store instructions in memory 106. The processor 104 also outputs simulations resulting from the user inputs onto the media output component 108 or stores the output simulation in memory 106.

[0044] A CAD system 1 14 and a Multiphysics modeling module 1 16, are both stored in memory7106 and both are accessible by the processor 104. The CAD system 114 is a three-virtual environment in which a CAD model is represented. The Multi physics modeling module 116 executes Multiphysics mathematical calculations and performs FEA simulations of CAD models.

[0045] In one embodiment, a computer program is provided, and the program is embodied on a computer readable medium (such as memory 106). In some embodiments, the system includes multiple components distributed among a plurality of computing devices. One or more components may be in the form of computer-executable instructions embodied in a computer-readable medium. As used herein, the terms “software” and “firmware” are interchangeable, and include any computer program stored in memory 106 for execution by the processor 104. including RAM memory, ROM memory. EPROM memory, EEPROM memory, and non-volatile RAM (NVRAM) memory. The above memory types are example only, and are thus not limiting as to the ty pes of memory7usable for storage of a computer program.

[0046] Figure 2 illustrates an exemplary article of manufacture 200 (hereinafter referred to as “article 200”). In some embodiments, the article 200 is manufactured by inputting instructions from memory 106 (shown in Figure 1) into an additive manufacturing system such as, but not limited to, a Laser Power Bed Fusion (LPBF) system, Direct Metal Laser Melting (DMLM) system, a Selective Laser Sintering (SLS) system, a Direct Metal Laser Deposition (DMLD) system, a Direct Metal Laser Deposition (DMLD) system, a binder jetting additive manufacturing (BJAM), a powder blown additive system, and / or any other additive manufacturing system. As used herein, the terms “additive manufacturing” or "additive manufacturing techniques or processes” refer to manufacturing processes in which successive layers of material are deposited across underlying layers to build-up, layer-by-layer, a three-dimensional component. A first layer is deposited and fused onto a build plate, and successive layers are then partially melted or fused together to form a monolithic or integral component, such as article 200.

[0047] Figure 2 illustrates a region of interest 202 on an article 200 where stress may cause cracks in the manufactured article 200.

[0048] As a result of the repetitive melting and fusing of successive layers, residual stresses and distortion may be imparted to article 200. The melting and fusing also causes underlayers to expand or deform due to the temperature differential with the layer being applied across it. The residual stresses, distortion, and temperature differential may be simulated by FEA applications and methods.

[0049] One such method of simulating thermal and mechanical properties as disclosed herein uses an inherent strain simulation method. The inherent strain simulation method is a thermal-mechanical finite element method model that yields an approximation of the manufacturing-induced residual stresses and distortion (and other mechanical and thermal physical attributes generally). A three-dimensional virtual model of the article is imported into, or created in, FEA software. A three-dimensional mesh is applied across the model to segment into a matrix of cuboid elements. The matnx of cuboid elements is oriented in a three-dimensional space such that layers of cuboid elements are substantially parallel to the build plate and such that a sum of the layers defines a total height of the model.

[0050] In some embodiments, a first layer (the bottom-most layer disposed on the build plate) is constrained to represent the build plate stiffness. A negative strain is applied to an n-th layer (the top-most layer opposite the bottom-most layer), in which thermal strain associated with the metal cool-down and irreversible deformation is combined. For every successive intermediate layer applied across the first layer, a reduced mesh is obtained by discarding all later layers, and the finite element mathematical calculation provides stress and displacements associated with every successive intermediate layer. The final residual stresses and displacement are calculated by a summation of the results of each finite element mathematical calculation.

[0051] As used herein, the term “finite element analysis” or “FEA” shall denote a process, method, or computer-implemented method whereby a simulation or approximation of one or more physical attributes of a geometric model is represented virtually (through software) as a finite element model. The model is segmented into a matrix of elements which, taken together, form the finite element model. The matrix of elements is simulated by calculating mathematical formulas such as partial differential equations to simulate physical attributes of each individual element and to simulate interactions between adjacent elements. Physical attributes of the model are illustrated in simulation, withelements shaded in color scale where regions of greater physical attributes values are color- shaded differently than regions of lesser physical attributes values.

[0052] As used herein, the term "simulate / ’ “simulating” and “simulation” shall denote calculating Multiphysics mathematical formulas to determine a value of one or more mechanical physical attributes of fine elements and / or coarse elements, as well as simulating interactions between adjacent fine elements and / or coarse elements. In the Multiphysics calculation, boundary conditions of adjacent fine and / or coarse elements are extracted and are applied to the fine elements and / or coarse elements being simulated. The simulation and calculations of Multiphysics mathematical calculations are executed by a processor and / or an application (such as FEA software). Likewise, as used herein, the term “applying an inherent strain simulation” or “executing an inherent strain simulation” denotes executing calculating Multiphysics mathematical formulas in accordance with the inherent strain simulation method.

[0053] As used herein, the term “coarse element” resulting from applying a coarse mesh to the finite element model denotes a virtual segment of the finite element model having a cuboid shape and a volume. As used herein, the term “fine element” resulting from applying a fine mesh to the finite element model denotes a virtual segment of the finite element model having a cuboid shape and a volume. The volume of the fine element is less than the volume of the coarse element, and executing a simulation of fine elements results in a higher resolution than executing a simulation of coarse elements. In the exemplary embodiment, the fine mesh covers a subset of the geometry’ relative to the coarse mesh. In some additional embodiments, the fine mesh may be significantly smaller that the coarse mesh. In some of these embodiments, for example, consider a shape optimization application where someone wants to try to optimize a subset of the geometry'. It could be very natural to have the “fine mesh” and “coarse mesh” to have the same voxel / element size. This would still allow for quick and efficient test changes to the geometry' within the region of interest. In some embodiments, there are cases where someone prefers to use a larger voxel / element size within the region of interest.

[0054] In some embodiments, the elements are voxel elements used for displacement mapping and simulation, and the FEA systems and methods described herein utilize voxel-based modeling and voxel meshes for displacement mapping.

[0055] Figure 3A illustrates a perspective view of an exemplar}’ finite element model 300 of the article 200 (shown in Figure 2) simulated by the FEA computer device 100 (shown in Figure 1). Figure 3B illustrates a perspective view of the model 300 segmented into a matrix of coarse elements 302. Figure 3C illustrates a perspective view of the model 300 and the region of interest 202 segmented into a matrix of coarse elements 302. FIG. 3D illustrates a submodel 320 of the region of interest 202 of the model 300 (shown in FIG. 3A). Each of the views show n in Figures 3A-3D are virtual representations displayed on the at least one media output component 108 (shown in Figure 1) and may be rotated or manipulated by the user 102 (shown in Figure 1). By way of example, the user 102 may rotate and / or selectively enlarge any of the views by providing inputs through the input device 110. The region of interest 202 may also be arbitrarily selected by the user 102 by providing inputs through the input device 110. In the illustrated embodiments, the region of interest 202 may be selected by the user 102 because the region of interest 202 may represent a w eak area of the model 300 or because the user 102 may intend to optimize the shape of the region of interest. Each of the views shown in Figures 3A through 3D are arbitrarily oriented in X-Y-Z planes.

[0056] In the exemplary embodiment, the submodel 320 shown in FIG. 3D is segmented into fine elements 304, and executing a simulation of the submodel 320 results in a higher resolution relative to the model 300, which is segmented into coarse elements 302. To obtain a higher resolution, the entire model 300 may be simulated with fine elements 304. However, executing a simulation of fine elements 304 requires substantially more processing resources relative to executing the simulation of coarse elements 302. By w ay of example, in one embodiment, to perform a FEA simulation of the finite element model 300 with a fine mesh (with the matrix of fine elements 304), at least fifteen hours of computational time may be needed, whereas in comparison, to perform a FEA simulation of only the submodel 320, only about nine minutes of computational time may be needed.

[0057] Embodiments of the present invention generally relate to systems and methods for simulating one or more mechanical physical attributes of a submodel 320 of a geometric model 300 of a physical article 200 for additive manufacturing applications using the FEA system and method. The attributes may include, but are not limited to only including, structural, fluid, or thermal behavior, as well as residual stresses, deformation, ordisplacement of the article 200. The method includes having a computer device, such as the FEA computer device 100 (show n in Figure 1) defining a region of interest 202 of a model 300 in at least two dimensions. The FEA computer device 100 subtracts the region of interest 202 from the model 300, where the region of interest 202 defines a submodel 320. The FEA computer device 100 applies a compliance matrix to the model 300. The FEA computer device 100 applies an inherent strain simulation to each of the matrices of the at least one physical attribute is attributed to a coarse layer. The FEA computer device 100 applies a compliance submatrix to the submodel 320. The FEA computer device 100 applies a mapping matrix between the compliance matrix and the compliance submatrix. The FEA computer device 100 solves for displacement of the submodel 320. The resulting systems of equations of the submodel 320 facilitates automatic local redesign for minimization of the at least one physical attribute and retain design specification.

[0058] Figure 4A illustrates a model 400 of the region of interest 202 and the remaining section 402. The remaining section 402 has a coarse mesh compliance map having coarse elements 302. The region of interest 202 is to be cut from the model 400 to leave behind the remaining section 402.

[0059] Figure 4B illustrates the model 400 with just the remaining section 402 (also known as the global domain) after the region of interest 202 (also known as the subdomain) has been removed. Figure 4C illustrates the removed region of interest 202. The region of interest 202 has a fine mesh compliance map having fine elements 304. The region of interest 202 also shows high stress areas 404 and low stress areas 406. The geometry split between the region of interest 202 and the remaining section 402 is the first major step of the FEA method as described herein. In one example, the subdomain 202 has a 0.2mm mesh applied to it, while the global domain 402 has a one mm mesh applied to it.

[0060] In processing, the FEA computer device 100 performs substructuring on the global domain 402. The FEA computer device 100 summarizes the global domain 402 in view of compliance and load as a substructure to include all elements. This can be summarized as a small linear system. And is valid regardless of subdomain 202. The FEA computer device 100 performs mapping at each layer of fine mesh layer. The FEA computer device 100 evaluates stress layerwise. The FEA computer device 100 is able to map the global substructure to simulated fine submodels, with the substructure layer matchedwith the current layer of the subdomain 202. This includes simulating the thermal load in the subdomain 202. When the simulated subdomain 202 is applied to the global structure, the FEA computer device 100 calculates the stress assumptions and determines solutions for each fine layer. The stress in the submodel's geometry can be quickly evaluated for many geometries. The splitting of the geometries means that the subdomain can be evaluated and re-evaluated many times, while the global structure of the global domain 402 only needs to be evaluated once.

[0061] After the geometric splitting, the FEA computer device 100 evaluates the subdomain 202 to optimize the shape for residual stress minimization. The FEA computer device 100 performs baseline parameterization of the subdomain 202 to determine a plurality of parameters for the subdomain 202. For example, the FEA computer device 100 may determine 10 parameters to be evaluated and / or measured for a subdomain 202. The FEA computer device 100 executes and optimization loop on the parameters. The FEA computer device 100 performs parameter sampling and geometry morphing and mesh on the parameters and the subdomain 202. The FEA computer device 100 performs residual stress calculations to maximize the loss of stress in the simulated subdomain 202. Then when a completion criterion has been achieved, the FEA computer device 100 selects the best results of the simulation. In the exemplary embodiment, the FEA computer device 100 uses the fast residual stress evaluation criteria. In the exemplary embodiment, the FEA computer device 100 executes multiple optimization loops to determine the optimal parameters for the subdomain 202 and thereby the shape for building the subdomain 202. Then the optimal subdomain is tested in view of the global domain 402. In some embodiments, the FEA computer device 100 adjusts one or more of the parameters after the evaluation with the global domain 402.

[0062] In some embodiments, the geometric splitting includes the voxelization of the subdomain 202. The voxelization has an effect on the residual stress, improves geographic morphing, and optimization ( / .e., gradient descent).

[0063] Figure 5 illustrates the comparison of an example subdomain 202 which is meshed at 0.2 mm and a global domain 402 which is meshed at 0.8 mm. The FEA computer device 100 is able to process the fine meshed subdomain 202 with the coarsely meshed global domain 402 significantly faster than a finely meshed complete model, suchas model 300 (shown in Figure 3). To perform a finite element analysis of the model 300 with a fine mesh throughout requires fifteen hours of computational time. To perform the finite element analysis of only the submodel 320 takes nine minutes of computational time. This significant computational resource savings is at the core of this disclosure.

[0064] Figure 6 illustrates a process for finite element analysis (FEA) in accordance with at least one embodiment. In the exemplary embodiment, the steps of process 600 are performed by the FEA computer device 100 (shown in Figure 1).

[0065] In the exemplary embodiment, the FEA computer device 100 divides 605 a model 300 (shown in Figure 3) of the AM part or article of manufacture 200 (shown in Figure 2) into a submodel 320 (shown in Figure 3) of a region of interest 202 (shown in Figure 2) and the global domain or remaining section 402 (shown in Figure 4B). The submodel 320 of the region of interest 202 is where the residual stress needs to be reduced. Typically, the part cracks at a given location, so the subdomain includes the location of that crack, plus the region around that crack that is allowed to be modified.

[0066] In the exemplary embodiment, the FEA computer device 100 meshes 610 the global domain or remaining section 402. The global domain or remaining section 402 is meshed 610 so that in can be split into layers. In some embodiments, the global domain or remaining section 402 is meshed 610 as a voxel mesh. The mesh size for the global domain or remaining section 402 is coarse, typical of what would be required for a distortion simulation, allowing a reasonable solution time.

[0067] In the exemplary embodiment, the FEA computer device 100 calculates 615 the compliance of the article 200 for each layer based upon the coarse mesh. The FEA computer device 100 retains the nodes laying at one or more boundaries between the subdomain 202 and global domain 402 as degrees of freedom. The FEA computer device 100 generates a linear system of equation size by the number of degrees of freedom at the boundary of the subdomain 202 and global domain 402, which is referred to as a compliance matrix. This is also referred to as substructuring herein. The FEA computer device 100 calculates 615 a compliance matrix for each layer of the global domain 402 based upon each layer of the coarse mesh. Each compliance matrix is the size of the number of degrees of freedom at the boundary of the subdomain 202 and the global domain 402. In someembodiments, the layers below the region of interest 202 are skipped as they do not contribute to the stress in the region of interest 202.

[0068] In the exemplary embodiment, the FEA computer device 100 performs shape optimization on the submodel 320.

[0069] In the exemplary embodiment, the FEA computer device 100 generates a configuration of the submodel 320 to be tested. The FEA computer device 100 meshes 620 the submodel with a fine mesh. The FEA compute device 100 divides 625 the submodel 320 into layers based upon the fine mesh 304 (shown in Figure 3D).

[0070] In the exemplary embodiment, the FEA computer device 100 analyzes 630 each layer of the submodel 320 based upon the mesh. In the exemplary embodiment, the FEA computer device 100 applies a lay er- wise inherent strain method to the finely meshed submodel 320. The FEA computer device 100 determines 635 an effect of the remaining section 420 of the article 200 on the region of interest 202. In these embodiments, the FEA computer device 100 uses the compliance matrices determined in Step 615. In some embodiments, the effect includes at least one of stiffness or load.

[0071] The FEA computer device 100 determines a mapping at each step between the degrees of freedom of the remaining section 402 at the remaining section 402 region of interest 202 interface and the degrees of freedom of the subdomain 202 at the same interface. In some embodiments, the FEA computer device 100 determines the mapping by establishing one or more constraint equations on these degrees of freedom. Moreover, the FEA computer device 100 improves the consistency of this mapping by shifting the submodel 320 up or down to make the top layer of the current subdomain 202 vertical position match the top layer of the remaining section 402 vertical position. Moreover, since the height of the submodel 320 does not necessarily matches the height of the void left in the remaining section 402 after the submodel 320 was subtracted, additional layers are meshed below the submodel 320 and are used to complete the submodel 320 as needed so that there are always nodes at the lower boundary.

[0072] In the exemplary embodiment, the FEA computer device 100 generates 640 an updated submodel 320 based upon the analysis and the effect of the remaining section 402 on the submodel 320. In some embodiments, the FEA computer device 100 applies the updated submodel 320 to the remaining section 402 to generate a build fde for an additive manufacturing machine.ADDITIONAL CONSIDERATIONS

[0073] Embodiments of the disclosure provide an advantage over existing FEA systems and methods that do not have the capability to quickly simulate a fine element model. By implementing inherent strain simulation method for a submodel of the model, finite element simulations need only be executed on a submodel of the model. The described system and methods thus provide modeling a finite element submodel of the CAD model at a higher resolution in a manner that requires fewer processing resources than would be necessary simulating the entire model. By way of example, in one embodiment, to perform a FEA simulation of a finite element model with a fine mesh, up to about fifteen hours of computational time may be needed, whereas to perform a FEA simulation of only the submodel with a fine mesh, only up to about nine minutes of computational time may be needed.

[0074] The methods, systems, and compositions disclosed herein are not limited to the specific embodiments described herein, but rather, steps of the methods, elements of the systems, and / or elements of the compositions may be utilized independently and separately from other steps and / or elements described herein. For example, the methods, systems, and compositions are not limited to practice with only a rotary machine as described herein. Rather, the methods, systems, and compositions may be implemented and utilized in connection with many other applications.

[0075] Although specific features of various embodiments may be shown in some drawings and not in others, this is for convenience only. Moreover, references to “one embodiment” in the above description are not intended to be interpreted as excluding the existence of additional embodiments that also incorporate the recited features. In accordance with the principles of the disclosure, any feature of a drawing may be referenced and / or claimed in combination with any feature of any other drawing.

[0076] As will be appreciated based upon the foregoing specification, the above-described embodiments of the disclosure may be implemented using computer programming or engineering techniques including computer software, firmware, hardware or any combination or subset thereof. Any such resulting program, having computer- readable code means, may be embodied or provided within one or more computer-readable media, thereby making a computer program product, i.e., an article of manufacture, according to the discussed embodiments of the disclosure. The computer-readable media may be, for example, but is not limited to, a fixed (hard) drive, diskette, optical disk, magnetic tape, semiconductor memory such as read-only memory (ROM), and / or any transmitting / receiving medium such as the Internet or other communication network or link. The article of manufacture containing the computer code may be made and / or used by executing the code directly from one medium, by copying the code from one medium to another medium, or by transmitting the code over a network.

[0077] These computer programs (also known as programs, software, software applications, “apps,” or code) include machine instructions for a programmable processor and can be implemented in a high-level procedural and / or object-oriented programming language, and / or in assembly / machine language. As used herein, the terms “machine-readable medium’’ “computer-readable medium” refers to any computer program product, apparatus and / or device (e.g., magnetic discs, optical disks, memory', Programmable Logic Devices (PLDs)) used to provide machine instructions and / or data to a programmable processor, including a machine-readable medium that receives machine instructions as a machine-readable signal. The “machine-readable medium” and “computer-readable medium,” however, do not include transitory' signals. The term “machine-readable signal” refers to any signal used to provide machine instructions and / or data to a programmable processor.

[0078] As used herein, the term “database” can refer to either a body of data, a relational database management system (RDBMS), or to both. As used herein, a database can include any collection of data including hierarchical databases, relational databases, flat file databases, object-relational databases, object-oriented databases, and any other structured collection of records or data that is stored in a computer system. The above examples are example only, and thus are not intended to limit in any way the definition and / ormeaning of the term database. Examples of RDBMS’ include, but are not limited to including, Oracle® Database, MySQL, IBM® DB2, Microsoft® SQL Server, Sybase®, NoSQL, and PostgreSQL. However, any database can be used that enables the systems and methods described herein. (Oracle is a registered trademark of Oracle Corporation, Redwood Shores, California; IBM is a registered trademark of International Business Machines Corporation, Armonk, New York; Microsoft is a registered trademark of Microsoft Corporation, Redmond, Washington; and Sybase is a registered trademark of Sybase, Dublin. California.)

[0079] As used herein, a processor may include any programmable system including systems using micro-controllers, reduced instruction set circuits (RISC), application specific integrated circuits (ASICs), logic circuits, and any other circuit or processor capable of executing the functions described herein. The above examples are example only and are thus not intended to limit in any way the definition and / or meaning of the term “processor.”

[0080] As used herein, the terms “software” and “firmware” are interchangeable and include any computer program stored in memory for execution by a processor, including RAM memory, ROM memory, EPROM memory. EEPROM memory, and non-volatile RAM (NVRAM) memory'. The above memory types are example only and are thus not limiting as to the types of memory’ usable for storage of a computer program.

[0081] In another example, a computer program is provided, and the program is embodied on a computer-readable medium. In an example, the system is executed on a single computer system, without requiring a connection to a server computer. In a further example, the system is being run in a Windows® environment (Windows is a registered trademark of Microsoft Corporation, Redmond, Washington). In yet another example, the system is run on a mainframe environment and a UNIX® server environment (UNIX is a registered trademark of X / Open Company Limited located in Reading. Berkshire, United Kingdom). In a further example, the system is run on an iOS® environment (iOS is a registered trademark of Cisco Systems, Inc. located in San Jose, CA). In yet a further example, the system is run on a Mac OS® environment (Mac OS is a registered trademark of Apple Inc. located in Cupertino, CA). In still yet a further example, the system is run on Android® OS (Android is a registered trademark of Google. Inc. of Mountain View, CA).In another example, the system is run on Linux® OS (Linux is a registered trademark of Linus Torvalds of Boston, MA). The application is flexible and designed to run in various different environments without compromising any major functionality.

[0082] In some embodiments, the system includes multiple components distributed among a plurality of computing devices. One or more components may be in the form of computer-executable instructions embodied in a computer-readable medium. The systems and processes are not limited to the specific embodiments described herein. In addition, components of each system and each process can be practiced independent and separate from other components and processes described herein. Each component and process can also be used in combination with other assembly packages and processes.

[0083] As used herein, an element or step recited in the singular and proceeded with the word “a” or “an’’ should be understood as not excluding plural elements or steps, unless such exclusion is explicitly recited. Furthermore, references to “example” or “one example” of the present disclosure are not intended to be interpreted as excluding the existence of additional examples that also incorporate the recited features. Further, to the extent that terms “includes,” “including,” “has,” “contains,” and variants thereof are used herein, such terms are intended to be inclusive in a manner similar to the term “comprises” as an open transition word without precluding any additional or other elements. The terms “optional” or “optionally” means that the subsequently described event or circumstance may or may not occur, and that the description includes instances where the event occurs and instances where it does not.

[0084] Unless otherwise indicated, approximating language, such as “generally,” “substantially,” and “about,” as used herein indicates that the term so modified may apply to only an approximate degree, as would be recognized by one of ordinary skill in the art, rather than to an absolute or perfect degree. Accordingly, a value modified by a term or terms, such as “about,” “approximately.” and “substantially,” is not to be limited to the precise value specified. In at least some instances, the approximating language may correspond to the precision of an instrument for measuring the value. Here and throughout the specification and claims, range limitations may be identified. Such ranges may be combined and / or interchanged and include all the sub-ranges contained therein unless context or language indicates otherwise.

[0085] Additionally, unless otherwise indicated, the terms ‘'first,” “second,” etc. are used herein merely as labels, and are not intended to impose ordinal, positional, or hierarchical requirements on the items to which these terms refer. Moreover, reference to, for example, a “second” item does not require or preclude the existence of, for example, a ■‘first” or lower-numbered item or a “third” or higher-numbered item.

[0086] Furthermore, as used herein, the term “real-time” refers to at least one of the time of occurrence of the associated events, the time of measurement and collection of predetermined data, the time to process the data, and the time of a system response to the events and the environment. In the examples described herein, these activities and events occur substantially instantaneously.

[0087] The patent claims at the end of this document are not intended to be construed under 35 U.S.C. § 112(f) unless traditional means-plus-function language is expressly recited, such as “means for” or “step for” language being expressly recited in the claim(s).

[0088] This written description uses examples to disclose the invention, including the best mode, and also to enable any person skilled in the art to practice the invention, including making and using any devices or systems and performing any incorporated methods. The patentable scope of the invention is defined by the claims, and may include other examples that occur to those skilled in the art. Such other examples are intended to be within the scope of the claims if they have structural elements that do not differ from the literal language of the claims, or if they include equivalent structural elements with insubstantial differences from the literal language of the claims.

[0089] Further aspects of the invention are provided by the subject matter of the following clauses:

[0090] A computer system for implementing finite element analysis. The computer system using at least one processor in communication with at least one memory' device. The at least processor is programmed to: divide a model of an additive manufacturing (AM) article of manufacture into a submodel of a region of interest and a remaining section; mesh the remaining section with a coarse mesh; calculate a compliance matrix for each layerof the remaining section based upon the coarse mesh; mesh the submodel with a fine mesh, wherein the fine mesh covers a subset of the geometry relative to the coarse mesh; divide the submodel into layers based upon the fine mesh; analyze each layer of the submodel based upon the fine mesh; determine an effect of the remaining section on the submodel based upon the plurality of compliance matrices; and generate an updated submodel based upon the analysis and the effect of the remaining section on the submodel.

[0091] The computer system in accordance with any of the preceding clauses, wherein the at least one processor is further programmed to select the region of interest where residual stress needs to be reduced.

[0092] The computer system in accordance with any of the preceding clauses, wherein the at least one processor is further programmed to select the region of interest based on one or more reports of cracks in the article of manufacture.

[0093] The computer system in accordance with any of the preceding clauses, wherein the region of interest further includes an additional region around where the cracks were reported.

[0094] The computer system in accordance with any of the preceding clauses, wherein the at least one processor is further programmed to divide the remaining section into layers based upon the coarse mesh.

[0095] The computer system in accordance with any of the preceding clauses, wherein the coarse mesh is a voxel mesh.

[0096] The computer system in accordance with any of the preceding clauses, wherein the at least one processor is further programed to retain one or more nodes laying at one or more boundaries between the submodel and the remaining section as degrees of freedom.

[0097] The computer system in accordance with any of the preceding clauses, wherein the compliance matrix is a linear system of equation size by the number of degrees of freedom at the boundary of the submodel and the remaining section.

[0098] The computer system in accordance with any of the preceding clauses, wherein the at least one processor is further programmed to determine a mapping at each step between the degrees of freedom of the remaining section at the remaining section submodel interface and the degrees of freedom of the submodel at the same interface.

[0099] The computer system in accordance with any of the preceding clauses, wherein the at least one processor is further programmed to determine the mapping by establishing one or more constraint equations on the degrees of freedom.

[0100] The computer system in accordance with any of the preceding clauses, wherein the at least one processor is further programmed to skip one or more layers of the remaining section below the submodel.

[0101] The computer system in accordance with any of the preceding clauses, wherein the at least one processor is further programmed to perform shape optimization on the submodel.

[0102] The computer system in accordance with any of the preceding clauses, wherein the at least one processor is further programmed to generate a configuration of the submodel to be tested.

[0103] The computer system in accordance with any of the preceding clauses, wherein the at least one processor is further programmed to apply a layer-wise inherent strain method to the finely meshed submodel.

[0104] The computer system in accordance with any of the preceding clauses, wherein the effect includes at least one of stiffness or load.

[0105] The computer system in accordance with any of the preceding clauses, wherein the at least one processor is further programmed to shift the submodel up or down to make a top layer of the submodel vertical position match a top layer of the remaining section vertical position.

[0106] The computer system in accordance with any of the preceding clauses, wherein the at least one processor is further programmed to apply the updated subdomain to the remaining section to generate a build file for an additive manufacturing machine.

[0107] A computer implemented method for finite element analysis. The method is implemented on a computer system including at least one processor in communication with at least one memory device. The method includes: dividing a model of an additive manufacturing (AM) article of manufacture into a submodel of a region of interest and a remaining section; meshing the remaining section with a coarse mesh; calculating a compliance matrix for each layer of the remaining section based upon the coarse mesh; meshing the submodel with a fine mesh, wherein the fine mesh covers a subset of the geometry relative to the coarse mesh; dividing the submodel into layers based upon the fine mesh; analyzing each layer of the submodel based upon the fine mesh; determining an effect of the remaining section on the submodel based upon the plurality of compliance matrices; and generating an updated submodel based upon the analysis and the effect of the remaining section on the submodel.

[0108] The method in accordance wi th any of the preceding clauses, further comprising selecting the region of interest where residual stress needs to be reduced.

[0109] The method in accordance with any of the preceding clauses, further comprising dividing the remaining section into layers based upon the coarse mesh.

Claims

WHAT IS CLAIMED IS:

1. A computer system for implementing finite element analysis, the computer system comprising at least one processor in communication with at least one memory device, wherein the at least processor is programmed to: divide a model of an additive manufacturing (AM) article of manufacture into a submodel of a region of interest and a remaining section; mesh the remaining section with a coarse mesh; calculate a compliance matnx for each layer of the remaining section based upon the coarse mesh; mesh the submodel with a fine mesh, wherein the fine mesh covers a subset of the geometry relative to the coarse mesh; divide the submodel into layers based upon the fine mesh; analyze each layer of the submodel based upon the fine mesh; determine an effect of the remaining section on the submodel based upon the plurality of compliance matrices; and generate an updated submodel based upon the analysis and the effect of the remaining section on the submodel.

2. The computer system of Claim 1 , wherein the at least one processor is further programmed to select the region of interest where residual stress needs to be reduced.

3. The computer system of Claim 2, wherein the at least one processor is further programmed to select the region of interest based on one or more reports of cracks in the article of manufacture.

4. The computer system of Claim 3, wherein the region of interest further includes an additional region around where the cracks were reported.

5. The computer system of Claim 1. wherein the at least one processor is further programmed to divide the remaining section into layers based upon the coarse mesh.

6. The computer system of Claim 1, wherein the coarse mesh is a voxel mesh.

7. The computer system of Claim 1 , wherein the at least one processor is further programed to retain one or more nodes laying at one or more boundaries between the submodel and the remaining section as degrees of freedom.

8. The computer system of Claim 1, wherein the compliance matrix is a linear system of equation size by the number of degrees of freedom at the boundary of the submodel and the remaining section.

9. The computer system of Claim 8. wherein the at least one processor is further programmed to determine a mapping at each step between the degrees of freedom of the remaining section at the remaining section submodel interface and the degrees of freedom of the submodel at the same interface.

10. The computer system of Claim 9, wherein the at least one processor is further programmed to determine the mapping by establishing one or more constraint equations on the degrees of freedom.

11. The computer system of Claim 1. wherein the at least one processor is further programmed to skip one or more layers of the remaining section below the submodel.

12. The computer system of Claim 1. wherein the at least one processor is further programmed to perform shape optimization on the submodel.

13. The computer system of Claim 1. wherein the at least one processor is further programmed to generate a configuration of the submodel to be tested.

14. The computer system of Claim 1, wherein the at least one processor is further programmed to apply a layer-wise inherent strain method to the finely meshed submodel.

15. The computer system of Claim 1 , wherein the effect includes at least one of stiffness or load.

16. The computer system of Claim 1, wherein the at least one processor is further programmed to shift the submodel up or dow n to make a top layer of the submodel vertical position match a top layer of the remaining section vertical position.

17. The computer system of Claim 1 , wherein the at least one processor is further programmed to apply the updated subdomain to the remaining section to generate a build file for an additive manufacturing machine.

18. A computer implemented method for finite element analysis, method implemented on a computer system comprising at least one processor in communication with at least one memory device, wherein the method comprises: dividing a model of an additive manufacturing (AM) article of manufacture into a submodel of a region of interest and a remaining section; meshing the remaining section with a coarse mesh; calculating a compliance matrix for each layer of the remaining section based upon the coarse mesh; meshing the submodel with a fine mesh, wherein the fine mesh covers a subset of the geometry relative to the coarse mesh; dividing the submodel into layers based upon the fine mesh; analyzing each layer of the submodel based upon the fine mesh; determining an effect of the remaining section on the submodel based upon the plurality of compliance matrices; and generating an updated submodel based upon the analysis and the effect of the remaining section on the submodel.

19. The computer implemented method of Claim 18 further comprising selecting the region of interest where residual stress needs to be reduced.

20. The computer implemented method of Claim 18 further comprising dividing the remaining section into layers based upon the coarse mesh.

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