WO2025122390A1

WO2025122390A1 - Generating a finite element mesh, improving a design, generating a component, computer system

Info

Publication number: WO2025122390A1
Application number: PCT/US2024/057447
Authority: WO
Inventors: Jovana CHEMIN; Jonathan Makem; Harry FOGG; Nilanjan Mukherjee
Original assignee: Siemens Industry Software Limited; Siemens Industry Software Inc.; Siemens Industry Software Nv
Priority date: 2023-12-08
Filing date: 2024-11-26
Publication date: 2025-06-12

Abstract

A computer-implemented method for generating a finite element mesh of a component for the numerical solution of partial differential equations for the description of technical-physical circumstances to which the component is subjected in its intended operation. The invention further relates to a method for improving the components design and generating the component. Furthermore, the invention relates to a system for performing such method. Furthermore, the invention relates to a computer-readable medium encoded with executable instructions, that when executed, cause the computer system to carry out a method according to the invention.

Description

Generating a finite element mesh, improving a design, generating a component, computer system

Technical Field

The present invention relates to a method for computer-implemented method for generating a finite element mesh of a component for the numerical solution of partial differential equations for the description of technical-physical circumstances to which the component is subjected in its intended operation, comprising:

(a) Providing a surface-geometry-model of said component, said surface-geometry- model comprising points;

(b) Defining boundary edges connecting said points dividing the surface-geometry- model into parts;

(c) Defining blocks of the surface-geometry-model based on the boundary edges;

(d) meshing each block to generate a block-structured mesh containing a plurality of finite elements;

(e) Generating a block-structured mesh on the entire component.

Furthermore, the invention relates to a method for improving the components design and generating the component. Furthermore, the invention relates to a system for performing such method. Furthermore, the invention relates to a computer-readable medium encoded with executable instructions, that when executed, cause the computer system to carry out a method according to the invention.

Background

Today's technology design and development relies largely on numerical methods to solve partial differential equations [PDEs], PDEs are mathematical equations that describe physical phenomena such as heat transfer, fluid flow, and structural behavior which are important for technical component design. Such evaluations are obligatory to determine the ability of the respective component to cope with the operational requirements for the intended use. For example, a gas turbine blade is assessed by evaluation of Newton's Second Law, Navier- Stokes equations and others. Such work is normally done using Computer Aided Engineering [CAE] tools which are commercially available e.g., as Siemens Simcenter 3D.

In most cases, generating a mesh is required for numerical methods used to solve PDEs. Meshing is the process of dividing the problem domain into smaller elements or points respectively lattice points, allowing equations to be formulated and solved within each element or lattice point. Networking is particularly important for methods such as the finite element method [FEM] and the finite difference method [FDM], The so-called Boundary Element Method [BEM] uses a mesh at the boundary of the problem domain to discretize and approximate the boundary conditions of the problem.

In such numerical analyses, meshing requires a significant amount of effort, especially for complex geometries or large-scale problems, and is a crucial step in ensuring accurate and reliable results. The meshing process typically includes steps such as geometry preparation, mesh generation, refinement, and quality checks. Typically, specialized software tools are used to handle complex geometries, ensure proper element connectivity, and achieve appropriate mesh density.

In this context a block-structured mesh, also known as a structured mesh, is a type of mesh where the elements are organized in blocks. Benefits of using a block-structured mesh are improved numerical accuracy, faster convergence, computational efficiency, ease of mesh generation, grid refinement capabilities, better boundary alignment, and simplified postprocessing.

Numerical methods to solve partial differential equations (PDEs) are often applied to large and complex entities. One example for illustration of the problem underlying the invention is an airframe of an aircraft. The airframe encompasses all mechanical parts of an aircraft except the propulsion system, and it undergoes many elaborate aerospace engineering analyses to fulfill the requirements of strict quality and safety controls. The computational efficiency and accuracy of the analyses’ results are highly dependent on the airframe’s mesh quality. Directly meshing an entire airframe model presents numerous obstacles due to its complex geometry and topology. Instead of treating the airframe model as a whole, decomposing it into individual parts and constructing a virtual topology network allows the meshing of each part separately and generates a block-structured mesh of the entire airframe meeting rigorous aerospace criteria.

In the context of the invention a virtual topology network refers to a representation that allows the meshing of each part separately while maintaining connectivity information between the parts. This decomposition into smaller, more manageable parts or subdomains can be done based on geometric features or functional requirements. Each part can then be meshed separately to simplify the analysis and improve computational efficiency. A virtual topology network serves as a way to define the relationships and connectivity between the individual parts. It captures the information about how the parts are interconnected or adjacent to each other in the original structure. This network allows for the construction of a block-structured mesh of the entire structure by combining the meshes of the individual parts while maintaining the connectivity between them. Utilizing a virtual topology network improves automation of the meshing process and reduces the complexity of handling the overall structure. The virtual topology network enables efficient mesh generation algorithms to create a block-structured mesh that aligns with the decomposed parts.

The description of the invention uses the term ‘part’ in a more general meaning than the term ‘block’. While part indicates that some object or component is divided by a line, edge or boundary the term ‘block’ means a clearly defined are with closed boundary edges defining this block from its surrounding area.

Step (c) of defining blocks of the surface geometry model based on the bounding edges is called building a virtual topology or a virtual topology network. The blocks are linked to each other by connectivity information, but in addition, the model information is reduced by omitting unnecessary information such as graphical details.

Building virtual topology network is a difficult and time-consuming task and is associated to several problems. In particular these problems comprise:

(P1) Multiblocking technology (PDE based approach, Cartesian slabbing, Medial Axis, etc.), (P2) Multiblocking space (2D and 3D),

(P3) Multiblocking data (straight split lines, curved split lines consisting of many points), and (P4) geometries containing artefacts (seam edges, scar edges, unconnected point loops).

As often is the case, decomposing a model into individual parts is primarily dictated by the limitations of the available virtual topology engine, rather than by the goal of optimizing mesh quality. This limitation poses a significant challenge for obtaining a suitable mesh to conduct technical-physical analyses for example rigorous aerospace engineering analyses.

From [1] a multiblocking strategy is known. The approach constructs a virtual topology network for models of industrial complexity, but it limits the space of operation to 2D (=>P1) and employs a multiblocking strategy that involves only straight multiblocking lines with no more than two points (=>P2). Additionally, it assumes CAD geometries without any artefacts (P4).

Another approach is known from [2], The method presented in this publication could potentially address the majority of the aforementioned issues (P1-P3). However, its effectiveness has only been demonstrated in academic contexts, particularly with regard to quadrilateral blocks and CAD geometries that are free from artefacts (P4). These limitations present significant challenges in a general industrial setting. From [3], [4] it is known that virtual operators represent a common CAE tool with varying capabilities among the different methodologies and packages while their purpose is not the construction of a virtual topology network but using boolean operators to perform a geometry simplification or clean-up.

References:

[1] Mukherjee, Nilanjan, and Jonathan E. Makem; “A cartesian slab based multiblocking strategy for irregular cylindrical surfaces” Procedia engineering 203 (2017): 232-244

[2] Jezdimirovic, Jovana, Alexandre Chemin, and Jean Francois Remacle. “Multi-block decomposition and meshing of 2D domain using Ginzburg-Landau PDE” Proceedings of the 28th International Meshing Roundtable (2019)

[3] Sheffer, Alla, et al. “Virtual topology operators for meshing.” International Journal of Computational Geometry & Applications 10.03 (2000)

[4] Tierney, Christopher M., et al. “Generating analysis topology using virtual topology operators.” Procedia Engineering 124 (2015) : 226 - 238

Summary of Invention

The invention is based on the problem of improving the known computer-implemented method for the generation of a finite element mesh of a component such that a further optimization regarding the named challenge is reached.

It is another objective of the invention to improve the determination and technical-physical parameters of technical circumstances to which a component is subjected in its intended operation or during an intended use of said component.

To solve the problem the invention proposes a method of the incipiently defined kind for generating a finite element mesh characterized in that step (b) additionally comprises:

(b 1 ) Defining a direction of rotation for a listing of connected points;

(b2) Generating point connectivity data by generating for each point a consistently ordered point connection list listing along said predefined direction of rotation all points connected to said point; and that step (c) additionally comprises:

(c1) Defining each block’s boundary on the basis of said point connectivity data;

(c2) Repeating step (c1) for every point not yet being assigned to a block until all points are assigned to at least one block. The invention enables automatically defining virtual blocks of any model, which facilitates the individual meshing of complex parts and enables generating a high-quality block-structured mesh, in particular a quad mesh. One essential element of the invention is using only the model’s point connectivity data. This feature allows to be independent from the choice of any multiblocking strategy, other data, and space geometry as well as geometrical artefacts.

In the context of the invention a surface geometry model refers to a representation or description of the external shape or form of a technical component. Most often that model is provided as a computer-aided design [CAD], The surface geometry model may be generated by an engineer using CAD-software or by using mathematical equations or algorithms to define the shape of the object. Often the surface is represented by splines or NURBS (non- uniform rational basis splines).

Surface geometry models can be represented in different file formats, such as STL (Standard Tessellation Language), IGES (Initial Graphics Exchange Specification), or STEP (Standard for the Exchange of Product Data), allowing them to be shared, exchanged, and utilized across different software applications and systems.

In the context of this invention, a multiblocking engine refers to a software component or algorithm that facilitates the generation of a structured or block-structured mesh for complex geometries. Such a structured mesh is composed of interconnected blocks or structured elements, such as quadrilaterals in 2D or hexahedra in 3D. Each block typically represents a portion of the domain and is meshed independently. The blocks are then assembled to form the overall mesh. A multiblocking engine automatically decomposes a complex geometry into individual blocks or subdomains by taking into account the geometric features and connectivity of the domain to create a decomposition that allows for efficient meshing. The multiblocking engine may employ various techniques, such as octree decomposition, advancing front method, or domain decomposition algorithms, to generate the block structure. After the decomposition meshes may be generated for each block separately allowing for localized control over mesh properties, like mesh density. The multiblocking engine is a crucial component in meshing software as it enables the efficient generation of structured or block-structured meshes for complex geometries. It simplifies the meshing process by breaking down the problem into manageable blocks while ensuring connectivity and compatibility between the blocks. In the context of the invention, a virtual topology network refers to a representation of the connectivity between elements or blocks in a mesh. It defines the relationships and interactions between elements, rather than representing the physical layout or shape of the structure being analyzed. The virtual topology may be defined through connectivity information, such as nodal connectivity or block connectivity or element connectivity. It specifies which points are shared between elements and how they are connected. This information is crucial for assembling the system equations and solving the governing equations of the problem over blocks, points, or elements.

In the context of this invention an endless cyclic list, also known as an infinite cyclic list, is a data structure that represents a list of elements that continues indefinitely in a cyclical manner. It can be visualized as a list that has no beginning or end and loops back on itself. This means that the last element in the list points back to the first element, creating a continuous cycle.

Description of Embodiments

According to one embodiment it is proposed that step (b) of defining boundary edges connecting said points dividing the surface-geometry-model into parts is performed by using a multi-blocking engine. Known multiblock engines provide this function and are able to generate point connectivity data according to step (b2).

Another preferred embodiment provides that step (c1) provides defining each block’s boundary only on the basis of said point connectivity data. The invention enables this stable and reliable process resulting in a high-quality block structure due to the consistency of the point connectivity data.

Furthermore, said point connection lists may be endless cyclic such that after the last element of the list follows the first element of the list again. This feature enables error free navigation through the lists searching for neighboring list elements.

Another advantageous embodiment of the method provides that wherein step (c1) includes further sub-steps:

(i) connecting a starting point to any point from its point connection list;

(ii) connecting a next point selected from the point connection list of the last connected point in previous step (i), which is listed as the point before the last connected point; (iii) Repeat previous step (ii) until the starting point is again selected as the next connection point so that the block’s boundary is closed.

Consistently following any of the two alternative procedures results in a clean and errorfree block structure.

The invention further relates to a computer-implemented method for determination of physical parameters of technical-physical circumstances to which the component is subjected in its intended operation, said method comprising a method according to one of the preceding claims, comprising an additional step:

(f) Applying at least one partial differential equation and boundary conditions to the finite element mesh and solving the resulting model by a computer-implemented numerical method to obtain physical parameters for evaluating the technical performance of the component. The method according to the invention beneficially enable quick and save convergence of the calculation saving time, energy and computing resources. The resulting high quality block structured mesh enables fast solutions of the underlying physical technical problem fulfilling high accuracy requirements. The efficient meshing technology according to the invention and its embodiments directly saves computational resources by improving speed and convergence behavior of the numerical computer-calculation. The method according to the invention and its embodiments further improves the sustainability of performing modelling and simulation when the meshing method according to the invention is applied.

Beneficially the above calculation results may be shared with a user comfortably by an additional step (g) of the method providing displaying said parameters and/or key figures calculated from said parameters or images illustrating said parameter fields to a user. The user may efficiently monitor the improvement of the design performance via a monitor display.

Still another embodiment of the invention relates to a computer-implemented method for improving a component’s design wherein said method comprises the above method of determination of physical parameters, comprising an additional step (h) of providing said component design to an iterative component design process for improving the technical performance of the component by variations of the components design and monitoring the change of the parameters. This kind of improvement or optimization process becomes even more efficient and faster due to the accelerated and reliable convergence due to the improved mesh properties according to the invention.

Physical-technical parameters that may be optimization targets in such iterative design improvement process are for example:

- Density: Reducing the weight or volume of the design component without compromising its structural integrity or functionality.

- Stress: Minimizing the stress levels experienced by the design under various loads and conditions to prevent material failure or deformation.

- Force: Optimizing the distribution and application of forces within the design to ensure efficient load transfer and minimize unnecessary stresses.

- Pressure loss: Reducing pressure losses in fluid flow systems by optimizing the design of pipes, valves, fittings, or other components to minimize energy losses and improve overall system efficiency. This may include fluid flow parameters like reduction of turbulence, reduction of pressure loss, reduction of maximum velocity or Reynolds number.

- Noise emission: Reducing noise levels generated by the design, such as through the use of noise-damping materials, improved component design, or optimized airflow patterns.

- Heat dissipation: Enhancing the design's ability to dissipate heat efficiently to prevent overheating and maintain optimal operating temperatures.

- Vibration reduction: Minimizing vibrations generated by the design to improve stability, reduce wear and tear, and enhance user comfort.

- Efficiency: Increasing the overall efficiency of the design, such as by minimizing energy consumption, optimizing power transfer, or reducing frictional losses.

- Material selection: Identifying and using materials that offer the desired properties, such as strength, durability, corrosion resistance, or thermal conductivity, while minimizing weight or cost.

- Environmental impact: Minimizing the environmental impact of the design by using sustainable materials, reducing energy consumption, or optimizing waste management processes.

These physical-technical terms provide specific areas where optimization can be targeted during the iterative design improvement process to achieve desired outcomes. The result of the evaluation of these parameters is to be understood as the technical performance of the component. Another teaching of the invention relates to a method according to the above definition comprising an additional step (i) of generating said component according to a design which’s technical performance has been evaluated and/or which was improved by said iterative component design process. In this context generating a component means producing a physical object corresponding to the respective design evaluated, improved or optimized. The generating may comprise e.g., casting, machining, like milling or lathing, injection molding, 3D printing/additive manufacturing, forming, welding, extrusion stamping, powder metallurgy or forging to only name a few options.

Another teaching of the invention relates to a computer system arranged and configured to execute the computer-based steps of the computer-implemented method according to any one of the above embodiments. Any of the mentioned steps of the methods defined may be computer implemented or at least computer controlled.

Another teaching of the invention relates to a computer -readable medium encoded with executable instructions, that when executed, cause the above defined computer system to perform the method according to the invention or one of its embodiments.

Independent of the grammatical term usage, individuals with male, female or other gender identities are included within the term.

Brief Description of the Drawings

The properties, features and advantages of this invention described above, as well as the manner they are achieved, become clearer and more understandable in the light of the following description and embodiments, which will be described in more detail in the context of the drawings. This following description does not limit the invention on the contained embodiments. Same components or parts can be labeled with the same reference signs in different figures. In general, the figures are not for scale. It shall be understood that a preferred embodiment of the present invention can also be any combination of the dependent claims or above embodiments with the respective independent claim. The drawings respectively show:

Figure 1 : an overview of a work pipeline for generating a block-structured mesh;

Figure 2: an illustration of a seam edge (LHS) and the corresponding point connectivity (RHS); Figure 3: an illustration of scar edges (LHS) and generated Delaunay triangulation (RHS) Figure 4: an illustration of an unconnected point loop (LHS) and generated split line (RHS);

Figure 5: examples of arranging point connectivity data;

Figure 6: a simple example of a graph generated from a method according to the invention;

Figure 7: an example of generating planar graph embedding of a cube;

Figure 8: an example of generating planar graph embedding of a 2D model (disk);

Figure 9: an illustration of a box-imprint based multiblocking pipeline;

Figure 10: a selection of the examples of block building according to the method according to the invention;

Figure 11: an example illustrating the impact of virtual topology building according to the invention using consistently ordered point connection data from a multiblocking engine on the mesh quality,

- LHS: The unstructured meshes generated without the virtual topology builder (no multiblocking engine deployed);

- RHS: The block-structured meshes obtained using the proposed virtual topology builder (Box-imprint based multiblocking engine deployed).

Description of Examples

Figure 1 shows a flow diagram illustrating the workflow and its components of a method according to the invention. The invention primarily deals with a computer-implemented method for generating a finite element mesh of a component for the numerical solution of partial PRT differential equations for the description of technical-physical circumstances to which the component CMP of a specific design DSG is subjected in its intended operation. The design DSG is a starting design, which may preferably be parametrized such that variations may easily be defined, preferably variations are defined computer-based automatically or are predefined within certain ranges of design parameters. The method is performed in steps, as follows:

(a) Providing a surface-geometry-model SGM of said component CMP, said surface- geometry-model SGM comprising points PNT;

(b) Defining boundary edges BDE connecting said points PNT dividing the surface- geometry-model SGM into parts PRT, comprising the sub-steps of:

(b1) Defining a direction of rotation DOR for a listing of connected points PNT - this is chosen to be clockwise CW, here. The choice may as well be counterclockwise; (b2) Generating point PNT connectivity data CDT by generating for each point PNT a consistently ordered point PNT connection list CNL listing along said predefined direction of rotation DOR all points PNT connected to said point PNT wherein said point PNT connection lists CNL are endless cyclic such that after the last element of the list follows the first element of the list again; wherein step (b) of defining boundary edges BDE connecting said points PNT dividing the surface-geometry-model SGM into parts PRT is performed by using a multi-blocking engine MBE;

(c) Defining blocks BLC of the surface-geometry-model SGM based on the boundary edges BDE; comprising the sub-steps of:

(c1) Defining each block’s BLC boundary on the basis of said point PNT connectivity data CDT, further comprising the sub-steps of:

(i) Connecting a starting point PNT to any point PNT from its point PNT connection list CNL;

(ii) Connecting a next point PNT selected from the point PNT connection list CNL of the last connected point PNT in step (i), which is listed as the point PNT before or behind the last connected point PNT;

(iii) Repeating step (ii) until the starting point is again selected as the next connection point so that the block’s boundary is closed.

(c2) Repeating step (c1) for every point PNT not yet being assigned to a block BLC until all points PNT are assigned to at least one block BLC

(d) Meshing MSH each block BLC to generate a block-structured BST mesh MSH containing a plurality of finite elements FEM;

(e) Generating a block-structured BST mesh MSH on the entire component CMP;

(f) Applying at least one partial differential equation PDE and boundary conditions BCD to the finite element FEM mesh MSH and solving SLV the resulting model MDL by a computer- implemented numerical method to obtain physical parameters PRM for evaluating the technical performance of the component CMP;

(g) displaying said parameters PRM and/or key figures calculated from said parameters PRM or images illustrating parameter PRM fields for example key performance indicators KFG to a user USR, preferably via a display DSP;

(h) providing said component’s CMP design DSG to an iterative component CMP design process ITD for improving the technical performance of the component CMP by variations of the components CMP design and monitoring the change of the parameters PRM; (i) generating said component CMP according to a design which’s technical performance has been evaluated and/or which was improved by said iterative component CMP design process and thereby obtaining a real, physical, tangible object OBJ.

The invention further relates to a computer system CSY arranged and configured to execute the steps of the computer-implemented method according to the above description and any embodiment disclosed herein.

Computer-readable medium CRM encoded with executable instructions, that when executed, cause the computer system CSY defined above to carry out a method as explained herein.

The figures 2-11 show specific examples of the invention and some special aspects of the meshing when putting the invention into practice.

Next to references defined above further nomenclature of essential components shown in the illustrations are: edge = edge generated by a multiblocking engine block = collection of connected virtual edges creating a polygon seam edge = axis-aligned virtual edge of a cylindrical surface (FIG. 2) scar edge = edge that remains on the model’s surface after the trimming or stitching operation (as shown in FIG. 3) point loop = collection of all boundary points of a face or a virtual block.

Defining blocks in a mesh, sometimes referred to as virtual blocks - essentially relies on the method steps (1. - 5.):

1. Collecting the model’s point PNT connectivity data CDT from any deployed multi-blocking engine MBE

2. Establishing the well-defined point connectivity data CDT by selecting and applying connectivity treatment on geometrical artefacts. Geometrical artefacts may be one or several of the following:

(a) Seam edges: no treatment is needed because well-defined connectivity of the points is already established (shown in FIG. 2)

(b) Scar edges: generating the Delaunay triangulation on a given set of points of the face, and updating the point connectivity data (shown in FIG. 3)

(c) Unconnected point loops: generating a split line connecting the point loops, and updating the point connectivity data (shown in FIG. 4) 3. Associating consistent orientation data to each point by establishing the cyclic order of points adjacent with any given point.

This task is accomplished by placing a virtual clock’s center at the specified point and ordering its neighboring points either in a clockwise or counterclockwise manner based on their respective positions on the virtual clock’s hands (FIG. 5 on the right-hand side). For the sake of convenience, a counter-clockwise (COW) order is applied. This step ensures that all virtual blocks are well-defined for meshing, i.e., obtaining a planar graph F with a crossing-free embedding.

4. Generating the graph F = {V,E} with vertices V = {T 1 , T2, . . . , Tn} and oriented edges E = {{T 1 , T2}, {T2, T3}, . . . , {Tj , Tn}} relying on the adaptation of mathematical theory of planar graph embedding from the model’s ordered point connectivity data to define virtual blocks for meshing (FIG. 6, 7). Below the process of generating the block’s BLC boundary on the basis of point PNT connectivity data CDT is listed step by step in a computer- language-like description:

Generating the graph F

Input: Ordered Point Connectivity Data

Output: Virtual Blocks

1 : while there is a non-traversed oriented edge {T,Tt} do

2: Take the first edge TiTj

3: Take Tk - the COW oriented neighbor of Tj which is before Ti 4: Take Tt - the COW oriented neighbor of Tk which is before Tj 5: etc. ... etc.

6: T ake Tn - the COW oriented neighbor of Tq which is before T p 7: if Tn == Ti then

8: Define the block BI={Ti, Tj, Tk, Tt, ... , Tp, Tq, Ti} 9: end if

10: end while

5. Discarding virtual blocks consisting only of points on the physical boundary of 2D models - as shown in Figure 8.

The robustness of the method according to the invention may be tested using the ordered point connectivity data CDT from the box-imprint based multiblocking engine as shown in FIG. 9. Corresponding examples are shown in FIG. 10. To illustrate the impact of the method according to the invention on the mesh quality figure 11 illustrates the difference of conventional meshing and meshing according to the invention. On the left-hand side, the unstructured mesh MSH generated without the method according to the invention, and on the right-hand side, the block-structured mesh MSH obtained are depicted. Clearly visible is the more systematic beneficial block structure when applying the method according to the invention on the right-hand side.

PHRASENSAMMLUNG:

TECHNICAL FIELD

The present disclosure is directed, in general, to

BACKGROUND

SUMMARY

Variously disclosed embodiments include systems and methods that may be used to ...

In one example, a system may comprise at least one processor. The at least one processor may be configured to

Further, the at least one processor may be configured to use the

In another example, a method may include

A further example may include non-transitory computer readable medium encoded with executable instructions (such as a software component on a storage device) that when executed, causes at least one processor to carry out this described method. The foregoing has outlined rather broadly the technical features of the present disclosure so that those skilled in the art may better understand the detailed description that follows. Additional features and advantages of the disclosure will be described hereinafter that form the subject of the claims. Those skilled in the art will appreciate that they may readily use the conception and the specific embodiments disclosed as a basis for modifying or designing other structures for carrying out the same purposes of the present disclosure. Those skilled in the art will also realize that such equivalent constructions do not depart from the spirit and scope of the disclosure in its broadest form.

Before undertaking the Detailed Description below, it may be advantageous to set forth definitions of certain words or phrases that may be used throughout this patent document. For example, the terms “include” and “comprise,” as well as derivatives thereof, mean inclusion without limitation. The singular forms “a”, “an” and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise. Further, the term “and/or” as used herein refers to and encompasses any and all possible combinations of one or more of the associated listed items. The term “or” is inclusive, meaning and/or, unless the context clearly indicates otherwise. The phrases “associated with” and “associated therewith,” as well as derivatives thereof, may mean to include, be included within, interconnect with, contain, be contained within, connect to or with, couple to or with, be communicable with, cooperate with, interleave, juxtapose, be proximate to, be bound to or with, have, have a property of, or the like. Also, although the terms “first”, “second”, “third” and so forth may be used herein to describe various elements, functions, or acts, these elements, functions, or acts should not be limited by these terms. Rather these numeral adjectives are used to distinguish different elements, functions or acts from each other. For example, a first element, function, or act could be termed a second element, function, or act, and, similarly, a second element, function, or act could be termed a first element, function, or act, without departing from the scope of the present disclosure. In addition, phrases such as “processor is configured to” carry out one or more functions or processes, may mean the processor is operatively configured to or operably configured to carry out the functions or processes via software, firmware, and/or wired circuits. For example, a processor that is configured to carry out a function/process may correspond to a processor that is actively executing the software/firmware which is programmed to cause the processor to carry out the function/process and/or may correspond to a processor that has the software/firmware in a memory or storage device that is available to be executed by the processor to carry out the function/process. ft should also be noted that a processor that is “configured to” carry out one or more functions or processes, may also correspond to a processor circuit particularly fabricated or “wired” to carry out the functions or processes (e.g., an ASIC or FPGA design). Further the phrase “at least one” before an element (e.g., a processor) that is configured to carry out more than one function may correspond to one or more elements (e.g., processors) that each carry out the functions and may also correspond to two or more of the elements (e.g., processors) that respectively carry out different ones of the one or more different functions. The term “adjacent to” may mean: that an element is relatively near to but not in contact with a further element; or that the element is in contact with the further portion, unless the context clearly indicates otherwise. Definitions for certain words and phrases are provided throughout this patent document, and those of ordinary skill in the art will understand that such definitions apply in many, if not most, instances to prior as well as future uses of such defined words and phrases. While some terms may include a wide variety of embodiments, the appended claims may expressly limit these terms to specific embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates ...

DETAILED DESCRIPTION

Various technologies that pertain to systems and methods for generating meshes for object models will now be described with reference to the drawings, where like reference numerals represent like elements throughout. The drawings discussed below, and the various embodiments used to describe the principles of the present disclosure in this patent document are by way of illustration only and should not be construed in any way to limit the scope of the disclosure. Those skilled in the art will understand that the principles of the present disclosure may be implemented in any suitably arranged apparatus. It is to be understood that functionality that is described as being carried out by certain system elements may be performed by multiple elements. Similarly, for instance, an element may be configured to perform functionality that is described as being carried out by multiple elements. The numerous innovative teachings of the present application will be described with reference to exemplary non-limiting embodiments.

Many forms of product systems (such as CAE and CAD software) are operative to manipulate and process various types of three dimensional (3D) object models (such as stored in CAD files) that represent a structure for an object (e.g., parts, assemblies and subassemblies). In particular CAE software may be used to carry out testing and/or simulations on object models. Such simulations for example, may include the application of various loads and the calculation of how the structure behaves responsive to such loads based on a generated mesh for the structure. For example, in an example embodiment the simulation soft- ware may carry out stress analysis for a structure using a generated mesh for the object model of the structure. In other examples, simulation software may be capable of using meshes to simulate the physical effect of an automobile collision (or other test) on many connected structures represented by object models. To carry out simulations on a structure, an object model of a structure may undergo a meshing process which divides a surface of the structure into a mesh of many connected four-sided geometric shapes.

Simulation software may use such meshes, as well as user configurable properties of one or more object models (such as the materials the structures are to be made of) and user configurable analysis parameters, to carry out mathematical processes such as finite element analysis in order to derive information regarding the effects (e.g., physical changes, displacements) that a simulation (e.g., a static load, collision) may have on a structure. With reference to FIG. 1 , an example system 100 that facilitates ...

Claims

1. Computer-implemented method for generating a finite element mesh of a component for the numerical solution of partial (PRT) differential equations for the description of technical-physical circumstances to which the component (CMP) is subjected in its intended operation, comprising:

(a) Providing a surface-geometry-model (SGM) of said component (CMP), said surface-geometry-model (SGM) comprising points (PNT);

(b) Defining boundary edges (BDE) connecting said points (PNT) dividing the surface- geometry-model (SGM) into parts (PRT);

(c) Defining blocks (BLC) of the surface-geometry-model (SGM) based on the boundary edges (BDE);

(d) Meshing (MSH) each block (BLC) to generate a block-structured (BST) mesh (MSH) containing a plurality of finite elements (FEM);

(e) Generating a block-structured (BST) mesh (MSH) on the entire component (CMP); characterized in that step (b) additionally comprises:

(b1) Defining a direction of rotation (DOR) for a listing of connected points (PNT);

(b2) Generating point (PNT) connectivity data (CDT) by generating for each point (PNT) a consistently ordered point (PNT) connection list (CNL) listing along said predefined direction of rotation (DOR) all points (PNT) connected to said point (PNT); and that step (c) additionally comprises:

(c1) Defining each block’s (BLC) boundary on the basis of said point (PNT) connectivity data (CDT);

(c2) Repeating step (c1) for every point (PNT) not yet being assigned to a block (BLC) until all points (PNT) are assigned to at least one block (BLC).

2. Method according to claim 1, wherein step (b) of defining boundary edges (BDE) connecting said points (PNT) dividing the surface-geometry-model (SGM) into parts (PRT) is performed by using a multi-blocking engine (MBE).

3. Method according to one of the preceding claims, wherein step (c1) provides defining each block’s (BLC) boundary only on the basis of said point (PNT) connectivity data (CDT).

4. Method according to one of the preceding claims, wherein said point (PNT) connection lists (CNL) are endless cyclic such that after the last element of the list follows the first element of the list again.

5. Method according to one of the preceding claims, wherein step (c1) includes further substeps:

(i) connecting a starting point (PNT) to any point (PNT) from its point (PNT) connection list (CNL);

(ii) connecting a next point (PNT) selected from the point (PNT) connection list (CNL) of the last connected point (PNT) in step (i), which is listed as the point (PNT) before the last connected point (PNT);

(iii) Repeat step (ii) until the starting point is again selected as the next connection point so that the block’s boundary is closed.

6. Computer-implemented method for determination of physical parameters (PRM) of technical-physical circumstances to which the component (CMP) is subjected during an intended use of said component (CMP), said method comprising a method according to one of the preceding claims, comprising an additional step:

(f) Applying at least one partial differential equation (PDE) and boundary conditions (BCD) to the finite element (FEM) mesh (MSH) and solving the resulting model (MDL) by a computer-implemented numerical method to obtain physical parameters (PRM) for evaluating the technical performance of the component (CMP).

7. Computer-implemented method according to claim 6, comprising an additional step of:

(g) displaying said parameters (PRM) and/or key figures calculated from said parameters (PRM) or images illustrating said parameter (PRM) fields to a user (USR).

8. Computer-implemented method for improving a component’s design said method comprising a method according to one of the preceding claims 6 or 7, comprising an additional step of:

(h) providing said component (CMP) design to an iterative component (CMP) design process for improving the technical performance of the component (CMP) by variations of the components (CMP) design and monitoring the change of the parameters (PRM).

9. Computer-implemented method comprising a method according to claim 8, comprising an additional step of:

(i) generating said component (CMP) according to a design which’s technical performance has been evaluated and/or which was improved by said iterative component (CMP) design process.

10. Computer system arranged and configured to execute the steps of the computer- implemented method according to any one of the preceding claims.

11. Computer-readable medium encoded with executable instructions, that when executed, cause the computer system (CSY) according to claim 10 to carry out a method according to any one of claims 1 to 9.