DESC:FIELD OF THE INVENTION

[001] The present invention relates generally to finite element analysis, and more particularly, to systems and methods of checking and correcting the quality of meshing in the finite element analysis.

BACKGROUND OF THE INVENTION

[002] Finite element analysis (FEA) is a powerful numerical method for solving mathematical problems in engineering and physics. Finite element analysis is particularly relevant for determining the physical characteristics of an object such as a machine part, a hydraulic system, or printed circuit board. The fundamental concept of the finite element method is that any continuous physical characteristic, such as temperature, pressure, heat, or electric field, can be approximated by a discrete model composed of a set of piecewise continuous functions. These functions are defined over a finite number of subdomains of the object.

[003] Finite element analysis is used in a variety of applications including solid mechanics, fluid mechanics, biomechanics, heat transfer, geomechanics, aeromechanics, coupled systems, chemical reactions, acoustics, and electric and magnetic fields.

[004] Finite element analysis software adapted for use with solid mechanics is available from a wide variety of commercial suppliers. FEA begins by using finite element software to generate a finite element model of the system. In this model, the component is reduced into a number of finite elements. A simulated load or other influence is applied to the system and the resulting effect is analyzed using conventional mathematical methodologies.

[005] The pre-processing step of generating an acceptable mesh for analysis is the primary bottleneck in employing finite element analysis. Present mesh generation methods can take from hours to days, depending upon the method employed. Meshing is major time and effort consuming process performed using meshing tools such as Hypermesh, Patron, etc which are essential to make the components into infinitesimal finite element.

[006] The quality of mesh decides accuracy of analysis results and also an unqualified mesh cannot be acceptable by analysis tools of Computer Aided Engineering (CAE) like ANSYS, ABQUS, and NASTRAN. The assembly of components including cut outs and various materials, meshing is a major time consuming process of all fields of engineering design and analysis. Meshing takes around 40% of project cost.

[007] Typically, the user is required to pick nodes, edges and elements in the mesh in order to make changes to satisfy a predefined quality criterion. The practicing engineer who is not an expert in finite element analysis is thus not likely to make the best correction. Moreover, once the regions with errors are fixed for the errors, the neighbouring elements get changed. The changed elements may again give additional errors, so correcting on error gives rise to more errors. The user has to again fix the new errors. This goes on iteratively until there are no errors left on the mesh.

[008] The mesh that results may contain a number of errors such as warpage, jacobian, aspect ratio, skew angle etc, The elements that have poor aspect ratios, e.g., the ratio of the longest side of an element to its shortest side that could skew the analysis. For example the warpage which is amount by which an element or element face (solid elements) deviates from being planar. Aspect Ratio is the ratio of the longest edge of an element to its shortest edge. Jacobian is measure of the deviation of an element from an ideally shaped element. The Jacobian value ranges from 0 to 1.0, where 1.0 represents a perfectly shaped element.

[009] Only the expertise of the user can prevent this. For this reason, many companies employ expensive specialists to perform finite element analysis on their products. Examples of prior FEA methods that incorporate this type of pre-processing are the ANSYS FEA program, NASTRAN FEA program, the Patran FEA Program. These and other prior FEA methods require continued user input in generating and fixing the mesh quality of elements. Meshing is major time and effort consuming process performed using meshing tools.

[0010] In view of the disadvantages inherent in the available systems and methods for assuring a desired quality criterion of a finite element mesh in a finite element analysis, there exists need for a system and method for for assuring a desired quality criterion of a finite element mesh in a finite element analysis which overcomes the problems in the prior art in an easy and effective way which is inexpensive, compact and capable of overcoming disadvantages inherent in prior art in a cost effective, secure, and environmental friendly manner. The present invention fulfils this need and provides further advantages as described in the following summary.

SUMMARY OF THE INVENTION

[0011] In view of the foregoing disadvantages inherent in the prior arts, the general purpose of the present invention is to provide an improved combination of convenience and utility, to include the advantages of the prior art, and to overcome the drawbacks inherent therein.

[0012] A primary objective of the present invention is to provide a system and method for for assuring a desired quality criterion of a finite element mesh in a finite element analysis having advantages not taught by the prior art.

[0013] In one aspect, the present invention provides a method for method for assuring a desired quality criterion of a finite element mesh in a finite element analysis. The method comprises providing the finite element (FE) mesh of a structure including a plurality of elements, nodes, edges, performing a desired quality check for the finite element mesh for each of a node, a element, a edge in the FE mesh, checking a normal alignment of each of the element, checking a connection of each element with another element, highlighting the elements that do not meet the desired quality check in predefined colors, fixing the errors of mesh quality in order to satisfy desired quality criterion, redefining the desired quality criterion after fixing the errors and repeating steps till the desired quality criterion is satisfied.

[0014] In another aspect of the present invention the desired quality check includes checking includes checking at least one including a warpage, a jacobian, an aspect ratio, a skew angle or a combination thereof.

[0015] In yet another aspect of the present invention the warpage, jacobian, aspect ratio, skew angle values have to be within a predefined limit.

[0016] In another aspect of the present invention the step of checking the connection of each element with another element includes checking there are no free edges without any connection. In one preferred embodiment, the presence of the free edges shows a duplicate node.

[0017] In one aspect of the present invention, highlighting the elements includes highlighting in colors different for different errors.

[0018] In yet another aspect, the present invention provides a system for assuring a desired quality criterion of a finite element mesh in a finite element analysis using the method of the present invention. The system including a computing device operably configured to provide the finite element (FE) mesh of a structure including a plurality of elements, nodes, edges, perform a desired quality check for the finite element mesh for each of a node, a element, a edge in the FE mesh, check a normal alignment of each of the element, check a connection of each element with another element, highlight the elements that do not meet the desired quality check in predefined colors, fix the errors of mesh quality in order to satisfy desired quality criterion, redefine the desired quality criterion after fixing the errors and repeat steps till the desired quality criterion is satisfied.

[0019] These together with other aspects of the invention, along with the various features of novelty that characterize the invention, are pointed out with particularity in the claims annexed hereto and forming a part of this disclosure. For a better understanding of the invention, its operating advantages and the specific objects attained by its uses, reference should be had to the accompanying drawings and descriptive matter in which there are illustrated exemplary embodiments of the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

[0020] The advantages and features of the present invention will become better understood with reference to the following more detailed description taken in conjunction with the accompanying drawings in which:

[0021] FIG. 1 illustrates a flowchart of the method for for assuring a desired quality criterion of a finite element mesh in a finite element analysis, according to one embodiment of the present invention;

[0022] FIG. 2 illustrates the warpage definition in finite element mesh;

[0023] FIG. 3 illustrates the aspect ratio definition in finite element mesh for different shapes of elements;

[0024] FIG. 4 illustrates the skew angle definition in finite element mesh for different shapes of elements;

[0025] FIG. 5 illustrates the free edge and duplicate nodes highlighted, according to one embodiment of the present invention;

[0026] FIG. 6 illustrates the elements with incorrect normal alignment highlighted, according to one embodiment of the present invention; and

[0027] FIG. 7 illustrates the elements with different errors.

[0028] Like reference numerals refer to like parts throughout the several views of the drawings.

DETAILED DESCRIPTION OF THE DRAWINGS

[0029] In the following description, for purposes of explanation, numerous specific details are set forth in order to provide a thorough understanding of the present invention. It will be apparent, however, to one skilled in the art that the present invention may be practiced without these specific details.

[0030] As used herein, the term ‘plurality’ refers to the presence of more than one of the referenced item and the terms ‘a’, ‘an’, and ‘at least’ do not denote a limitation of quantity, but rather denote the presence of at least one of the referenced item.

[0031] In an exemplary embodiment, the present invention provides a system and method for assuring a desired quality criterion of a finite element mesh in a finite element analysis. The system and method for assuring a desired quality criterion of a finite element mesh in a finite element analysis of the present invention may be used in an easy, cost effective, environment friendly and productive way.

[0032] It is to be understood that the improvements of the present invention are applicable to any of a number of systems and methods for assuring a desired quality criterion of a finite element mesh in a finite element analysis, other than those which are specifically described below. Such systems and methods will be readily understood by the person of ordinary skill in the art, and are achievable by causing various changes that are themselves known in state of the art.

[0033] Reference herein to “one embodiment” or “another embodiment” means that a particular feature, structure, or characteristic described in connection with the embodiment can be included in at least one embodiment of the invention. The appearances of the phrase “in one embodiment” in various places in the specification are not necessarily all referring to the same embodiment, nor are separate or alternative embodiments mutually exclusive of other embodiments.

[0034] Referring to FIG. 1 that illustrates a flowchart of the method 100 for assuring a desired quality criterion of a finite element mesh in a finite element analysis, according to one embodiment of the present invention. The structure may be may be a mechanical component or a machine part with several components assembled to work interactively.

[0035] The method 100 starts with step 110 of providing the finite element mesh of a structure including a plurality of elements, nodes and edges. The structure with plurality of components is meshed using a finite element (FE) meshing tool such as HYPERMESH or other similar tools available in art. The meshed structure may have a plurality of finite elements with plurality of nodes and edges as a part of mesh.

[0036] Now in step 120 a desired quality check for the finite element mesh is performed for each of the node, element and edge in the FE mesh of the structure. The elements are checked for different errors. In one embodiment of the present invention the desired quality check includes checking a warpage, jacobian, aspect ratio, skew angle or a combination of one or more. In one preferred embodiment, the warpage, jacobian, aspect ratio, skew angle values have to be within a predefined limit.

[0037] The warpage of the quadrilateral elements is defined as the deviation from a best-fit plane that contains the element as shown in FIG. 2. It is not always a case to define a plane with 4 nodes. Therefore, a node of the quadrilateral element may be formed outside of a plane. The warpage is a measurement how this node has been deviated, and as it gets closer to 0, the elements become more planar. For the quadrilateral elements, the warpage is found as shown in the figure. For solid element (Hexa, Wedge), it calculates the warpage for each element faces and assigns with the maximum value.

[0038] The Jacobian calculation is done at the integration points of elements commonly known as Gauss Point. At each intergration point, Jacobian Determinant is calculated, and the Jacobian ratio is found by the ratio of the maximum and minimum determinant value. The Jacobian Determinant of 2D elements is calculated after it has been projected on to a plane, and the determinant of 3D elements is found by direct calculation. If the quadrilateral element is not convex, the negative Jacobian ratio will be obtained, and elements with the negative Jacobian Ratio cannot be solved with correct result. Measure of the deviation of an element from an ideally shaped element ranges from 0 to 1.0, where 1.0 represents a perfectly shaped element. Should be greater than 0.6.

[0039] The aspect ratio of 2D element is defined as the ratio of its shortest edge length to its longest edge length. A square has the aspect ratio of 1 since its sides have the same length. As it gets away from the square shape, the aspect ratio becomes smaller than 1. The aspect ratio is defined for different shape elements in FIG. 3.

[0040] An angle is formed by the two lines which pass through the midpoints of the sides of the quadrilateral. The skew angle represents the absolute value of the difference between the angle and 90 degree. A rectangle has the skew angle of 0 since the formed angle between lines is 90 degree. For the triangle and quadrilateral elements, the skew angle is found as shown in the figure. For solid element (Tetra, Hexa, Wedge), it calculates the skew angle for each element faces and assigns with the minimum value. The skew angle is defined for different shape elements in FIG. 4. In another embodiment of the present invention, other errors in finite elements of the mesh such as collapse, twist may also be checked at this step.

[0041] At step 130, normal alignment of each of the element in the mesh is checked. In one embodiment of the present invention, the checking of the normal alignment includes checking if the normals of elements in a same plane are in same direction. The normals of elements in the same plane have to be parallel to each other, and if they are not parallel it is an error in meshing.

[0042] At step 140, the connection of each element with another element is checked. The elements in the mesh which are supposed to be connected share the load. But if they are disconnected at any point then that is error and not desired for further analysis. In one embodiment of the present invention, checking the connection of each element with another element includes checking there are no free edges without any connection. If there is no connection between two elements, it leaves free edges between them. The presence of the free edges shows a duplicate node. FIG. 5 shows the free edge which is due to disconnection between the horizontal and vertical portion of the component at the common edge. Free edges are characterized by duplicated nodes. The common nodes which are part of both the elements on both sides of the common edges get separated, when there is disconnection and results in two nodes with same node ID. This is error of duplicate node and has to be avoided.

[0043] Highlighting the elements that do not meet the desired quality check in predefined colors in step 150. All the errors obtained during the quality check are highlighted in colors. Different colors are used to highlight different types of errors. As shown in FIG. 6, the elements having incorrect normal alignment than expected are highlighted. Similarly FIG. 7 shows element in different colors for different errors.

[0044] Now in step 160 the errors of mesh quality are fixed in order to satisfy the desired quality criterion. The errors obtained in the mesh in above steps are fixed. The incorrect alignments of normals are fixed so that all the elements in same plane have normals parallel to each other. The free edges are joined and duplicate nodes are removed to fix the errors. A proprietary algorithm is used to fix the errors in the meshing.

[0045] The errors identified by the highlighted colors may be selected and the algorithm runs to make changes in the mesh to remove errors. The uniform color of the mesh represents removal of error.

[0046] During error correction some of the nodes, elements are changed and this may disturb neighbouring elements, thereby producing new errors which have to be fixed.

[0047] The desired quality criterion after fixing the errors may be redefined based on the changes in mesh for correction. The renewed quality criterion is then used to perform desired quality check.

[0048] The steps 120 to 170 are repeated with renewed desired quality criterion till the desired quality criterion is satisfied. The renewed desired quality criterion may be dependent on the overall quality criterion needed for the entire mesh. When the desired quality criterion is met, all elements have same color and this is the indication of perfect quality mesh. The perfect quality mesh is then used for finite element analysis to produce desired results.

[0049] In another embodiment, the present invention further provides a system for assuring a desired quality criterion of a finite element mesh in a finite element analysis using the method 100 of the present invention.

[0050] The system for assuring a desired quality criterion of a finite element mesh in a finite element analysis, the system including a computing device operably configured to provide the finite element (FE) mesh of a structure including a plurality of elements, nodes, edges, perform a desired quality check for the finite element mesh for each of a node, a element, a edge in the FE mesh, check a normal alignment of each of the element, check a connection of each element with another element, highlight the elements that do not meet the desired quality check in predefined colors, fix the errors of mesh quality in order to satisfy desired quality criterion, redefine the desired quality criterion after fixing the errors and repeat steps till the desired quality criterion is satisfied.

[0051] The method 100 may be executed electronically in a computer environment. The application may be run on a PC or Work station having sufficient memory to timely process and optimize the finite element mesh. Programming to host the present invention may be implemented With C and/or C++programming languages. Other programming languages may also be utilized however.

[0052] The system and method of the present invention may be implemented as an add-on to existing meshing software such as Hypermesh or FEA tool or it can be implemented as an independent software application. The software may be made available as a desktop application or using cloud infrastructure.

[0053] In one embodiment the system and method of the present invention may be implemented as a software tool in which the finite element mesh of the structure is fed as input and the correct mesh with desired quality is obtained as output. The software tool then makes the correct mesh and FEA model available for performing the FEA.

[0054] The system and method of the present invention may be used along with any meshing software available in the art and finite element analysis tools like ANSYS, ABQUS, NASTRAN or any such FEA tools.

[0055] In another alterative embodiment the system and method of the present invention may be implemented as a module of FEA software or as standalone software.

[0056] The system and method of the present invention provided several advantages including:
• Eliminates human participation for mesh quality check,
• Ensures 100% quality of mesh,
• Eliminates time for remeshing
• Checklist Elimination
• Any addition of fasteners can be automatically taken care
• Re adjust the mesh due to fastener points,
• Connectivity of large number of components and assembled in Finite element model can be handled
• Any changes in existing mesh
• It will automatically remove duplicate elements

[0057] Although a particular exemplary embodiment of the invention has been disclosed in detail for illustrative purposes, it will be recognized to those skilled in the art that variations or modifications of the disclosed invention, including the rearrangement of steps of the method may be possible. Accordingly, the invention is intended to embrace all such alternatives, modifications and variations as may fall within the spirit and scope of the present invention.

[0058] The foregoing descriptions of specific embodiments of the present invention have been presented for purposes of illustration and description. They are not intended to be exhaustive or to limit the invention to the precise forms disclosed, and obviously many modifications and variations are possible in light of the above teaching. The embodiments were chosen and described in order to best explain the principles of the invention and its practical application, to thereby enable others skilled in the art to best utilize the invention and various embodiments with various modifications as are suited to the particular use contemplated. It is understood that various omissions, substitutions of equivalents are contemplated as circumstance may suggest or render expedient, but is intended to cover the application or implementation without departing from the spirit or scope of the claims of the present invention.
,CLAIMS:We Claim:

1. A method for assuring a desired quality criterion of a finite element mesh in a finite element analysis, comprising the steps of:
a) providing the finite element (FE) mesh of a structure including a plurality of elements, nodes, edges;
b) performing a desired quality check for the finite element mesh for each of a node, a element, a edge in the FE mesh;
c) checking a normal alignment of each of the element;
d) checking a connection of each element with another element;
e) highlighting the elements that do not meet the desired quality check in predefined colors;
f) fixing the errors of mesh quality in order to satisfy desired quality criterion;
g) redefining the desired quality criterion after fixing the errors; and
h) repeating steps b to g till the desired quality criterion is satisfied.

2. The method for assuring desired quality of a finite element mesh according to claim 1, wherein the desired quality check includes checking includes checking at least one including a warpage, a jacobian, an aspect ratio, a skew angle or a combination thereof.

3. The method for assuring desired quality of a finite element mesh according to claim 1, wherein the checking of the normal alignment includes checking if the normals of elements in a same plane are in same direction.

4. The method for assuring desired quality of a finite element mesh according to claim 1, wherein the checking the connection of each element with another element includes checking there are no free edges without any connection.

5. The method for assuring desired quality of a finite element mesh according to claim 4, wherein presence of the free edges shows a duplicate node.

6. The method for assuring desired quality of a finite element mesh according to claim 2, wherein the warpage, the jacobian, the aspect ratio, the skew angle values have to be within a predefined limit.

7. The method for assuring desired quality of a finite element mesh according to claim 1, wherein highlighting the elements includes highlighting in different colors for different errors.

8. A system for assuring a desired quality criterion of a finite element mesh in a finite element analysis, the system including a computing device operably configured to:
a) provide the finite element (FE) mesh of a structure including a plurality of elements, nodes, edges;
b) perform a desired quality check for the finite element mesh for each of a node, a element, a edge in the FE mesh;
c) check a normal alignment of each of the element;
d) check a connection of each element with another element;
e) highlight the elements that do not meet the desired quality check in predefined colors;
f) fix the errors of mesh quality in order to satisfy desired quality criterion;
g) redefine the desired quality criterion after fixing the errors; and
h) repeat steps b to g till the desired quality criterion is satisfied.