Description:“A NOVEL BI-DIRECTIONAL MESH COARSENING STRATEGY FOR 3D FINITE ELEMENT MODELS AND A PROCEDURE THEREOF”

FIELD OF THE INVENTION:
The present invention relates to the field of finite element modelling (FEM) which is widely used for design and analysis of components that find application in various domains of engineering. It discloses a novel and an efficient method for a quick, bi-directional transition from fine mesh into coarse mesh in 3D finite element models maintaining aspect ratios.

BACKGROUND OF THE INVENTION/PRIOR ART:
Background description includes information that may be useful in understanding the present invention. It is not an admission that any of the information provided herein is prior art or relevant to the presently claimed invention, or that any publication specifically or implicitly referenced is prior art.

Finite element modelling is the method of performing some sort of a computational analysis that simulates a physical process, by way of discretizing a big continuum (representing the actual component) into an equivalent model consisting of elements whose corner points are defined by nodes. Based on the physical process that is desired to be simulated, various types of loads viz. thermal or mechanical can be applied on different elements or on nodes. While for simple geometric shapes, mechanically and thermally induced deformations, strains and stresses can be computed easily by established formulas, but for components with complex geometries, such formula based calculations are not possible. In such cases, the FEM is resorted to, wherein the 1D, 2D (or) 3D model of the component is created firstly, it is meshed into as many number of elements as required, based on the expected accuracy levels of the results, in the second stage. Various material properties are defined for the material with which the component is made of. Then, thermal / mechanical loads are applied, either in a static manner or as a time marching transient manner. Thereafter, solutions are obtained using Finite Element solvers.

Wherever the FEM is applied for performing computational analysis, the number of elements, the quality of the elements viz. aspect ratio, included angle between the faces used are factors that dictate the computational complexity of the problem, which in turn decides the total solving time for the analysis. Since the results could only be extracted at nodes, it is a good engineering practice to mesh the finite element models in such a way that closely spaced nodes exist in certain important areas of interest, as decided by the engineer performing the FE simulation, and quickly transitioning the fine mesh into a coarse mesh composed of larger sized elements with nodes spaced apart. The distance over which the transitions happens is very important for obtaining results that are both quicker and accurate. In many cases, the endeavour would be to produce this transition in the shortest possible distance.

In this context, the present invention discloses a novel mesh coarsening procedure that will enable the coarsening of mesh in a 3D FE model simultaneously in two directions. This can help in greatly reducing the computational resources and complexity of the meshed models and thus the solving times also.

PRIOR ART:
Reference may be made to the following known arts:

US patent US6560570B1 specifies a method of connecting dissimilar finite element meshes wherein the first mesh is designated as the master mesh, and a second mesh is designated as slave mesh. Each of these has interface surfaces proximal to another. Each interface surface has a corresponding interface mesh comprising a plurality of interface nodes. Each slave interface node is assigned new coordinates locating the interface node on the interface surface of the master mesh and joining in meshes is done. This is significantly different from the proposed invention because the latter specifies a procedure for coarsening of 3D finite element mesh from smaller sized hexahedral elements to larger sized hexahedral elements using a novel transition pattern that allows for mesh coarsening in two directions simultaneously.

US patent US7295205B2 discloses a novel computer-implemented method and a system thereof for optimizing a finite element mesh. Computing devices are configured to determine a quality score for at least one original element in a finite element mesh based upon two or more quality attributes simultaneously. Depending on whether the quality score so determined exceeds the minimum cut-off value, the re-meshing is done to improve the quality score until the required score is achieved. But, the proposed invention is aimed at providing a mesh coarsening procedure that uses a novel bi-directional transition pattern with which a fine mesh can be transformed into a coarse mesh in two directions simultaneously.

US patent US8289322B1 describes various techniques for coarsening a quadrilateral mesh into larger sized elements. The regions to be coarsened are identified firstly, the fine elements already present in this regions are removed secondly and thirdly, the node pairs along opposite sides of the path are identified. Lastly, the node pairs along the path are then merged to collapse the path and result in larger sized elements. While this prior art specifies coarsening method only in one direction at a time, the present invention puts forward a novel mesh coarsening procedure where the transition from fine mesh to coarse mesh is achieved by using a special pattern that allows for coarsening to happen in two directions simultaneously thereby resulting in fewer number of elements.

US patent US8174525B2 describes a tetrahedral mesh generating method for finite-element analysis executable by a computer, comprising two steps. In the first step, a high-density tetrahedral mesh of a solid model of a product is created and in the second step, the high-density tetrahedral mesh is simplified into a low-density tetrahedral mesh, partially and retaining the original high-density tetrahedral mesh, in certain places, as decided by the user. This prior art is markedly different from the present invention because the latter uses a novel mesh coarsening procedure to transform a fine mesh of hexahedral elements into a coarse mesh of larger sized hexahedral elements, simultaneously in two directions by employing a special transition pattern. The prior art has not disclosed any method for coarsening of mesh comprising of hexahedral elements, instead it has only dealt with tetrahedral elements.

It is seen that none of the prior arts cited above, have disclosed a procedure for effecting mesh coarsening simultaneously in two directions using a special transition pattern, so that a fine mesh comprising smaller sized hexahedral elements can be transformed into coarser mesh of larger sized hexahedral elements.

OBJECTS OF THE INVENTION:
An object of the invention is to provide a novel mesh coarsening procedure for meshing finite element 3D models, using a Bi-Directional Torch (BDT) transition pattern.

Another object of the present invention is to provide a procedure for quick transition from a fine mesh to coarse mesh in a 3D FE model, wherein the coarsening is done simultaneously in two directions.

Still another object of the invention is its usefulness in meshing complex three dimensional geometries with reduced number of elements.

These and other objects and advantages of the present invention will be apparent to those skilled in the art after a consideration of the following detailed description taken in conjunction with the accompanying drawings in which a preferred form of the present invention is illustrated.

SUMMARY OF THE INVENTION:
One or more drawbacks of conventional systems and process are overcome, and additional advantages are provided through the apparatus/composition and a method as claimed in the present disclosure. Additional features and advantages are realized through the technicalities of the present disclosure. Other embodiments and aspects of the disclosure are described in detail herein and are considered to be part of the claimed disclosure.

According to the invention, a novel procedure for coarsening of fine mesh into a mesh with larger sized elements, such that coarsening happens simultaneously in two directions, has been disclosed. In case of FEM for different engineering applications, it is essential to use a fine mesh in the areas of interest and later on this needs to be changed to a coarse mesh in those areas where there is no analysis being made or where there is no need for extraction of any results. Generally, three dimensional meshed finite elements are begun with 8 node hexahedral elements in the areas of interest. Then, these are slowly transitioned into a coarse mesh wherein the hexahedral elements are joined with larger sized elements in the form of a ‘Y’ or in the form of a ‘torch’. These mesh coarsening methods are already known widely and readily available in public domain (these are shown in Figures 1 and 2). However, using these mesh coarsening techniques, the coarsening can be achieved only in one direction at a time, but, with the procedure disclosed in this invention, it will be possible to achieve a faster coarsening i.e. a type of mesh transitioning wherein the coarsening happens along two directions simultaneously. This is done by introducing certain special elements in the form of a ‘Bi-directional torch’ (abbreviated as BDT and referred as ‘BDT’ hereinafter). The new method proposed in this invention firstly enables the FE engineer to model the job with lesser number of elements, which also ensures faster determination. The biggest advantage is that in transient time marching FE analysis, this will be very useful because each and every iteration of the FE analysis with increasing time steps runs only with reduced number of elements thereby helping to bring about a great reduction in the overall solution time of the FE analysis.

Various objects, features, aspects, and advantages of the inventive subject matter will become more apparent from the following detailed description of preferred embodiments, along with the accompanying drawing figures in which like numerals represent like components.

It is to be understood that the aspects and embodiments of the disclosure described above may be used in any combination with each other. Several of the aspects and embodiments may be combined to form a further embodiment of the disclosure.

The foregoing summary is illustrative only and is not intended to be in any way limiting. In addition to the illustrative aspects, embodiments, and features described above, further aspects, embodiments, and features will become apparent by reference to the drawings and the following detailed description.

BRIEF DESCRIPTION OF THE ACCOMPANYING DRAWINGS:
The illustrated embodiments of the subject matter will be best understood by reference to the drawings, wherein like parts are designated by like numerals throughout. The following description is intended only by way of example, and simply illustrates certain selected embodiments of devices, systems, and processes that are consistent with the subject matter as claimed herein, wherein:

Figure 1 shows: 3D hexahedral elements with a transition technique involving a ‘Y’ pattern in one direction only in prior art.
Figure 2 shows: 3D hexahedral elements with a transition technique involving a ‘torch’ pattern in one direction only in prior art.
Figure 3 shows: Proposed ‘bi-directional torch (BDT)’ pattern that is capable of producing mesh coarsening simultaneously in two directions according to the present invention.

Figure 4 shows: Procedure of placing the BDT in a typical 3 dimensional meshed model, so as to achieve a simultaneous bi-directional coarsening.

Figure 5 shows: Three meshed FE models with different mesh coarsening schemes.

The figures depict embodiments of the disclosure for purposes of illustration only. One skilled in the art will readily recognize from the following description that alternative embodiments of the structures and methods illustrated herein may be employed without departing from the principles of the disclosure described herein.

DETAILED DESCRIPTION OF A PREFERRED EMBODIMENT OF THE INVENTION WITH REFERENCE TO THE ACCOMPANYING DRAWINGS
While the embodiments of the disclosure are subject to various modifications and alternative forms, specific embodiment thereof have been shown by way of example in the figures and will be described below. It should be understood, however, that it is not intended to limit the disclosure to the particular forms disclosed, but on the contrary, the disclosure is to cover all modifications, equivalents, and alternative falling within the scope of the disclosure.

In this invention, there is disclosed a novel mesh coarsening procedure that is used for quick transition from a fine mesh made of smaller sized 3D elements to a coarse mesh made of larger sized 3D elements. The novel feature is that this mesh coarsening procedure discloses a special type of a coarsening procedure by using the ‘Bi-Directional Torch’ pattern, which is described in detail hereinafter.

Finite Element Modelling (FEM) is a very powerful computational technique used for simulating a variety of physical processes, with an aim of understanding the thermal and mechanical behavior of a given component when subjected to the physical process under investigation. The Finite Element Modelling (FEM) comprises of four major steps namely modelling the component, meshing the component, definition of loads and boundary conditions, solution and post processing. Out of these four steps, the second step namely the ‘meshing’ is the focus area of the present invention. The meshing of a given 3D model is to be done in such a way that a fine mesh comprising of smaller sized elements are present in the areas on interest or areas where loads are defined and then the fine mesh needs to be transitioned into a coarse mesh comprising of larger sized elements. The transition of a fine mesh into a coarse mesh is done using many techniques that are already known in the prior art.

For instance, the Figure 1 shows a scheme of transition of fine mesh into coarse mesh using the ‘Y’ pattern. Two numbers of eight-node 3D hexahedral elements (1) are taken at a time and these are transitioned using a ‘Y’ pattern shown in Figure 1. This results in a situation where two hexahedral elements (1) are merged using the Y pattern (2), so that it results in the formation of a larger sized element (3). This means that the ‘Y’ pattern (2) has transitioned two smaller sized hexahedral elements (1) into a single larger sized hexahedral element (3). This is one of the already known procedures of mesh coarsening.

Besides the ‘Y’ pattern of transitioning into coarse mesh, there is also yet another pattern of coarsening which is the ‘torch’ pattern (5) shown in Figure 2. In this pattern, three numbers of smaller sized, 3D hexahedral elements (4) are transitioned into a one larger sized hexahedral element (6). In this case, on the top side of the torch pattern (5), there are three smaller sized 3D elements, and on the bottom side of the torch pattern (5), only a single hexahedral element is present, indicating that the three smaller elements have transitioned in a single hexahedral element. This is also one of the already known procedures of mesh coarsening.

The commonality seen in both the above procedures is that both the types of the transition procedures result only in one-directional mesh coarsening but does not have the capability of resulting in a bi-directional coarsening, which is the claimed novel feature of the present invention.

For resulting in a bi-directional coarsening of a 3D finite element mesh, it is necessary to use a transition pattern called ‘Bi-Directional Torch’ (BDT) which is shown in Figure 3. In this transition pattern, two ‘torch’ transitions (7) and (8) exist on planes at right angle to each other. In other words, in the BDT transition pattern, two one-directional torch transitions happen simultaneously, such that the planes containing the two transitions are at right angles to one another. The wireframe model of the BDT transition (10) clearly shows that it is able to effect the transition with only five elements. Further, it also results in a bi-directional transition. On comparison with a one-directional torch transition (5) shown in Figure 2, it is seen that one-directional torch transition (5) uses four numbers of elements for transition, but transition happens only in one direction. Whereas the BDT pattern (Figure 3) has effected the transition using five elements, but in two directions which is highly advantageous compared to the one-directional torch transition (5) as shown in Figure 2.

It is worth mentioning that the BDT is not a simple combination of two, one-directional torch patterns (5) shown in Figure 2, because it is only after lots of analysis, the authors of the present invention, could finalize the transition pattern using the BDT pattern. Had the second torch transition of the BDT been placed in face (9) of Figure 3, then, the bi-directional transition would not have been made possible. Thus, the BDT pattern (Figure 3) is not a plain addition or combination of two one-directional torch patterns (5).

The procedure of placing the BDT in a typical 3 dimensional meshed model, so as to achieve a simultaneous bi-directional coarsening, is shown in Figure 4. The BDT transition is introduced in such a way that element (7) of the BDT pattern is joined with element (12) and similarly the element (8) of the BDT pattern is joined with element (11). After introduction of BDT transition pattern, the larger edge (13) is obtained as resultant. By looking at the transition brought about by the introduction of the BDT pattern, it can be understood that it has helped in the coarsening of the mesh both in the negative ‘Y’ direction and positive ‘X’ direction simultaneously.

The relative advantage of introducing the BDT pattern over two other known approaches are presented in Figure 5. Three meshed FE models namely (14), (15) and (16) are compared in Figure 5. The meshed model (14) has a fine mesh comprising smaller sized elements all across without any transition. This takes the maximum time to determine, since the number of elements are highest in this case. In the meshed model (15), only a one-directional transition has taken place as seen in the encircled areas. Hence, this is better than meshed model (14), in terms of the total number of elements and also in terms of the time to determine. Now, in the meshed model (16), by introducing the BDT pattern of transition, the mesh has been coarsened both in the negative Y direction and in the positive X direction, thereby resulting in a simultaneous bi-directional coarsening, thus ending up in larger sized elements (17) and (18) in Figure 5.

The advantages of using the mesh coarsening procedure using the BDT transition are listed herein below:

- Simultaneous bi-direction coarsening of mesh resulting in fewer number of elements;
- Faster computational times;
- In case of transient FE analysis, the advantage of faster computational time is realized in every time step;
- Less memory capacity of the result files after solving and easier post-processing of the 3D meshed model using BDT transition are possible with lesser number of elements.

Thus, with all the above stated advantages, the above mentioned novel/inventive mesh coarsening procedure can be used in modelling and solving of a variety of engineering problems using FEM.

Working of Invention:

The present invention helps in drastically reducing the number of elements and nodes involved in the formation of matrix and thus, reduces the computational time drastically.

Each of the appended claims defines a separate invention, which for infringement purposes is recognized as including equivalents to the various elements or limitations specified in the claims. Depending on the context, all references below to the "invention" may in some cases refer to certain specific embodiments only. In other cases, it will be recognized that references to the "invention" will refer to subject matter recited in one or more, but not necessarily all, of the claims.

Groupings of alternative elements or embodiments of the invention disclosed herein are not to be construed as limitations. Each group member can be referred to and claimed individually or in any combination with other members of the group or other elements found herein. One or more members of a group can be included in, or deleted from, a group for reasons of convenience and/or patentability. When any such inclusion or deletion occurs, the specification is herein deemed to contain the group as modified thus fulfilling the written description of all groups used in the appended claims.

It will be understood by those within the art that, in general, terms used herein, and especially in the appended claims (e.g., bodies of the appended claims) are generally intended as “open” terms (e.g., the term “including” should be interpreted as “including but not limited to,” the term “having” should be interpreted as “having at least,” the term “includes” should be interpreted as “includes but is not limited to,” etc.). It will be further understood by those within the art that if a specific number of an introduced claim recitation is intended, such an intent will be explicitly recited in the claim, and in the absence of such recitation no such intent is present. For example, as an aid to understanding, the following appended claims may contain usage of the introductory phrases “at least one” and “one or more” to introduce claim recitations. However, the use of such phrases should not be construed to imply that the introduction of a claim recitation by the indefinite articles “a” or “an” limits any particulars claim containing such introduced claim recitation to inventions containing only one such recitation, even when the same claim includes the introductory phrases “one or more” or “at least one” and indefinite articles such as “a” or “an” (e.g., “a” and/or “an” should typically be interpreted to mean “at least one” or “one or more”); the same holds true for the use of definite articles used to introduce claim recitations. In addition, even if a specific number of an introduced claim recitation is explicitly recited, those skilled in the art will recognize that such recitation should typically be interpreted to mean at least the recited number (e.g., the bare recitation of “two recitations,” without other modifiers, typically means at least two recitations, or two or more recitations). Furthermore, in those instances where a convention analogues to “at least one of A, B and C, etc.” is used, in general such a construction is intended in the sense one having skill in the art would understand the convention (e.g., “a system having at least one of A, B and C” would include but not be limited to systems that have A alone, B alone, C alone, A and B together, A and C together, B and C together, and/or A, B, and C together, etc.). In those instances where a convention analogous to “at least one of A, B, or C, etc.” is used, in general such a construction is intended in the sense one having skill in the art would understand the convention (e.g., “a system having at least one of A, B, or C” would include but not be limited to systems that have A alone, B alone, C alone, A and B together, A and C together, B and C together, and/or A, B, and C together, etc.). It will be further understood by those within the art that virtually any disjunctive word and/or phrase presenting two or more alternative terms, whether in the description, claims, or drawings, should be understood to contemplate the possibilities of including one of the terms, either of the terms, or both terms. For example, the phrase “A or B” will be understood to include the possibilities of “A” or “B” or “A and B”.

The above description does not provide specific details of manufacture or design of the various components. Those of skill in the art are familiar with such details, and unless departures from those techniques are set out, techniques, known, related art or later developed designs and materials should be employed. Those in the art are capable of choosing suitable manufacturing and design details.

The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the present disclosure. It will be appreciated that several of the above-disclosed and other features and functions, or alternatives thereof, may be combined into other systems or applications. Various presently unforeseen or unanticipated alternatives, modifications, variations, or improvements therein may subsequently be made by those skilled in the art without departing from the scope of the present disclosure as encompassed by the following claims.

The claims, as originally presented and as they may be amended, encompass variations, alternatives, modifications, improvements, equivalents, and substantial equivalents of the embodiments and teachings disclosed herein, including those that are presently unforeseen or unappreciated, and that, for example, may arise from applicants/patentees and others.

While various aspects and embodiments have been disclosed herein, other aspects and embodiments will be apparent to those skilled in the art. The various aspects and embodiments disclosed herein are for purposes of illustration and are not intended to be limiting, with the true scope and spirit being indicated by the following claims.
, Claims:We Claim

1. A novel mesh coarsening procedure for meshed finite element 3D models, using a Bi-Directional Torch (BDT) transition pattern (figure 3), wherein the procedure comprises steps of:

- transition of smaller sized hexahedral elements to larger sized hexahedral elements by the BDT transition pattern;
- making two ‘torch’ transitions simultaneously in two planes that are at right angles to each other (as seen in figure 2), wherein the BDT transition causes a mesh coarsening along two directions simultaneously, wherein these two directions are perpendicular to one another; in which
- the BDT transition pattern involves the use of five hexahedral elements as shown in wireframe model (figure 3).

2. The novel mesh coarsening procedure as claimed in claim 1, which has the advantage of faster mesh coarsening, fewer number of elements in the 3D meshed model and consequently faster computation times.

3.The novel mesh coarsening procedure as claimed in claim 1, which has ability to maintain aspect ratios of the original model simultaneously in two directions.

4. The novel mesh coarsening procedure as claimed in claim 1, which has ability to coarsen mesh by having greater control on the included angle between the faces of the hexahedral elements.